WEBVTT 00:00:00.000 --> 00:00:01.973 align:middle line:90% [SQUEAKING] 00:00:01.973 --> 00:00:03.937 align:middle line:90% [RUSTLING] 00:00:03.937 --> 00:00:07.374 align:middle line:90% [CLICKING] 00:00:07.374 --> 00:00:10.320 align:middle line:90% 00:00:10.320 --> 00:00:12.580 align:middle line:84% HAZHIR RAHMANDAD: The predator-prey model, 00:00:12.580 --> 00:00:15.440 align:middle line:84% if you have looked at the classical model 00:00:15.440 --> 00:00:18.880 align:middle line:84% or have even heard of it before, you associate it 00:00:18.880 --> 00:00:19.780 align:middle line:90% with oscillation. 00:00:19.780 --> 00:00:25.320 align:middle line:84% It's kind of the primary mode that the Lotka-Volterra has 00:00:25.320 --> 00:00:28.160 align:middle line:90% introduced in the literature. 00:00:28.160 --> 00:00:30.680 align:middle line:84% It's interesting because the oscillations are 00:00:30.680 --> 00:00:32.220 align:middle line:90% motivated by real phenomenon. 00:00:32.220 --> 00:00:35.520 align:middle line:84% So there were kind of fish populations that oscillated, 00:00:35.520 --> 00:00:38.760 align:middle line:84% hare and lynx populations that oscillate. 00:00:38.760 --> 00:00:42.640 align:middle line:84% So this provided a theory for these oscillations that 00:00:42.640 --> 00:00:44.420 align:middle line:90% was plausible and made sense. 00:00:44.420 --> 00:00:47.600 align:middle line:84% But when you look at the actual model, 00:00:47.600 --> 00:00:49.340 align:middle line:84% it doesn't have the saturation effect. 00:00:49.340 --> 00:00:52.160 align:middle line:84% That is basically each predator is 00:00:52.160 --> 00:00:57.020 align:middle line:84% consuming a fraction of the prey every period of time. 00:00:57.020 --> 00:00:58.600 align:middle line:90% And that's very weird. 00:00:58.600 --> 00:01:01.480 align:middle line:84% You can't consume a fraction of the prey. 00:01:01.480 --> 00:01:05.360 align:middle line:84% You can consume a number of prey, 00:01:05.360 --> 00:01:06.740 align:middle line:90% and that makes a big difference. 00:01:06.740 --> 00:01:10.440 align:middle line:84% So that's the mechanism that was missing in the classical one 00:01:10.440 --> 00:01:13.680 align:middle line:84% that we discussed how to approach it and model it 00:01:13.680 --> 00:01:15.280 align:middle line:90% last time. 00:01:15.280 --> 00:01:18.480 align:middle line:84% And basically, those saturation effects 00:01:18.480 --> 00:01:21.460 align:middle line:84% create some additional non-linearity, 00:01:21.460 --> 00:01:23.820 align:middle line:84% although the original model is non-linear, 00:01:23.820 --> 00:01:27.320 align:middle line:84% but it kind of creates a more subtle non-linearity. 00:01:27.320 --> 00:01:30.500 align:middle line:84% Now, when you add those saturation effects, 00:01:30.500 --> 00:01:34.660 align:middle line:84% basically, the model is much less likely to oscillate. 00:01:34.660 --> 00:01:39.600 align:middle line:84% In fact, you have to make some strange formulations, 00:01:39.600 --> 00:01:44.600 align:middle line:84% and very narrow parameter ranges create oscillations. 00:01:44.600 --> 00:01:49.080 align:middle line:84% So the predator-prey story of oscillations 00:01:49.080 --> 00:01:54.840 align:middle line:84% actually is not quite right in a way, which opens up 00:01:54.840 --> 00:01:59.730 align:middle line:84% the question of, OK, what creates those oscillations 00:01:59.730 --> 00:02:02.530 align:middle line:90% in the real world? 00:02:02.530 --> 00:02:06.090 align:middle line:84% So the mode of behavior that comes out 00:02:06.090 --> 00:02:09.229 align:middle line:84% of the more realistic predator-prey model, 00:02:09.229 --> 00:02:12.810 align:middle line:84% and it is not the model that is-- we are not the first ones 00:02:12.810 --> 00:02:14.750 align:middle line:84% creating it here in this class, of course. 00:02:14.750 --> 00:02:19.170 align:middle line:84% There are kind of lots mathematical, biology 00:02:19.170 --> 00:02:22.450 align:middle line:84% work that has built those saturation effects into it. 00:02:22.450 --> 00:02:25.470 align:middle line:84% Many of them use the formulations you had, 00:02:25.470 --> 00:02:29.370 align:middle line:84% which was 1 over 1 plus that x that we tried. 00:02:29.370 --> 00:02:32.370 align:middle line:90% 00:02:32.370 --> 00:02:37.250 align:middle line:84% There are names even for these formulations, the first order 00:02:37.250 --> 00:02:38.310 align:middle line:90% saturation effect. 00:02:38.310 --> 00:02:40.670 align:middle line:84% And then they have a second order saturation effect. 00:02:40.670 --> 00:02:42.690 align:middle line:90% and so on. 00:02:42.690 --> 00:02:46.310 align:middle line:84% So those don't usually oscillate. 00:02:46.310 --> 00:02:49.770 align:middle line:84% They usually end up with overshoot and collapse 00:02:49.770 --> 00:02:54.370 align:middle line:84% or overshoot and equilibrium type of dynamics. 00:02:54.370 --> 00:02:58.930 align:middle line:84% And then the real-world oscillations in these systems, 00:02:58.930 --> 00:03:01.290 align:middle line:84% perhaps, are coming from other mechanisms 00:03:01.290 --> 00:03:04.230 align:middle line:84% that are not captured in a simple predator-prey model. 00:03:04.230 --> 00:03:10.570 align:middle line:84% Most likely, there are a movement of populations 00:03:10.570 --> 00:03:13.430 align:middle line:90% inside geographic regions. 00:03:13.430 --> 00:03:18.610 align:middle line:84% That is, you deplete some part of the population 00:03:18.610 --> 00:03:20.410 align:middle line:90% in a neighborhood. 00:03:20.410 --> 00:03:22.950 align:middle line:84% And then from other Neighborhoods, 00:03:22.950 --> 00:03:26.090 align:middle line:84% gradually, populations of prey come in, 00:03:26.090 --> 00:03:29.730 align:middle line:84% and the predators in the central area leave. 00:03:29.730 --> 00:03:33.410 align:middle line:84% And that might be the more likely source of oscillations 00:03:33.410 --> 00:03:36.130 align:middle line:90% in the real world. 00:03:36.130 --> 00:03:39.210 align:middle line:84% So that's one set of more connecting 00:03:39.210 --> 00:03:41.050 align:middle line:90% with the empirics in this case. 00:03:41.050 --> 00:03:44.150 align:middle line:84% The other thing is that when you add these saturation effects, 00:03:44.150 --> 00:03:46.810 align:middle line:84% we didn't really go through the equilibrium conditions 00:03:46.810 --> 00:03:47.770 align:middle line:90% last time. 00:03:47.770 --> 00:03:50.610 align:middle line:84% But putting the model into equilibrium becomes harder. 00:03:50.610 --> 00:03:53.030 align:middle line:84% So some of you tried to put it in equilibrium. 00:03:53.030 --> 00:03:57.730 align:middle line:84% It is fairly straightforward with the classical formulation. 00:03:57.730 --> 00:04:02.010 align:middle line:84% But with these more non-linear saturation effects, 00:04:02.010 --> 00:04:05.090 align:middle line:84% you have to write the equations and see if you can find it. 00:04:05.090 --> 00:04:08.890 align:middle line:84% You may end up choosing a saturation function that 00:04:08.890 --> 00:04:10.930 align:middle line:84% is more solvable analytically, which 00:04:10.930 --> 00:04:13.890 align:middle line:90% is another common approach. 00:04:13.890 --> 00:04:18.216 align:middle line:84% But anyway, that becomes a hard problem. 00:04:18.216 --> 00:04:22.370 align:middle line:84% So that's another thing to keep in mind 00:04:22.370 --> 00:04:24.810 align:middle line:90% with this class of models. 00:04:24.810 --> 00:04:29.470 align:middle line:84% The last item is that something we didn't discuss, 00:04:29.470 --> 00:04:33.910 align:middle line:84% but it is very common in the biologically motivated models, 00:04:33.910 --> 00:04:39.410 align:middle line:84% is that in outflow from the prey, which is the hunting, 00:04:39.410 --> 00:04:44.890 align:middle line:84% directly becomes the inflow into the stock of the predator, 00:04:44.890 --> 00:04:48.510 align:middle line:84% with a fractional conversion rate. 00:04:48.510 --> 00:04:53.100 align:middle line:84% That is basically conservation of biomass. 00:04:53.100 --> 00:04:56.220 align:middle line:84% You eat animals that turns to the bodyweight 00:04:56.220 --> 00:04:59.740 align:middle line:84% of other animals, which reduces one degree of freedom 00:04:59.740 --> 00:05:00.640 align:middle line:90% from the model. 00:05:00.640 --> 00:05:03.580 align:middle line:84% So your growth rate for the predator 00:05:03.580 --> 00:05:05.780 align:middle line:84% is not completely independent parameter 00:05:05.780 --> 00:05:07.460 align:middle line:84% that you can play with while keeping 00:05:07.460 --> 00:05:09.540 align:middle line:90% everything else in place. 00:05:09.540 --> 00:05:13.860 align:middle line:84% It actually would get-- and that is the main feedback rather than 00:05:13.860 --> 00:05:19.660 align:middle line:84% the death rate of the predator in the typical models for how 00:05:19.660 --> 00:05:22.180 align:middle line:84% the feedback of the predator availability 00:05:22.180 --> 00:05:25.600 align:middle line:84% impacts the growth rate of the predator. 00:05:25.600 --> 00:05:27.540 align:middle line:84% So you look at the classical model, that's 00:05:27.540 --> 00:05:29.540 align:middle line:84% how it is formulated, but also all 00:05:29.540 --> 00:05:32.060 align:middle line:84% of those more advanced or more complex models 00:05:32.060 --> 00:05:36.240 align:middle line:84% that have these saturations still make this assumption. 00:05:36.240 --> 00:05:38.495 align:middle line:84% So those are just a few reflections 00:05:38.495 --> 00:05:39.620 align:middle line:90% on the predator-prey model. 00:05:39.620 --> 00:05:42.140 align:middle line:90% 00:05:42.140 --> 00:05:48.060 align:middle line:84% With that, let's get started talking about our model 00:05:48.060 --> 00:05:55.460 align:middle line:84% for today, which is the pharma or drug pipeline model. 00:05:55.460 --> 00:05:59.140 align:middle line:84% And let's get started with your reflections and things 00:05:59.140 --> 00:06:05.940 align:middle line:84% that you found to be challenging that 00:06:05.940 --> 00:06:09.860 align:middle line:84% are helpful to probably attend to a little bit more 00:06:09.860 --> 00:06:11.900 align:middle line:90% as we discuss. 00:06:11.900 --> 00:06:16.740 align:middle line:90% So thoughts here and online. 00:06:16.740 --> 00:06:19.320 align:middle line:84% AUDIENCE: When I added the failure rates, 00:06:19.320 --> 00:06:25.200 align:middle line:84% I couldn't account for adjustment in the stock 00:06:25.200 --> 00:06:28.560 align:middle line:84% so that everything stays at equilibrium. 00:06:28.560 --> 00:06:31.620 align:middle line:84% And I'm sure that my model is wrong. 00:06:31.620 --> 00:06:35.620 align:middle line:84% HAZHIR RAHMANDAD: Equilibrium with failure rates 00:06:35.620 --> 00:06:39.880 align:middle line:90% and adjustment for stocks. 00:06:39.880 --> 00:06:42.140 align:middle line:84% These are very important formulations 00:06:42.140 --> 00:06:44.980 align:middle line:84% that we definitely want to discuss today. 00:06:44.980 --> 00:06:46.380 align:middle line:90% Other challenges, [INAUDIBLE]. 00:06:46.380 --> 00:06:49.220 align:middle line:84% AUDIENCE: I have issues approaching the controller side, 00:06:49.220 --> 00:06:56.220 align:middle line:84% but the decision-making that goes into how the timing to-- 00:06:56.220 --> 00:06:59.340 align:middle line:84% the supply chain of itself was a lot more tangible than 00:06:59.340 --> 00:07:02.100 align:middle line:90% [INAUDIBLE]. 00:07:02.100 --> 00:07:05.460 align:middle line:84% HAZHIR RAHMANDAD: So start rate for drugs as a function 00:07:05.460 --> 00:07:09.860 align:middle line:90% of what you want to achieve. 00:07:09.860 --> 00:07:12.040 align:middle line:90% Is that the core formulation? 00:07:12.040 --> 00:07:14.480 align:middle line:84% So this is probably the most important formulation. 00:07:14.480 --> 00:07:19.500 align:middle line:84% Ultimately, the rest of this model is basically physics. 00:07:19.500 --> 00:07:23.460 align:middle line:84% The real decision is the start rate of new drugs 00:07:23.460 --> 00:07:28.980 align:middle line:84% to drive the desired revenue ultimately. 00:07:28.980 --> 00:07:31.720 align:middle line:84% So that's absolutely the heart of the model. 00:07:31.720 --> 00:07:34.940 align:middle line:84% We should definitely dig deeper into it. 00:07:34.940 --> 00:07:36.140 align:middle line:90% Very good. 00:07:36.140 --> 00:07:38.220 align:middle line:90% Other challenges, other issues? 00:07:38.220 --> 00:07:44.700 align:middle line:90% 00:07:44.700 --> 00:07:48.750 align:middle line:90% So these are good. 00:07:48.750 --> 00:07:50.510 align:middle line:84% I thought maybe I share with you when 00:07:50.510 --> 00:07:53.350 align:middle line:84% I enter looking at any of these models, what 00:07:53.350 --> 00:07:56.370 align:middle line:84% are the things in my mind that I'm looking for 00:07:56.370 --> 00:07:58.710 align:middle line:84% so that it kind of gives you a little bit of a lens 00:07:58.710 --> 00:08:02.810 align:middle line:84% to more generally critique, think about models. 00:08:02.810 --> 00:08:13.310 align:middle line:84% So there are basics like the units non-negativity 00:08:13.310 --> 00:08:16.330 align:middle line:84% of physical stocks keeping those in mind. 00:08:16.330 --> 00:08:19.950 align:middle line:84% So that's for every model applies I think, 00:08:19.950 --> 00:08:21.010 align:middle line:90% very straightforward. 00:08:21.010 --> 00:08:24.037 align:middle line:84% And we are building those habits of looking at those basics. 00:08:24.037 --> 00:08:25.870 align:middle line:84% I'm seeing that the models you're submitting 00:08:25.870 --> 00:08:28.930 align:middle line:84% are usually unit OK, which is great. 00:08:28.930 --> 00:08:31.430 align:middle line:90% Thank you. 00:08:31.430 --> 00:08:36.350 align:middle line:84% Then the stock adjustment, that is, how do you 00:08:36.350 --> 00:08:37.929 align:middle line:90% adjust what is in the stock? 00:08:37.929 --> 00:08:41.030 align:middle line:84% And Ali mentioned that is a non-trivial formulation 00:08:41.030 --> 00:08:41.690 align:middle line:90% for this one. 00:08:41.690 --> 00:08:44.049 align:middle line:84% So generally, you need a desired level, 00:08:44.049 --> 00:08:46.470 align:middle line:84% and you need to compare that with the current level 00:08:46.470 --> 00:08:48.670 align:middle line:90% and make an adjustment. 00:08:48.670 --> 00:08:51.110 align:middle line:84% But what is the desired level here? 00:08:51.110 --> 00:08:55.610 align:middle line:84% When you have two factors that are making it complex, 00:08:55.610 --> 00:08:57.350 align:middle line:84% one is the failure rate, the other 00:08:57.350 --> 00:08:59.630 align:middle line:84% is the possibility of the growth. 00:08:59.630 --> 00:09:03.070 align:middle line:84% So for a system that is in a steady state, 00:09:03.070 --> 00:09:08.950 align:middle line:84% it is relatively straightforward to put together 00:09:08.950 --> 00:09:11.030 align:middle line:84% a desired level for a system that you 00:09:11.030 --> 00:09:13.070 align:middle line:90% want it to be also growing. 00:09:13.070 --> 00:09:15.990 align:middle line:84% What is the desired level that allows it to grow at the rate 00:09:15.990 --> 00:09:17.710 align:middle line:90% that you want it to grow? 00:09:17.710 --> 00:09:21.030 align:middle line:84% And then the same two considerations 00:09:21.030 --> 00:09:23.290 align:middle line:84% come into the replacement question. 00:09:23.290 --> 00:09:27.910 align:middle line:84% That is, now we have these drugs basically becoming obsolete 00:09:27.910 --> 00:09:29.210 align:middle line:90% or going out of patent. 00:09:29.210 --> 00:09:31.070 align:middle line:84% And therefore, they wouldn't be contributing 00:09:31.070 --> 00:09:32.350 align:middle line:90% much to your revenue. 00:09:32.350 --> 00:09:38.390 align:middle line:84% So how do you replace to account for the significant delays 00:09:38.390 --> 00:09:43.385 align:middle line:84% in the pipeline process that then interact with the growth 00:09:43.385 --> 00:09:44.010 align:middle line:90% rates you want? 00:09:44.010 --> 00:09:51.750 align:middle line:84% So if I want to grow 5% a year and I'm retiring 10 drugs today, 00:09:51.750 --> 00:09:54.110 align:middle line:84% what I'm entering on the other side 00:09:54.110 --> 00:09:58.830 align:middle line:84% will become a new drug years from now. 00:09:58.830 --> 00:10:02.150 align:middle line:84% So I need to actually account for a lot more that 00:10:02.150 --> 00:10:07.750 align:middle line:84% need to go into the process to get the growth rates 00:10:07.750 --> 00:10:08.490 align:middle line:90% that I want. 00:10:08.490 --> 00:10:12.990 align:middle line:84% Otherwise, just replacing what goes out will not do the trick. 00:10:12.990 --> 00:10:15.290 align:middle line:84% And then I'll think about equilibrium. 00:10:15.290 --> 00:10:18.150 align:middle line:84% And this is one of those models that you definitely need 00:10:18.150 --> 00:10:19.570 align:middle line:90% to put it into equilibrium. 00:10:19.570 --> 00:10:23.450 align:middle line:84% Otherwise, so many things will happen inside the model, 00:10:23.450 --> 00:10:25.890 align:middle line:84% you can't trace what is happening. 00:10:25.890 --> 00:10:33.230 align:middle line:84% So for good analysis, having equilibrium is key. 00:10:33.230 --> 00:10:37.810 align:middle line:84% So that's the key things I'm looking for. 00:10:37.810 --> 00:10:39.590 align:middle line:84% And I think we already have talked 00:10:39.590 --> 00:10:42.860 align:middle line:84% about the idea of the model last week. 00:10:42.860 --> 00:10:45.880 align:middle line:84% So I think everybody here knows what the basic problem 00:10:45.880 --> 00:10:48.600 align:middle line:90% definition was. 00:10:48.600 --> 00:10:51.280 align:middle line:84% Any thoughts while I'm opening the models that 00:10:51.280 --> 00:10:57.320 align:middle line:84% have been submitted so that we can take a look. 00:10:57.320 --> 00:10:59.595 align:middle line:90% 00:10:59.595 --> 00:11:01.220 align:middle line:84% AUDIENCE: We'll probably get into this. 00:11:01.220 --> 00:11:05.940 align:middle line:84% But my guess is the standard stock management formulation, 00:11:05.940 --> 00:11:11.160 align:middle line:84% which has first order negative feedback controls for comparing 00:11:11.160 --> 00:11:20.440 align:middle line:84% desired level to actual isn't enough to hit 00:11:20.440 --> 00:11:25.048 align:middle line:84% desired [INAUDIBLE] when there's a growth. 00:11:25.048 --> 00:11:26.340 align:middle line:90% HAZHIR RAHMANDAD: That's right. 00:11:26.340 --> 00:11:28.800 align:middle line:90% That's right. 00:11:28.800 --> 00:11:29.740 align:middle line:90% It's not enough. 00:11:29.740 --> 00:11:32.940 align:middle line:90% 00:11:32.940 --> 00:11:37.628 align:middle line:84% So the simple equilibrium one is relatively simple. 00:11:37.628 --> 00:11:39.420 align:middle line:84% You just need to account for failure rates. 00:11:39.420 --> 00:11:41.920 align:middle line:84% Otherwise, it's kind of the standard formulation you already 00:11:41.920 --> 00:11:42.420 align:middle line:90% know. 00:11:42.420 --> 00:11:46.380 align:middle line:84% So the real challenge, in my view, at least coming into this, 00:11:46.380 --> 00:11:51.720 align:middle line:84% was how can you incorporate the growth trajectories. 00:11:51.720 --> 00:11:54.320 align:middle line:84% Now we'll see what are the other challenging 00:11:54.320 --> 00:11:59.765 align:middle line:84% things that may surface as we look at the model. 00:11:59.765 --> 00:12:01.500 align:middle line:90% So first the basics. 00:12:01.500 --> 00:12:06.520 align:middle line:84% We have the three phases of drugs in different phases 00:12:06.520 --> 00:12:10.380 align:middle line:84% and then of clinical trials and then drugs in the market. 00:12:10.380 --> 00:12:12.800 align:middle line:84% So the basic physics are all there. 00:12:12.800 --> 00:12:17.880 align:middle line:84% We have failure rates to nowhere. 00:12:17.880 --> 00:12:25.500 align:middle line:84% And then we have the time for going out of patent. 00:12:25.500 --> 00:12:28.440 align:middle line:84% And in this case, basically for drugs, 00:12:28.440 --> 00:12:31.640 align:middle line:84% they lose 90%, 95% of their revenue 00:12:31.640 --> 00:12:33.360 align:middle line:84% once they're out of patent the same day 00:12:33.360 --> 00:12:39.960 align:middle line:84% basically because generics are introduced in the market 00:12:39.960 --> 00:12:40.760 align:middle line:90% right away. 00:12:40.760 --> 00:12:43.500 align:middle line:84% People know what date the patents are expiring, 00:12:43.500 --> 00:12:47.340 align:middle line:84% and they bring generics the same day that are much cheaper, 00:12:47.340 --> 00:12:50.740 align:middle line:90% and everybody switches to those. 00:12:50.740 --> 00:12:52.360 align:middle line:90% So that's good. 00:12:52.360 --> 00:12:56.860 align:middle line:84% Then we have the basic flows for every stage. 00:12:56.860 --> 00:13:03.600 align:middle line:84% So the drug finishing phase 1 is the number of drugs in phase 1 00:13:03.600 --> 00:13:07.920 align:middle line:84% divided by average phase 1 trial time. 00:13:07.920 --> 00:13:11.680 align:middle line:84% Drugs finishing phase 2 similarly, phase 3 similarly. 00:13:11.680 --> 00:13:16.120 align:middle line:84% And then that is divided between drugs 00:13:16.120 --> 00:13:18.640 align:middle line:84% that go to nowhere versus drugs that 00:13:18.640 --> 00:13:21.160 align:middle line:84% go to the next phase based on these success 00:13:21.160 --> 00:13:22.680 align:middle line:90% rates for each phase. 00:13:22.680 --> 00:13:24.580 align:middle line:90% So that's all good. 00:13:24.580 --> 00:13:27.540 align:middle line:84% And this model is under development. 00:13:27.540 --> 00:13:29.600 align:middle line:84% So I think I opened the version of the model that 00:13:29.600 --> 00:13:33.520 align:middle line:90% was extended but not finished. 00:13:33.520 --> 00:13:36.660 align:middle line:90% So this is pretty standard. 00:13:36.660 --> 00:13:41.360 align:middle line:84% I think most of you probably were using similar ideas here. 00:13:41.360 --> 00:13:45.960 align:middle line:90% So that's good, those basics. 00:13:45.960 --> 00:13:55.720 align:middle line:84% Then let's look at what is happening with the desired 00:13:55.720 --> 00:13:56.300 align:middle line:90% drugs. 00:13:56.300 --> 00:13:58.680 align:middle line:84% So you have the desired revenue here. 00:13:58.680 --> 00:14:02.660 align:middle line:84% That's kind of driving the system. 00:14:02.660 --> 00:14:04.160 align:middle line:84% And the way Alban has formulated it 00:14:04.160 --> 00:14:07.800 align:middle line:84% it's some initial multiplied by some input. 00:14:07.800 --> 00:14:09.540 align:middle line:90% That's a good formulation. 00:14:09.540 --> 00:14:11.500 align:middle line:84% So then you can change those inputs. 00:14:11.500 --> 00:14:13.125 align:middle line:84% And I think view 2 may have the inputs. 00:14:13.125 --> 00:14:13.625 align:middle line:90% Yes. 00:14:13.625 --> 00:14:14.860 align:middle line:90% So you can have a step. 00:14:14.860 --> 00:14:16.360 align:middle line:90% You can have a ramp. 00:14:16.360 --> 00:14:18.800 align:middle line:90% You can have exponential growth. 00:14:18.800 --> 00:14:20.140 align:middle line:90% You can have sinusoid. 00:14:20.140 --> 00:14:24.200 align:middle line:84% So this is a good formulation to get whatever input you 00:14:24.200 --> 00:14:27.880 align:middle line:90% want into your desired revenue. 00:14:27.880 --> 00:14:33.200 align:middle line:84% And then desired revenue divided by annual revenue per drug 00:14:33.200 --> 00:14:36.890 align:middle line:84% gives you the desired drugs in the market. 00:14:36.890 --> 00:14:40.010 align:middle line:90% So that's also good. 00:14:40.010 --> 00:14:43.130 align:middle line:84% You also calculate current revenue using that. 00:14:43.130 --> 00:14:46.950 align:middle line:84% So this is desired drugs in the market, which is correct. 00:14:46.950 --> 00:14:49.030 align:middle line:90% So that's what you look at. 00:14:49.030 --> 00:14:52.390 align:middle line:84% You can then initialize your drugs in the market using that. 00:14:52.390 --> 00:14:54.810 align:middle line:90% That's a good formulation. 00:14:54.810 --> 00:14:57.570 align:middle line:84% So drugs in market will be initialized 00:14:57.570 --> 00:14:59.930 align:middle line:90% by the desired value. 00:14:59.930 --> 00:15:01.890 align:middle line:90% And then you adjust. 00:15:01.890 --> 00:15:04.810 align:middle line:84% You look at the difference between the two 00:15:04.810 --> 00:15:09.650 align:middle line:84% to get the market adjustment from drugs in the market. 00:15:09.650 --> 00:15:10.670 align:middle line:90% That makes sense. 00:15:10.670 --> 00:15:13.770 align:middle line:84% This is the gap between the two divided by the time 00:15:13.770 --> 00:15:15.470 align:middle line:90% to adjust drugs in the market. 00:15:15.470 --> 00:15:19.010 align:middle line:90% 00:15:19.010 --> 00:15:22.450 align:middle line:90% So all of that is good. 00:15:22.450 --> 00:15:26.150 align:middle line:84% You have similar ideas downstream. 00:15:26.150 --> 00:15:28.030 align:middle line:90% So let's take a look at them. 00:15:28.030 --> 00:15:33.410 align:middle line:84% So right now, the formulation that we have here 00:15:33.410 --> 00:15:39.250 align:middle line:84% is saying how many drugs go out of patents, 00:15:39.250 --> 00:15:44.650 align:middle line:84% and then that with some delay, some kind of perception delay 00:15:44.650 --> 00:15:47.950 align:middle line:84% leads to your replacement rate of sorts. 00:15:47.950 --> 00:15:53.330 align:middle line:84% That is expected drug out of patent that adds up 00:15:53.330 --> 00:15:54.870 align:middle line:90% with the stock adjustment. 00:15:54.870 --> 00:15:57.090 align:middle line:84% So it is a replacement process stock adjustment, 00:15:57.090 --> 00:15:59.050 align:middle line:90% the classical formulation. 00:15:59.050 --> 00:16:01.430 align:middle line:84% Now what is problematic with this formulation? 00:16:01.430 --> 00:16:03.170 align:middle line:90% What doesn't it capture? 00:16:03.170 --> 00:16:10.026 align:middle line:90% 00:16:10.026 --> 00:16:14.462 align:middle line:84% AUDIENCE: [INAUDIBLE] if you have a desired growth pattern. 00:16:14.462 --> 00:16:16.170 align:middle line:84% HAZHIR RAHMANDAD: So it is not accounting 00:16:16.170 --> 00:16:17.790 align:middle line:90% for the desired growth pattern. 00:16:17.790 --> 00:16:19.410 align:middle line:90% That's definitely the case. 00:16:19.410 --> 00:16:21.170 align:middle line:84% Then there is something else that 00:16:21.170 --> 00:16:24.710 align:middle line:90% is a little bit more subtle. 00:16:24.710 --> 00:16:30.210 align:middle line:84% And that is if you want to replace 10 drugs that 00:16:30.210 --> 00:16:35.010 align:middle line:84% are expiring and your success rate over the whole pipeline 00:16:35.010 --> 00:16:39.610 align:middle line:84% is only 10%, how many drugs do you need to start? 00:16:39.610 --> 00:16:43.610 align:middle line:84% 100 per year or month or whatever is the unit. 00:16:43.610 --> 00:16:44.650 align:middle line:90% It's years here. 00:16:44.650 --> 00:16:47.970 align:middle line:84% That is not right now accounted for in this expected drug 00:16:47.970 --> 00:16:51.090 align:middle line:90% out-of-patent flow. 00:16:51.090 --> 00:16:58.830 align:middle line:84% So without accounting for that, this model will not do well. 00:16:58.830 --> 00:17:00.710 align:middle line:84% It cannot be put into equilibrium. 00:17:00.710 --> 00:17:04.050 align:middle line:84% It wouldn't generate what you need. 00:17:04.050 --> 00:17:07.250 align:middle line:84% Now I might be missing something down the road 00:17:07.250 --> 00:17:09.970 align:middle line:90% in the formulation. 00:17:09.970 --> 00:17:13.190 align:middle line:84% Because there is-- as you can see in Alban's model, 00:17:13.190 --> 00:17:16.290 align:middle line:84% there is this kind of a cascade that you 00:17:16.290 --> 00:17:20.290 align:middle line:84% have a desired three to market, which 00:17:20.290 --> 00:17:25.710 align:middle line:90% is, I think, the flow here. 00:17:25.710 --> 00:17:30.300 align:middle line:84% And that flow, you want it to be in equilibrium at least, 00:17:30.300 --> 00:17:33.480 align:middle line:84% the same as expected drug out of patent. 00:17:33.480 --> 00:17:38.408 align:middle line:90% 00:17:38.408 --> 00:17:40.940 align:middle line:84% AUDIENCE: [INAUDIBLE] just on your [INAUDIBLE] 00:17:40.940 --> 00:17:42.540 align:middle line:84% HAZHIR RAHMANDAD: Yes, so that's what 00:17:42.540 --> 00:17:44.300 align:middle line:84% I'm saying that maybe he's capturing it 00:17:44.300 --> 00:17:46.040 align:middle line:90% through that process. 00:17:46.040 --> 00:17:47.900 align:middle line:84% We wouldn't know that without simulating 00:17:47.900 --> 00:17:49.960 align:middle line:90% or asking Alban to explain. 00:17:49.960 --> 00:17:53.980 align:middle line:84% So Alban, if you are hearing us, you 00:17:53.980 --> 00:17:59.780 align:middle line:84% can unmute and tell us what the idea here is. 00:17:59.780 --> 00:18:02.180 align:middle line:84% AUDIENCE: Yeah, I'm trying to capture the success 00:18:02.180 --> 00:18:09.320 align:middle line:84% rate through that desire straight to market 00:18:09.320 --> 00:18:12.460 align:middle line:84% that is trying to balance the outflow and the stock 00:18:12.460 --> 00:18:13.420 align:middle line:90% management. 00:18:13.420 --> 00:18:18.540 align:middle line:84% And then that informed the desire drug 00:18:18.540 --> 00:18:23.552 align:middle line:84% in phase III, the stock, accounting for the success rate. 00:18:23.552 --> 00:18:29.460 align:middle line:84% But not everything [INAUDIBLE] will become straight to market. 00:18:29.460 --> 00:18:35.298 align:middle line:84% And so I can build the stuff more than-- 00:18:35.298 --> 00:18:36.840 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so basically, 00:18:36.840 --> 00:18:39.800 align:middle line:84% because when you go into the desired drugs in phase 3, 00:18:39.800 --> 00:18:43.440 align:middle line:84% you are accounting for the success rate of phase 3. 00:18:43.440 --> 00:18:46.620 align:middle line:90% So you are dividing this-- 00:18:46.620 --> 00:18:52.060 align:middle line:84% so desired 3 to market, multiply it by average phase 00:18:52.060 --> 00:18:57.500 align:middle line:84% 3 trial divided by average phase 3 success rate 00:18:57.500 --> 00:19:02.560 align:middle line:84% would expand the number of desired drugs in phase 3. 00:19:02.560 --> 00:19:05.840 align:middle line:84% So this is a good formulation for the desired phase 3. 00:19:05.840 --> 00:19:08.060 align:middle line:90% So this is a good practice. 00:19:08.060 --> 00:19:15.520 align:middle line:84% The only part that I'm wondering about is-- 00:19:15.520 --> 00:19:20.540 align:middle line:90% 00:19:20.540 --> 00:19:22.220 align:middle line:90% yeah, this should do fine. 00:19:22.220 --> 00:19:26.540 align:middle line:84% In equilibrium at least without growth and in equilibrium, 00:19:26.540 --> 00:19:30.400 align:middle line:84% you have the three to market adjustment. 00:19:30.400 --> 00:19:34.020 align:middle line:84% This would be zero because in equilibrium, this 00:19:34.020 --> 00:19:35.020 align:middle line:90% should be zero. 00:19:35.020 --> 00:19:37.820 align:middle line:84% So the desire to market is basically 00:19:37.820 --> 00:19:41.540 align:middle line:84% the out of patent rate, which would be the same as three 00:19:41.540 --> 00:19:43.460 align:middle line:90% to market rate. 00:19:43.460 --> 00:19:47.100 align:middle line:84% So this is the flow that should come out of this stock. 00:19:47.100 --> 00:19:52.340 align:middle line:84% And if you have that flow coming out of the stock set, 00:19:52.340 --> 00:19:56.520 align:middle line:84% you can calculate the desire to stock based on that flow. 00:19:56.520 --> 00:19:59.140 align:middle line:84% So this is a good formulation for the case 00:19:59.140 --> 00:20:03.220 align:middle line:84% that you don't have exponential growth. 00:20:03.220 --> 00:20:05.300 align:middle line:90% This works fine. 00:20:05.300 --> 00:20:07.840 align:middle line:84% And then the adjustment in the drug, 00:20:07.840 --> 00:20:12.340 align:middle line:84% you don't need to worry about it too much because it 00:20:12.340 --> 00:20:16.300 align:middle line:90% is in equilibrium zero. 00:20:16.300 --> 00:20:20.020 align:middle line:84% So it doesn't add to this desire thing. 00:20:20.020 --> 00:20:23.060 align:middle line:84% Now, this formulation does something that 00:20:23.060 --> 00:20:25.390 align:middle line:90% is a little bit more subtle. 00:20:25.390 --> 00:20:28.550 align:middle line:90% And this one is not-- 00:20:28.550 --> 00:20:30.490 align:middle line:90% there is no single right answer. 00:20:30.490 --> 00:20:33.810 align:middle line:84% But let's think about two ways of formulating this adjustment. 00:20:33.810 --> 00:20:38.350 align:middle line:84% So one way is to get the desired drug in phase 3 00:20:38.350 --> 00:20:41.350 align:middle line:84% from the expected drug out of patent 00:20:41.350 --> 00:20:47.910 align:middle line:84% or from this expected three to market without accounting 00:20:47.910 --> 00:20:51.070 align:middle line:84% for the adjustment for drugs in market. 00:20:51.070 --> 00:20:53.590 align:middle line:84% So if you are making a big adjustment 00:20:53.590 --> 00:20:56.070 align:middle line:84% in the drugs in the market, I'm not 00:20:56.070 --> 00:21:00.070 align:middle line:84% going to change drugs in phase 3 based 00:21:00.070 --> 00:21:02.410 align:middle line:84% on the adjustment of the market-- 00:21:02.410 --> 00:21:06.390 align:middle line:84% the desired in phase 3 based on the adjustment of the stock 00:21:06.390 --> 00:21:08.590 align:middle line:90% of drugs in the market. 00:21:08.590 --> 00:21:11.970 align:middle line:84% So if I'm missing a lot of drugs in the market, 00:21:11.970 --> 00:21:13.890 align:middle line:84% in the steady state, in the long term, 00:21:13.890 --> 00:21:17.670 align:middle line:84% I don't want to change my desired drugs in phase 3 00:21:17.670 --> 00:21:18.550 align:middle line:90% that much. 00:21:18.550 --> 00:21:21.110 align:middle line:84% I want my desired drugs in the phase 3 00:21:21.110 --> 00:21:25.910 align:middle line:84% to just flow based on what my total output I want it to be, 00:21:25.910 --> 00:21:31.590 align:middle line:84% total drugs in the market and out of patent I want them to be. 00:21:31.590 --> 00:21:34.710 align:middle line:90% So that's one way of doing it. 00:21:34.710 --> 00:21:39.330 align:middle line:84% The other is what Alban is doing here, which is you say, 00:21:39.330 --> 00:21:43.390 align:middle line:84% no, actually, I want to more aggressively adjust 00:21:43.390 --> 00:21:48.510 align:middle line:84% all of the intermediate stocks up or down based 00:21:48.510 --> 00:21:53.533 align:middle line:84% on the gaps in my desired stock as well. 00:21:53.533 --> 00:21:54.950 align:middle line:84% This is one of those things that I 00:21:54.950 --> 00:21:59.410 align:middle line:84% don't think there is a very clear best answer. 00:21:59.410 --> 00:22:02.790 align:middle line:90% Most of them have pros and cons. 00:22:02.790 --> 00:22:06.570 align:middle line:84% My preference is probably not to include this mechanism 00:22:06.570 --> 00:22:10.710 align:middle line:84% because it is harder to track what is happening 00:22:10.710 --> 00:22:12.950 align:middle line:90% when you have big gaps. 00:22:12.950 --> 00:22:15.570 align:middle line:84% But this is not wrong technically. 00:22:15.570 --> 00:22:16.950 align:middle line:90% Cathy, you had a question. 00:22:16.950 --> 00:22:19.110 align:middle line:84% AUDIENCE: Yeah, I was just wondering conceptually 00:22:19.110 --> 00:22:24.510 align:middle line:84% when you're adjusting for these intermediary stocks, 00:22:24.510 --> 00:22:29.410 align:middle line:84% you can't control directly the start rate into phase 3. 00:22:29.410 --> 00:22:30.930 align:middle line:90% It's like filtering through. 00:22:30.930 --> 00:22:36.990 align:middle line:84% So the way I approached it was to accumulate the entire supply 00:22:36.990 --> 00:22:39.270 align:middle line:84% line and then only adjust based on as 00:22:39.270 --> 00:22:41.850 align:middle line:84% if all three stocks in the supply line were-- 00:22:41.850 --> 00:22:44.990 align:middle line:84% HAZHIR RAHMANDAD: So tell us why you cannot do what you want 00:22:44.990 --> 00:22:45.710 align:middle line:90% to do. 00:22:45.710 --> 00:22:47.470 align:middle line:90% This kind of-- 00:22:47.470 --> 00:22:49.670 align:middle line:84% AUDIENCE: Or you can't do it directly. 00:22:49.670 --> 00:22:54.570 align:middle line:84% I can't start a drug from nothing and put it into phase 3. 00:22:54.570 --> 00:22:58.990 align:middle line:84% I have to go through phases 1 and 2 first. 00:22:58.990 --> 00:23:05.110 align:middle line:84% And so I suppose, yeah, in a deterministic model, 00:23:05.110 --> 00:23:08.250 align:middle line:84% you know how many you're going to get to phase 3 anyways. 00:23:08.250 --> 00:23:11.210 align:middle line:84% So I guess you can't directly control it in that sense, 00:23:11.210 --> 00:23:12.757 align:middle line:90% but I guess-- yeah. 00:23:12.757 --> 00:23:15.090 align:middle line:84% HAZHIR RAHMANDAD: So let's put this stochasticity aside. 00:23:15.090 --> 00:23:18.040 align:middle line:84% I think the stochasticity matters in this context, a lot 00:23:18.040 --> 00:23:20.300 align:middle line:84% because we are talking about a small numbers, 00:23:20.300 --> 00:23:23.720 align:middle line:84% but in expectation, actually, it doesn't make a big difference. 00:23:23.720 --> 00:23:27.480 align:middle line:84% That is, the expectations are fine, the deterministic model. 00:23:27.480 --> 00:23:29.280 align:middle line:84% So adding a stochasticity doesn't really 00:23:29.280 --> 00:23:30.520 align:middle line:90% make a big difference. 00:23:30.520 --> 00:23:35.280 align:middle line:84% Here this cascade method actually 00:23:35.280 --> 00:23:39.560 align:middle line:84% is perhaps the only way to put this model into equilibrium 00:23:39.560 --> 00:23:41.720 align:middle line:90% in a way that works well. 00:23:41.720 --> 00:23:47.320 align:middle line:84% That is, you start with whatever is the desired final stock. 00:23:47.320 --> 00:23:49.480 align:middle line:84% Based on that, you calculate what 00:23:49.480 --> 00:23:54.200 align:middle line:84% is the inflow into that stock that you want it to be. 00:23:54.200 --> 00:23:57.960 align:middle line:84% Based on that, you calculate the drugs in the phase 3 00:23:57.960 --> 00:24:02.040 align:middle line:84% that gives you that inflow to the drugs in the market 00:24:02.040 --> 00:24:04.460 align:middle line:84% and then move backwards like that. 00:24:04.460 --> 00:24:08.860 align:middle line:84% So that is actually the way to put this model in equilibrium. 00:24:08.860 --> 00:24:12.040 align:middle line:84% So this is well done on that front. 00:24:12.040 --> 00:24:14.760 align:middle line:84% The part that is more debatable is 00:24:14.760 --> 00:24:20.080 align:middle line:84% whether to include this third market adjustment in the desired 00:24:20.080 --> 00:24:24.800 align:middle line:84% three to market number that we have here 00:24:24.800 --> 00:24:28.880 align:middle line:90% or to do it in a different way. 00:24:28.880 --> 00:24:32.340 align:middle line:84% Now, there is another wrinkle here, 00:24:32.340 --> 00:24:34.280 align:middle line:84% and that is whether you get it out 00:24:34.280 --> 00:24:38.000 align:middle line:84% of expected drugs out of patent because this is just 00:24:38.000 --> 00:24:39.360 align:middle line:90% replacement. 00:24:39.360 --> 00:24:43.560 align:middle line:84% Or you get it from your desired annual revenue, 00:24:43.560 --> 00:24:50.040 align:middle line:84% which then drives how many you want to get the drugs out 00:24:50.040 --> 00:24:53.880 align:middle line:90% of patent at that point in time. 00:24:53.880 --> 00:24:59.240 align:middle line:84% So that is actually a more important consideration 00:24:59.240 --> 00:25:01.638 align:middle line:90% for doing the equilibrium. 00:25:01.638 --> 00:25:03.180 align:middle line:84% And that goes to the issue of growth. 00:25:03.180 --> 00:25:06.320 align:middle line:84% I think this model wouldn't handle the exponential growth 00:25:06.320 --> 00:25:08.940 align:middle line:90% phase the way it needs to. 00:25:08.940 --> 00:25:13.080 align:middle line:84% But I think for the equilibrium case, it does well. 00:25:13.080 --> 00:25:17.040 align:middle line:84% So I assume the rest of it is fairly straightforward, that is, 00:25:17.040 --> 00:25:20.820 align:middle line:90% replication of the same idea. 00:25:20.820 --> 00:25:24.040 align:middle line:84% So the desired drugs in phase 3 now lead 00:25:24.040 --> 00:25:28.840 align:middle line:84% to an adjustment for drugs in phase 3, so from 2 to 3. 00:25:28.840 --> 00:25:33.880 align:middle line:84% And that plus how many drugs are finishing phase 3 00:25:33.880 --> 00:25:35.860 align:middle line:90% leads to the desire 2 to 3. 00:25:35.860 --> 00:25:39.200 align:middle line:84% So this is, again, well captured. 00:25:39.200 --> 00:25:42.320 align:middle line:84% And the only kind of wrinkle is whether you include 00:25:42.320 --> 00:25:44.840 align:middle line:84% this adjustment in desire two to three 00:25:44.840 --> 00:25:48.400 align:middle line:84% or not when you want to calculate the desired 00:25:48.400 --> 00:25:50.840 align:middle line:90% levels for the previous phase. 00:25:50.840 --> 00:25:52.920 align:middle line:84% If you don't, then you add up all 00:25:52.920 --> 00:25:56.760 align:middle line:84% of these adjustments for stocks as a separate adjustment 00:25:56.760 --> 00:25:58.320 align:middle line:90% for a stock variable. 00:25:58.320 --> 00:26:03.120 align:middle line:84% And then the desired phase 1 start rate 00:26:03.120 --> 00:26:08.240 align:middle line:84% comes partly from this previous adjustments 00:26:08.240 --> 00:26:13.770 align:middle line:84% and partly from the total replacement rate. 00:26:13.770 --> 00:26:14.630 align:middle line:90% OK, good. 00:26:14.630 --> 00:26:17.090 align:middle line:84% So this is capturing several of the things 00:26:17.090 --> 00:26:20.130 align:middle line:90% that we want very well. 00:26:20.130 --> 00:26:23.830 align:middle line:90% Let's go with yet other model. 00:26:23.830 --> 00:26:24.330 align:middle line:90% Let's see. 00:26:24.330 --> 00:26:25.190 align:middle line:90% What is this one? 00:26:25.190 --> 00:26:26.411 align:middle line:90% So this is [? Hassam's. ?] 00:26:26.411 --> 00:26:27.690 align:middle line:90% AUDIENCE: Mine, yeah. 00:26:27.690 --> 00:26:29.970 align:middle line:90% HAZHIR RAHMANDAD: OK, so-- 00:26:29.970 --> 00:26:32.850 align:middle line:84% AUDIENCE: I looked at the pipeline different. 00:26:32.850 --> 00:26:36.150 align:middle line:84% So you know about this perspective. 00:26:36.150 --> 00:26:39.410 align:middle line:84% But in this model, I'm thinking that drugs that 00:26:39.410 --> 00:26:44.050 align:middle line:84% start in phase I and finish phase I don't necessarily get 00:26:44.050 --> 00:26:45.450 align:middle line:90% [INAUDIBLE] 00:26:45.450 --> 00:26:49.650 align:middle line:84% They sit in another stock waiting as potential candidates 00:26:49.650 --> 00:26:50.850 align:middle line:90% [INAUDIBLE]. 00:26:50.850 --> 00:26:53.050 align:middle line:84% And the same goes for phase II and phase III. 00:26:53.050 --> 00:26:57.330 align:middle line:84% And in reality, there can be multiple phase II drugs 00:26:57.330 --> 00:27:00.130 align:middle line:90% trials started in phase I. 00:27:00.130 --> 00:27:02.250 align:middle line:84% HAZHIR RAHMANDAD: But you have-- let me see, 00:27:02.250 --> 00:27:06.570 align:middle line:84% in terms of the phases, you have early-- oh, 00:27:06.570 --> 00:27:08.530 align:middle line:90% you have three phases. 00:27:08.530 --> 00:27:12.595 align:middle line:90% So where do they sit? 00:27:12.595 --> 00:27:13.970 align:middle line:84% AUDIENCE: Repeats for the three-- 00:27:13.970 --> 00:27:16.053 align:middle line:84% HAZHIR RAHMANDAD: I know, I know, so first of all, 00:27:16.053 --> 00:27:18.970 align:middle line:84% this is, formulation-wise, a more compact way of what 00:27:18.970 --> 00:27:21.950 align:middle line:90% we saw in Alban's structure. 00:27:21.950 --> 00:27:25.010 align:middle line:84% So drugs in trial are all subscripted, 00:27:25.010 --> 00:27:28.430 align:middle line:90% I assume, based on phase. 00:27:28.430 --> 00:27:30.430 align:middle line:84% Phase has phase I, phase II, phase III. 00:27:30.430 --> 00:27:32.030 align:middle line:90% So this saves the space. 00:27:32.030 --> 00:27:33.270 align:middle line:90% This is nice and clean. 00:27:33.270 --> 00:27:36.370 align:middle line:90% I like it. 00:27:36.370 --> 00:27:39.730 align:middle line:84% For our purpose, you could do this way or the way Alban did. 00:27:39.730 --> 00:27:41.010 align:middle line:90% Doesn't make a big difference. 00:27:41.010 --> 00:27:44.190 align:middle line:84% If you are doing it in practice for a larger model, 00:27:44.190 --> 00:27:49.350 align:middle line:84% this saves you some time in making the formulation. 00:27:49.350 --> 00:27:50.830 align:middle line:90% So that part is fine. 00:27:50.830 --> 00:27:53.010 align:middle line:84% Now, there is the more conceptual point 00:27:53.010 --> 00:27:58.690 align:middle line:84% that [? Hassam ?] is making, that drugs don't necessarily 00:27:58.690 --> 00:28:01.630 align:middle line:84% continue to the next phase even if they don't fail. 00:28:01.630 --> 00:28:04.830 align:middle line:84% That is, you may succeed in a phase II 00:28:04.830 --> 00:28:09.410 align:middle line:84% but decide that, eh, this is not high enough in my priority list 00:28:09.410 --> 00:28:12.050 align:middle line:84% in terms of the promise of this drug 00:28:12.050 --> 00:28:15.170 align:middle line:90% that you keep it on a warmer. 00:28:15.170 --> 00:28:19.050 align:middle line:84% It's maybe, two years from now, there 00:28:19.050 --> 00:28:22.110 align:middle line:84% is a new technology, new indication, 00:28:22.110 --> 00:28:24.350 align:middle line:84% something changes that I decide to use, 00:28:24.350 --> 00:28:26.110 align:middle line:90% push this forward or not. 00:28:26.110 --> 00:28:27.950 align:middle line:90% So that's conceptually right. 00:28:27.950 --> 00:28:29.670 align:middle line:84% In the level that we are modeling, 00:28:29.670 --> 00:28:34.170 align:middle line:84% it is not as critical because you can always say those drugs 00:28:34.170 --> 00:28:37.070 align:middle line:84% either will be continued or will be disposed of. 00:28:37.070 --> 00:28:39.970 align:middle line:84% So their pathway is one of these two. 00:28:39.970 --> 00:28:44.450 align:middle line:84% And you can incorporate that extra delay in the total phase 00:28:44.450 --> 00:28:47.090 align:middle line:90% ex delay that you have. 00:28:47.090 --> 00:28:51.790 align:middle line:84% So as such, fine conceptually, but for this model, 00:28:51.790 --> 00:28:54.910 align:middle line:84% it can do the trick accounting for that. 00:28:54.910 --> 00:28:58.130 align:middle line:84% And the fact that we are using first-order delays 00:28:58.130 --> 00:29:01.250 align:middle line:84% makes a lot of assumption of a lot of heterogeneity 00:29:01.250 --> 00:29:01.990 align:middle line:90% between drugs. 00:29:01.990 --> 00:29:03.970 align:middle line:84% That is, if you're in this phase, 00:29:03.970 --> 00:29:08.305 align:middle line:84% anyway, you are going to be kind going through a lot of variance. 00:29:08.305 --> 00:29:10.180 align:middle line:84% AUDIENCE: So the second conceptual difference 00:29:10.180 --> 00:29:12.500 align:middle line:84% is that you can have multiple phase II 00:29:12.500 --> 00:29:15.660 align:middle line:84% trials on the same phase I [INAUDIBLE] tasks, which 00:29:15.660 --> 00:29:17.120 align:middle line:84% is actually what happens out there. 00:29:17.120 --> 00:29:18.662 align:middle line:84% HAZHIR RAHMANDAD: So this is what you 00:29:18.662 --> 00:29:20.500 align:middle line:90% are doing in this model or not? 00:29:20.500 --> 00:29:22.360 align:middle line:84% AUDIENCE: So if here we have a [INAUDIBLE], 00:29:22.360 --> 00:29:23.985 align:middle line:84% we have the three different investments 00:29:23.985 --> 00:29:25.420 align:middle line:90% in three different phases. 00:29:25.420 --> 00:29:28.540 align:middle line:84% So one can put more money on phase III, 00:29:28.540 --> 00:29:31.945 align:middle line:84% initiating more phase III on the candidates they have, 00:29:31.945 --> 00:29:33.820 align:middle line:84% or initiating more phase II on the candidates 00:29:33.820 --> 00:29:36.560 align:middle line:84% they have of phase II for initiating more phase I. 00:29:36.560 --> 00:29:39.380 align:middle line:84% So it's not just one lever of starting down 00:29:39.380 --> 00:29:41.380 align:middle line:90% the line, but three levels. 00:29:41.380 --> 00:29:47.660 align:middle line:84% HAZHIR RAHMANDAD: OK, so that is a more complex formulation. 00:29:47.660 --> 00:29:51.020 align:middle line:84% AUDIENCE: We will get to the bad news or something [INAUDIBLE], 00:29:51.020 --> 00:29:52.880 align:middle line:90% the stuff that I'm happy I did. 00:29:52.880 --> 00:29:56.110 align:middle line:84% But then what happens at the end is that it becomes too complex. 00:29:56.110 --> 00:29:57.360 align:middle line:90% So I then put a lot of effort. 00:29:57.360 --> 00:30:00.060 align:middle line:84% So the decision-making part is not [INAUDIBLE]. 00:30:00.060 --> 00:30:03.860 align:middle line:84% HAZHIR RAHMANDAD: OK, so this is an interesting-- again, 00:30:03.860 --> 00:30:08.520 align:middle line:84% for going with phase II out of a candidate in phase I, 00:30:08.520 --> 00:30:10.000 align:middle line:90% you have different pathways. 00:30:10.000 --> 00:30:13.960 align:middle line:84% You could actually target it for different conditions. 00:30:13.960 --> 00:30:18.100 align:middle line:84% You could target even different ways of administering drug 00:30:18.100 --> 00:30:19.880 align:middle line:90% for the same condition. 00:30:19.880 --> 00:30:23.240 align:middle line:84% So there are possibilities that open up 00:30:23.240 --> 00:30:24.480 align:middle line:90% that is not a single one. 00:30:24.480 --> 00:30:26.880 align:middle line:84% And in the typical conceptualization, 00:30:26.880 --> 00:30:29.500 align:middle line:84% we don't make that distinction. [? Hassam ?] 00:30:29.500 --> 00:30:32.000 align:middle line:90% has done his PhD partly on this. 00:30:32.000 --> 00:30:37.700 align:middle line:84% So that's why he has the content domain 00:30:37.700 --> 00:30:40.960 align:middle line:84% knowledge that makes his model more complex on this front. 00:30:40.960 --> 00:30:41.680 align:middle line:90% And that's fine. 00:30:41.680 --> 00:30:42.320 align:middle line:90% That's good. 00:30:42.320 --> 00:30:45.343 align:middle line:84% But it also makes it harder to do the rest of the things that-- 00:30:45.343 --> 00:30:47.260 align:middle line:84% AUDIENCE: So the connection between the phases 00:30:47.260 --> 00:30:52.100 align:middle line:84% is that if a company starts making-- starts more phase II, 00:30:52.100 --> 00:30:54.380 align:middle line:84% then they're using the novelty of the ideas 00:30:54.380 --> 00:30:55.940 align:middle line:84% that they've already passed in phase 00:30:55.940 --> 00:30:57.980 align:middle line:84% I, so the nonlinear relationship that 00:30:57.980 --> 00:31:01.020 align:middle line:90% is consuming up their phase I. 00:31:01.020 --> 00:31:03.840 align:middle line:84% HAZHIR RAHMANDAD: OK, so let me look at the equation here. 00:31:03.840 --> 00:31:10.220 align:middle line:84% So phase drugs in any phase are increased with initiating trials 00:31:10.220 --> 00:31:13.400 align:middle line:84% and reduced by failing trials or passing trials. 00:31:13.400 --> 00:31:15.180 align:middle line:84% So that's fairly straightforward. 00:31:15.180 --> 00:31:18.740 align:middle line:84% AUDIENCE: The ones which are in trial. 00:31:18.740 --> 00:31:21.540 align:middle line:84% And then there's the ones that have passed. 00:31:21.540 --> 00:31:22.780 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:31:22.780 --> 00:31:26.460 align:middle line:84% And then drugs that have passed trials also 00:31:26.460 --> 00:31:31.500 align:middle line:90% have their own phases. 00:31:31.500 --> 00:31:34.620 align:middle line:90% So you may go into-- 00:31:34.620 --> 00:31:40.100 align:middle line:84% I have passed phase II, and I'm sitting there. 00:31:40.100 --> 00:31:42.240 align:middle line:84% AUDIENCE: Yeah, it won't go obsolete after one. 00:31:42.240 --> 00:31:46.180 align:middle line:84% HAZHIR RAHMANDAD: Yes, so if something passes phase III, 00:31:46.180 --> 00:31:48.860 align:middle line:84% that is the one that makes money. 00:31:48.860 --> 00:31:51.300 align:middle line:84% So this becomes the-- revenue generating 00:31:51.300 --> 00:31:55.100 align:middle line:84% is the phase III one multiplied by revenues on the market. 00:31:55.100 --> 00:31:56.140 align:middle line:90% Got it. 00:31:56.140 --> 00:32:02.110 align:middle line:84% But then the start rate for initiating trials, 00:32:02.110 --> 00:32:04.170 align:middle line:84% you have part of it based on the revenue. 00:32:04.170 --> 00:32:06.170 align:middle line:84% AUDIENCE: It depends on the budget and the cost. 00:32:06.170 --> 00:32:11.310 align:middle line:84% But then the success rate of each trial depends on how good 00:32:11.310 --> 00:32:13.430 align:middle line:90% the pool of candidates. 00:32:13.430 --> 00:32:16.310 align:middle line:84% HAZHIR RAHMANDAD: OK, so basically, 00:32:16.310 --> 00:32:19.010 align:middle line:84% this model's modeling something else. 00:32:19.010 --> 00:32:22.890 align:middle line:84% This is not modeling the stock adjustment problem we defined. 00:32:22.890 --> 00:32:25.450 align:middle line:84% It is modeling something that is important and interesting. 00:32:25.450 --> 00:32:29.890 align:middle line:84% But in light of how it is diverging into other areas, 00:32:29.890 --> 00:32:33.190 align:middle line:84% let's not spend too much time on this, not that this is not 00:32:33.190 --> 00:32:34.410 align:middle line:90% an interesting problem. 00:32:34.410 --> 00:32:37.830 align:middle line:84% Just then you don't know what is happening inside this one 00:32:37.830 --> 00:32:40.330 align:middle line:84% because that's not the problem you have thought about, 00:32:40.330 --> 00:32:42.130 align:middle line:84% so you don't get as much out of it. 00:32:42.130 --> 00:32:45.010 align:middle line:84% AUDIENCE: It was something else, so I just took the wrong-- 00:32:45.010 --> 00:32:48.030 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so reading the problem definition 00:32:48.030 --> 00:32:51.430 align:middle line:90% is a good starting point. 00:32:51.430 --> 00:32:54.990 align:middle line:84% I'm just joking, but I appreciate 00:32:54.990 --> 00:32:59.630 align:middle line:84% getting us to see some interesting additional ways 00:32:59.630 --> 00:33:00.810 align:middle line:90% of looking at this. 00:33:00.810 --> 00:33:02.690 align:middle line:90% So let's look at Kathy's. 00:33:02.690 --> 00:33:04.130 align:middle line:90% This is Kathy's. 00:33:04.130 --> 00:33:06.790 align:middle line:90% 00:33:06.790 --> 00:33:11.230 align:middle line:84% So again, fairly standard formulations 00:33:11.230 --> 00:33:13.070 align:middle line:90% that we already have seen. 00:33:13.070 --> 00:33:17.230 align:middle line:90% So for failing each-- 00:33:17.230 --> 00:33:19.510 align:middle line:84% or for success in each range, you 00:33:19.510 --> 00:33:25.690 align:middle line:84% have the success rate and the fraction, that pass. 00:33:25.690 --> 00:33:30.950 align:middle line:84% So this is P2 pass fraction multiplied 00:33:30.950 --> 00:33:34.590 align:middle line:90% by drugs divided by P2 time. 00:33:34.590 --> 00:33:38.230 align:middle line:84% And this would be 1 minus pass fraction. 00:33:38.230 --> 00:33:40.910 align:middle line:84% So this is very similar to Alban's. 00:33:40.910 --> 00:33:45.730 align:middle line:84% So Kathy has not created a separate variable 00:33:45.730 --> 00:33:50.750 align:middle line:84% that is total drugs exiting this phase, just has combined them. 00:33:50.750 --> 00:33:52.850 align:middle line:84% I don't think in this model it matters. 00:33:52.850 --> 00:33:54.210 align:middle line:90% It's perfectly fine. 00:33:54.210 --> 00:33:55.950 align:middle line:84% But in some other settings, it is 00:33:55.950 --> 00:33:59.650 align:middle line:84% good to have that total explicitly defined. 00:33:59.650 --> 00:34:01.430 align:middle line:84% You may use it in other variables. 00:34:01.430 --> 00:34:03.690 align:middle line:84% AUDIENCE: Which total, I'm sorry? 00:34:03.690 --> 00:34:06.070 align:middle line:84% HAZHIR RAHMANDAD: So total drugs leaving 00:34:06.070 --> 00:34:10.010 align:middle line:84% phase II, which would be the drugs divided by phase II time. 00:34:10.010 --> 00:34:13.389 align:middle line:84% And then that would go into entering and failing 00:34:13.389 --> 00:34:16.389 align:middle line:84% multiplied each by the pass fraction and 1 minus pass 00:34:16.389 --> 00:34:16.889 align:middle line:90% fraction. 00:34:16.889 --> 00:34:19.690 align:middle line:84% So you would introduce an extra variable, 00:34:19.690 --> 00:34:23.630 align:middle line:84% but then you don't need the P2 time and drug two phase to go 00:34:23.630 --> 00:34:26.070 align:middle line:90% into both of these equations. 00:34:26.070 --> 00:34:28.730 align:middle line:84% That's the alternative way of formulating it, 00:34:28.730 --> 00:34:31.710 align:middle line:84% which was what Alban had, but they are mathematically 00:34:31.710 --> 00:34:34.389 align:middle line:90% identical. 00:34:34.389 --> 00:34:37.610 align:middle line:84% Yeah, I like that alternative A little bit better, 00:34:37.610 --> 00:34:40.389 align:middle line:84% just because it makes it very salient and clear 00:34:40.389 --> 00:34:42.409 align:middle line:84% that there is a total that is coming out. 00:34:42.409 --> 00:34:44.870 align:middle line:84% If you need to use that, you can use that. 00:34:44.870 --> 00:34:48.190 align:middle line:84% You're dividing that into two different passes. 00:34:48.190 --> 00:34:49.909 align:middle line:90% OK, so that's good. 00:34:49.909 --> 00:34:53.550 align:middle line:84% Then my quick look at this model gives me 00:34:53.550 --> 00:34:55.429 align:middle line:84% a little bit of a pause about equilibrium 00:34:55.429 --> 00:34:59.320 align:middle line:84% because I see initial drugs in P1, P2, P3, 00:34:59.320 --> 00:35:01.480 align:middle line:84% and these initials don't have any inputs 00:35:01.480 --> 00:35:04.400 align:middle line:84% into them, which tells me the model is not put 00:35:04.400 --> 00:35:06.920 align:middle line:90% into equilibrium analytically. 00:35:06.920 --> 00:35:11.580 align:middle line:84% It just has some ad hoc initial values used. 00:35:11.580 --> 00:35:14.120 align:middle line:90% So I assume that's the case. 00:35:14.120 --> 00:35:15.340 align:middle line:90% AUDIENCE: Yeah, I can solve. 00:35:15.340 --> 00:35:17.780 align:middle line:84% And it might be because I did this aggregate thing. 00:35:17.780 --> 00:35:19.050 align:middle line:90% It was not working out. 00:35:19.050 --> 00:35:21.300 align:middle line:84% HAZHIR RAHMANDAD: Yeah, we can look at the other parts 00:35:21.300 --> 00:35:21.900 align:middle line:90% now together. 00:35:21.900 --> 00:35:26.640 align:middle line:84% So that is the equilibrium challenge here. 00:35:26.640 --> 00:35:29.120 align:middle line:84% Revenue is based on number of drugs 00:35:29.120 --> 00:35:32.640 align:middle line:84% in the market, annual revenue per drug. 00:35:32.640 --> 00:35:37.820 align:middle line:84% One thing that I should mention, it is not conceptually complex, 00:35:37.820 --> 00:35:41.140 align:middle line:84% but something to keep in mind is that the patent length is not 00:35:41.140 --> 00:35:46.280 align:middle line:84% what is the delay in the drugs in the market phase. 00:35:46.280 --> 00:35:48.840 align:middle line:84% So the patents for drugs are typically 00:35:48.840 --> 00:35:52.320 align:middle line:84% filed just before they start phase I. 00:35:52.320 --> 00:35:56.780 align:middle line:84% And then the clock is ticking, and that's one of the reasons, 00:35:56.780 --> 00:35:59.840 align:middle line:84% actually, they can't hold the drugs too much, too long 00:35:59.840 --> 00:36:02.880 align:middle line:90% on the back burner. 00:36:02.880 --> 00:36:05.920 align:middle line:84% So just conceptually, keep that in mind 00:36:05.920 --> 00:36:08.840 align:middle line:84% that the time in the market is the patent 00:36:08.840 --> 00:36:11.680 align:middle line:84% length minus the sum of all of these delays 00:36:11.680 --> 00:36:14.320 align:middle line:90% for the previous steps. 00:36:14.320 --> 00:36:16.660 align:middle line:84% You guys shouldn't necessarily know that. 00:36:16.660 --> 00:36:20.400 align:middle line:84% It's not an obvious fact of this market. 00:36:20.400 --> 00:36:23.360 align:middle line:84% You need to do some research on that. 00:36:23.360 --> 00:36:25.740 align:middle line:90% So revenue is calculated here. 00:36:25.740 --> 00:36:28.600 align:middle line:90% That's pretty straightforward. 00:36:28.600 --> 00:36:33.560 align:middle line:84% Now, the revenue is creating a revenue target based 00:36:33.560 --> 00:36:38.800 align:middle line:90% on basically a growth factor. 00:36:38.800 --> 00:36:40.600 align:middle line:84% So you look at the current revenue. 00:36:40.600 --> 00:36:43.740 align:middle line:84% You multiply it by the growth factor. 00:36:43.740 --> 00:36:47.840 align:middle line:84% And then you are adjusting towards that a smooth function 00:36:47.840 --> 00:36:51.160 align:middle line:90% to go into the revenue target. 00:36:51.160 --> 00:36:53.280 align:middle line:84% By the way, I'm looking at these, 00:36:53.280 --> 00:36:56.420 align:middle line:84% and I'm reading the formulations, 00:36:56.420 --> 00:36:58.860 align:middle line:84% making assumptions that, yes, this is happening. 00:36:58.860 --> 00:37:02.320 align:middle line:84% So two things, one is, if I'm making wrong assumptions, please 00:37:02.320 --> 00:37:03.560 align:middle line:90% speak up. 00:37:03.560 --> 00:37:04.440 align:middle line:90% Stop me. 00:37:04.440 --> 00:37:07.160 align:middle line:84% Second, if you are not following what is happening 00:37:07.160 --> 00:37:09.480 align:middle line:84% and why I'm making those assumptions, again, stop me 00:37:09.480 --> 00:37:12.860 align:middle line:84% and say, hey, I'm not following what is happening here. 00:37:12.860 --> 00:37:14.260 align:middle line:90% Can you show the equation? 00:37:14.260 --> 00:37:18.380 align:middle line:84% So I'm doing this to be faster and see more of the models, 00:37:18.380 --> 00:37:23.360 align:middle line:84% but if it means you get confused, don't let it go. 00:37:23.360 --> 00:37:24.100 align:middle line:90% Stop me. 00:37:24.100 --> 00:37:24.760 align:middle line:90% Alex. 00:37:24.760 --> 00:37:27.160 align:middle line:84% AUDIENCE: On that note, after this, or at some point, 00:37:27.160 --> 00:37:28.680 align:middle line:84% could we go back to a SaaS model because I 00:37:28.680 --> 00:37:30.722 align:middle line:84% didn't understand how the physics of the pipeline 00:37:30.722 --> 00:37:31.960 align:middle line:90% worked with the subscripts? 00:37:31.960 --> 00:37:33.520 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:37:33.520 --> 00:37:35.120 align:middle line:90% Sure, we can do that. 00:37:35.120 --> 00:37:37.240 align:middle line:84% Let me go through a few of these, 00:37:37.240 --> 00:37:39.440 align:middle line:90% and then we should do that. 00:37:39.440 --> 00:37:43.800 align:middle line:84% OK, so this part of the formulation, 00:37:43.800 --> 00:37:46.680 align:middle line:84% again, thinking about what it does, 00:37:46.680 --> 00:37:49.640 align:middle line:84% if you have a system that is working well, 00:37:49.640 --> 00:37:52.910 align:middle line:84% that is, it is doing what you want to do, that is, 00:37:52.910 --> 00:37:55.290 align:middle line:84% it is in equilibrium at the beginning, 00:37:55.290 --> 00:38:00.370 align:middle line:84% then having the revenue grow with this target revenue growth 00:38:00.370 --> 00:38:02.230 align:middle line:90% rate works fine. 00:38:02.230 --> 00:38:05.850 align:middle line:84% That is, it can generate a desired revenue process that 00:38:05.850 --> 00:38:09.490 align:middle line:84% grows exponentially as was specified in the problem 00:38:09.490 --> 00:38:10.530 align:middle line:90% definition. 00:38:10.530 --> 00:38:13.970 align:middle line:84% But if there is any problem down here that 00:38:13.970 --> 00:38:18.650 align:middle line:84% makes your annual revenue not to be fully consistent, 00:38:18.650 --> 00:38:21.810 align:middle line:84% then the exponential growth will not 00:38:21.810 --> 00:38:24.470 align:middle line:84% happen the way you want it to happen, 00:38:24.470 --> 00:38:26.410 align:middle line:90% and everything falls apart. 00:38:26.410 --> 00:38:28.490 align:middle line:84% Not everything falls apart, but it 00:38:28.490 --> 00:38:30.850 align:middle line:84% becomes too hard to figure out what 00:38:30.850 --> 00:38:34.370 align:middle line:84% is happening that is stopping your desired 00:38:34.370 --> 00:38:36.690 align:middle line:84% and your actual to match each other. 00:38:36.690 --> 00:38:39.110 align:middle line:84% So as such, even though this is fine, 00:38:39.110 --> 00:38:40.690 align:middle line:84% and it is actually, in some ways, 00:38:40.690 --> 00:38:43.010 align:middle line:84% more realistic because usually companies 00:38:43.010 --> 00:38:46.690 align:middle line:84% look at their current revenue and then make adjustments 00:38:46.690 --> 00:38:52.110 align:middle line:84% for what they want to see, for the purpose of this exercise, 00:38:52.110 --> 00:38:57.850 align:middle line:84% it's probably better, is cleaner to have an exogenous goal that 00:38:57.850 --> 00:39:00.090 align:middle line:84% is growing exponentially, just as Alban 00:39:00.090 --> 00:39:03.490 align:middle line:84% had with that exogenous input and some initial value. 00:39:03.490 --> 00:39:06.930 align:middle line:84% Or some other version would be fine. 00:39:06.930 --> 00:39:10.230 align:middle line:84% So this is just, again, nothing wrong here. 00:39:10.230 --> 00:39:13.890 align:middle line:84% In fact, conceptually, even more realistic 00:39:13.890 --> 00:39:17.130 align:middle line:84% but will make your analysis harder 00:39:17.130 --> 00:39:21.570 align:middle line:90% when you're doing it this way. 00:39:21.570 --> 00:39:24.510 align:middle line:84% AUDIENCE: You have a fully exogenous goal, though. 00:39:24.510 --> 00:39:30.490 align:middle line:84% Doesn't that sound-- disconnects as lot of what you're actually 00:39:30.490 --> 00:39:31.650 align:middle line:90% almost target-- 00:39:31.650 --> 00:39:35.850 align:middle line:84% I mean, the idea of exogenous goal growing by 10%. 00:39:35.850 --> 00:39:38.890 align:middle line:84% You have problems in the system or something. 00:39:38.890 --> 00:39:41.170 align:middle line:84% It feels like that is not realistic. 00:39:41.170 --> 00:39:44.270 align:middle line:84% A company's not going to just shove way, way more exponential 00:39:44.270 --> 00:39:44.770 align:middle line:90% growth. 00:39:44.770 --> 00:39:46.630 align:middle line:84% HAZHIR RAHMANDAD: Absolutely, so in that sense, 00:39:46.630 --> 00:39:47.630 align:middle line:90% you're absolutely right. 00:39:47.630 --> 00:39:51.130 align:middle line:84% And that's why I'm saying this is more realistic in practice. 00:39:51.130 --> 00:39:55.530 align:middle line:84% But if you do it that way, then you 00:39:55.530 --> 00:39:58.250 align:middle line:84% can see whether your policies allow 00:39:58.250 --> 00:40:03.090 align:middle line:84% you to track an exogenous goal of growing 5% per year 00:40:03.090 --> 00:40:04.770 align:middle line:90% or whatever it is. 00:40:04.770 --> 00:40:07.910 align:middle line:84% But if you don't do it exogenously, 00:40:07.910 --> 00:40:11.930 align:middle line:84% then whatever problem in your supply chain adjustment 00:40:11.930 --> 00:40:14.810 align:middle line:84% ends up changing your annual revenue, 00:40:14.810 --> 00:40:17.630 align:middle line:84% it will now be built into your goals, 00:40:17.630 --> 00:40:19.890 align:middle line:84% and therefore, it is much harder to see 00:40:19.890 --> 00:40:22.710 align:middle line:84% whether you can, with your equations, 00:40:22.710 --> 00:40:24.930 align:middle line:84% get to the target of adjusting the stock 00:40:24.930 --> 00:40:26.930 align:middle line:84% so that it can grow exponentially. 00:40:26.930 --> 00:40:29.550 align:middle line:84% That's the only reason to do it that way. 00:40:29.550 --> 00:40:31.050 align:middle line:90% OK. 00:40:31.050 --> 00:40:35.370 align:middle line:84% So then we have the desired drugs in the market. 00:40:35.370 --> 00:40:38.470 align:middle line:84% You compared that with the drugs in the market. 00:40:38.470 --> 00:40:41.390 align:middle line:84% This is the adjustment for the drugs in the market. 00:40:41.390 --> 00:40:44.010 align:middle line:90% 00:40:44.010 --> 00:40:47.450 align:middle line:84% Then you are doing this interesting thing 00:40:47.450 --> 00:40:49.590 align:middle line:90% of expected loss rate. 00:40:49.590 --> 00:40:52.370 align:middle line:84% That is, basically, you are looking at all of the loss rates 00:40:52.370 --> 00:40:55.730 align:middle line:84% from the three, four different stocks. 00:40:55.730 --> 00:41:00.170 align:middle line:84% And you're saying I need to replace for those losses. 00:41:00.170 --> 00:41:06.090 align:middle line:84% So I need also these numbers to go into the beginning 00:41:06.090 --> 00:41:08.490 align:middle line:90% of the system. 00:41:08.490 --> 00:41:15.990 align:middle line:84% So that idea makes sense for the case where you have equilibrium. 00:41:15.990 --> 00:41:19.850 align:middle line:90% You don't have growing stocks. 00:41:19.850 --> 00:41:23.350 align:middle line:84% But why doesn't it make sense for when you have growth? 00:41:23.350 --> 00:41:27.418 align:middle line:90% 00:41:27.418 --> 00:41:29.210 align:middle line:84% AUDIENCE: You would expect a growth pattern 00:41:29.210 --> 00:41:31.590 align:middle line:90% in those expected loss rates. 00:41:31.590 --> 00:41:34.930 align:middle line:90% 00:41:34.930 --> 00:41:36.430 align:middle line:90% Well, there'll be [INAUDIBLE]. 00:41:36.430 --> 00:41:41.542 align:middle line:90% 00:41:41.542 --> 00:41:43.250 align:middle line:84% AUDIENCE: Even when we don't have growth, 00:41:43.250 --> 00:41:47.700 align:middle line:84% it's like a similar formulation in the desired supply 00:41:47.700 --> 00:41:50.440 align:middle line:84% then because everything is being multiplied by the delay, 00:41:50.440 --> 00:41:54.580 align:middle line:90% so it grows exponentially. 00:41:54.580 --> 00:41:56.580 align:middle line:90% AUDIENCE: Yeah, it does grow. 00:41:56.580 --> 00:41:58.028 align:middle line:90% I couldn't get it not to grow. 00:41:58.028 --> 00:41:59.320 align:middle line:90% AUDIENCE: But you need to add-- 00:41:59.320 --> 00:42:01.362 align:middle line:84% HAZHIR RAHMANDAD: So this will grow exponentially 00:42:01.362 --> 00:42:03.780 align:middle line:84% because you have built in a reinforcing loop in the system 00:42:03.780 --> 00:42:06.740 align:middle line:84% that says, drugs in the market multiplied with some growth 00:42:06.740 --> 00:42:07.440 align:middle line:90% rate. 00:42:07.440 --> 00:42:09.260 align:middle line:90% So that's not the question. 00:42:09.260 --> 00:42:16.020 align:middle line:84% The question is, can you match a desired growth rate exactly 00:42:16.020 --> 00:42:20.540 align:middle line:84% in which you actually don't need to adjust your stocks? 00:42:20.540 --> 00:42:25.660 align:middle line:84% That is, the value of the stocks are endogenously 00:42:25.660 --> 00:42:27.380 align:middle line:90% getting the right value. 00:42:27.380 --> 00:42:30.420 align:middle line:84% So in the traditional stock adjustment model, 00:42:30.420 --> 00:42:33.060 align:middle line:84% you have these adjustments of stocks 00:42:33.060 --> 00:42:37.700 align:middle line:84% that go up and down if the stock is out of the equilibrium path. 00:42:37.700 --> 00:42:41.300 align:middle line:84% But as soon as the stock is adjusted to the equilibrium 00:42:41.300 --> 00:42:44.860 align:middle line:84% path-- with a step function, it does that after a while-- 00:42:44.860 --> 00:42:46.400 align:middle line:90% that adjustment shuts off. 00:42:46.400 --> 00:42:47.840 align:middle line:90% It's not doing anything. 00:42:47.840 --> 00:42:50.740 align:middle line:84% The stock is now in the right place, 00:42:50.740 --> 00:42:52.980 align:middle line:84% but that's with an equilibrium system. 00:42:52.980 --> 00:42:57.460 align:middle line:84% Now, can you do it that, when it is growing exponentially, 00:42:57.460 --> 00:42:59.480 align:middle line:84% the stock is always on the right track? 00:42:59.480 --> 00:43:02.980 align:middle line:84% That is, it matching the desired value all the time? 00:43:02.980 --> 00:43:08.240 align:middle line:84% That is the real challenging task here with the growth case. 00:43:08.240 --> 00:43:10.880 align:middle line:84% AUDIENCE: So with this won't achieve that? 00:43:10.880 --> 00:43:17.500 align:middle line:84% But if Kathy were to add in the desired expected loss. 00:43:17.500 --> 00:43:21.380 align:middle line:84% HAZHIR RAHMANDAD: Very good, so basically, for this to work, 00:43:21.380 --> 00:43:24.020 align:middle line:84% you actually need to have some adjustment that 00:43:24.020 --> 00:43:32.820 align:middle line:84% says, OK, the things that are lost here in the exiting market, 00:43:32.820 --> 00:43:40.380 align:middle line:84% to replace those folks, I need to start a lot more because I'm 00:43:40.380 --> 00:43:42.060 align:middle line:90% starting today. 00:43:42.060 --> 00:43:47.460 align:middle line:84% What I'm replacing is what will be exiting 10 years from now. 00:43:47.460 --> 00:43:53.220 align:middle line:84% And therefore, I need to account for how much more will 00:43:53.220 --> 00:43:55.000 align:middle line:90% be exiting 10 years from now. 00:43:55.000 --> 00:43:57.040 align:middle line:84% AUDIENCE: OK, so let me make sure I understand. 00:43:57.040 --> 00:43:59.580 align:middle line:84% So the problem is that, starting-- 00:43:59.580 --> 00:44:03.300 align:middle line:84% a drug failing P1 is a completely different probability 00:44:03.300 --> 00:44:04.588 align:middle line:90% than a failing exiting. 00:44:04.588 --> 00:44:06.880 align:middle line:84% HAZHIR RAHMANDAD: Not about the probability of failure. 00:44:06.880 --> 00:44:10.540 align:middle line:84% So let's assume there is no failure to keep things simple. 00:44:10.540 --> 00:44:12.020 align:middle line:90% This is about the growth. 00:44:12.020 --> 00:44:12.900 align:middle line:90% The failure comes in. 00:44:12.900 --> 00:44:15.140 align:middle line:84% That has its own issue, but it doesn't have 00:44:15.140 --> 00:44:17.280 align:middle line:90% a problem in your formulation. 00:44:17.280 --> 00:44:20.300 align:middle line:84% Failure is actually accounted for in your formulation. 00:44:20.300 --> 00:44:22.140 align:middle line:84% What is missing in your formulation 00:44:22.140 --> 00:44:24.220 align:middle line:90% is the possibility of growth. 00:44:24.220 --> 00:44:27.260 align:middle line:84% So let's break that down into these two pieces-- 00:44:27.260 --> 00:44:31.100 align:middle line:84% failure rates, success rates, failure rates. 00:44:31.100 --> 00:44:35.140 align:middle line:84% Because you have your outflows accounted 00:44:35.140 --> 00:44:38.390 align:middle line:84% for-- so you have your accounting for every outflow 00:44:38.390 --> 00:44:42.190 align:middle line:84% here, you are replacing into the system 00:44:42.190 --> 00:44:44.130 align:middle line:84% how much you're getting out of the system. 00:44:44.130 --> 00:44:49.350 align:middle line:84% Think of a stock that includes all of these four together. 00:44:49.350 --> 00:44:53.230 align:middle line:84% If you're replacing all of the things that come out of it, 00:44:53.230 --> 00:44:58.070 align:middle line:84% you will be in equilibrium once you have adjusted for the stocks 00:44:58.070 --> 00:45:00.010 align:middle line:90% to be in equilibrium. 00:45:00.010 --> 00:45:01.810 align:middle line:90% So then this is not a problem. 00:45:01.810 --> 00:45:04.310 align:middle line:84% That is, no matter what your success rates. 00:45:04.310 --> 00:45:07.590 align:middle line:90% This should work in equilibrium. 00:45:07.590 --> 00:45:10.550 align:middle line:90% So that is OK. 00:45:10.550 --> 00:45:12.470 align:middle line:84% The part that is not working well 00:45:12.470 --> 00:45:15.010 align:middle line:84% is, now, if you are growing exponentially-- 00:45:15.010 --> 00:45:19.190 align:middle line:84% so let's say I'm growing, doubling every year, OK, 00:45:19.190 --> 00:45:26.990 align:middle line:84% and it takes four years for starting something until it 00:45:26.990 --> 00:45:29.770 align:middle line:90% comes out of my system. 00:45:29.770 --> 00:45:33.090 align:middle line:84% In fact, it takes more than that, but let's say four years. 00:45:33.090 --> 00:45:35.450 align:middle line:84% So it comes out of exiting market 00:45:35.450 --> 00:45:38.850 align:middle line:84% and even if we didn't have any failures to keep things simple, 00:45:38.850 --> 00:45:41.430 align:middle line:90% so it's a one-way route. 00:45:41.430 --> 00:45:49.030 align:middle line:84% So if I'm exiting right now two drugs per year, in four years, 00:45:49.030 --> 00:45:51.610 align:middle line:84% how many drugs per year do I need to be exiting? 00:45:51.610 --> 00:45:53.110 align:middle line:90% AUDIENCE: 16. 00:45:53.110 --> 00:45:55.630 align:middle line:90% HAZHIR RAHMANDAD: Yes, six-- no. 00:45:55.630 --> 00:45:57.390 align:middle line:90% 32 or 60? 00:45:57.390 --> 00:46:03.470 align:middle line:84% Yes, yes, because 2 to the power of 4 multiplied by 2, so that's 00:46:03.470 --> 00:46:04.270 align:middle line:90% 32. 00:46:04.270 --> 00:46:08.590 align:middle line:84% So you need 32 drugs to be coming out four years from now. 00:46:08.590 --> 00:46:10.090 align:middle line:90% And now I'm discretizing. 00:46:10.090 --> 00:46:10.970 align:middle line:90% This is continuous. 00:46:10.970 --> 00:46:12.550 align:middle line:84% There is some numerical differences 00:46:12.550 --> 00:46:14.010 align:middle line:90% but conceptually the same. 00:46:14.010 --> 00:46:20.630 align:middle line:84% OK, so I need to start 32 drugs for the two 00:46:20.630 --> 00:46:26.190 align:middle line:84% that I'm exiting today because what is being replaced 00:46:26.190 --> 00:46:32.130 align:middle line:84% is actually what is going to be coming out four years from now, 00:46:32.130 --> 00:46:34.710 align:middle line:90% which needs to be 32, not two. 00:46:34.710 --> 00:46:38.930 align:middle line:84% So your formulation only replaces two for those guys. 00:46:38.930 --> 00:46:40.610 align:middle line:90% So that is for exiting market. 00:46:40.610 --> 00:46:44.190 align:middle line:84% Now, for failing P3, the number is different. 00:46:44.190 --> 00:46:46.710 align:middle line:90% It is not going to be 32. 00:46:46.710 --> 00:46:51.830 align:middle line:84% If each of these phases was one year, then it would be 16. 00:46:51.830 --> 00:46:56.190 align:middle line:84% That is, if you were exiting anything from failing three, 00:46:56.190 --> 00:46:58.870 align:middle line:84% for each of those, I needed to exit-- 00:46:58.870 --> 00:47:03.190 align:middle line:84% to enter 16 into the system that three years down the road-- 00:47:03.190 --> 00:47:05.790 align:middle line:90% not for each one, for each two. 00:47:05.790 --> 00:47:08.030 align:middle line:90% For each one, it would be 8. 00:47:08.030 --> 00:47:10.350 align:middle line:90% That's the same going backwards. 00:47:10.350 --> 00:47:15.670 align:middle line:84% AUDIENCE: OK, so to fix this, the expected loss rate 00:47:15.670 --> 00:47:18.547 align:middle line:84% should be like a growth in loss rate. 00:47:18.547 --> 00:47:19.630 align:middle line:90% HAZHIR RAHMANDAD: Exactly. 00:47:19.630 --> 00:47:20.290 align:middle line:90% AUDIENCE: I get it now. 00:47:20.290 --> 00:47:20.957 align:middle line:90% Thank you, yeah. 00:47:20.957 --> 00:47:22.730 align:middle line:84% HAZHIR RAHMANDAD: Yes, so is that clear? 00:47:22.730 --> 00:47:25.270 align:middle line:84% That is really at the heart of capturing the growth 00:47:25.270 --> 00:47:26.550 align:middle line:90% process here. 00:47:26.550 --> 00:47:31.870 align:middle line:84% It wouldn't work without having that factor into the system. 00:47:31.870 --> 00:47:36.420 align:middle line:84% But other than that, is for equilibrium, 00:47:36.420 --> 00:47:37.980 align:middle line:90% this should do fine. 00:47:37.980 --> 00:47:40.400 align:middle line:84% That is, you have an expected loss rate. 00:47:40.400 --> 00:47:45.280 align:middle line:84% You add adjustments for different stocks. 00:47:45.280 --> 00:47:48.020 align:middle line:84% Now, adjustments for different stocks. 00:47:48.020 --> 00:47:51.260 align:middle line:84% The way Kathy is doing it is saying, OK, 00:47:51.260 --> 00:47:54.520 align:middle line:84% I'm adding up all the supply lines. 00:47:54.520 --> 00:47:58.060 align:middle line:84% I'm comparing it with the desired supply line. 00:47:58.060 --> 00:48:00.260 align:middle line:84% And where do you get the desired supply line? 00:48:00.260 --> 00:48:06.520 align:middle line:84% You're getting it from the expected loss rate, plus-- 00:48:06.520 --> 00:48:09.060 align:middle line:84% AUDIENCE: There's a switch for the formula. 00:48:09.060 --> 00:48:10.200 align:middle line:90% There are two options. 00:48:10.200 --> 00:48:11.800 align:middle line:90% HAZHIR RAHMANDAD: Oh, OK. 00:48:11.800 --> 00:48:13.820 align:middle line:84% So let's see, the formula switch. 00:48:13.820 --> 00:48:17.960 align:middle line:84% Expected acquisition lag multiplied 00:48:17.960 --> 00:48:23.600 align:middle line:84% by desired acquisition rate or expected acquisition lag 00:48:23.600 --> 00:48:25.940 align:middle line:84% multiplied by expected loss rate. 00:48:25.940 --> 00:48:28.760 align:middle line:90% 00:48:28.760 --> 00:48:31.160 align:middle line:84% So tell us what you were thinking 00:48:31.160 --> 00:48:33.400 align:middle line:90% in doing this formulation. 00:48:33.400 --> 00:48:35.062 align:middle line:90% AUDIENCE: So the-- 00:48:35.062 --> 00:48:36.520 align:middle line:84% HAZHIR RAHMANDAD: So basically, you 00:48:36.520 --> 00:48:41.360 align:middle line:84% have these two drivers either expected loss rate or expected-- 00:48:41.360 --> 00:48:43.880 align:middle line:90% 00:48:43.880 --> 00:48:45.767 align:middle line:90% desired acquisition rate. 00:48:45.767 --> 00:48:47.600 align:middle line:84% AUDIENCE: Yeah, and desired acquisition rate 00:48:47.600 --> 00:48:50.013 align:middle line:90% is the loss plus-- 00:48:50.013 --> 00:48:52.180 align:middle line:84% HAZHIR RAHMANDAD: The sum of those two, OK, perfect. 00:48:52.180 --> 00:48:53.805 align:middle line:84% AUDIENCE: Essentially, it's including-- 00:48:53.805 --> 00:48:57.840 align:middle line:84% you're either including the adjustment for drugs and market, 00:48:57.840 --> 00:48:59.350 align:middle line:84% or you're only looking at those-- 00:48:59.350 --> 00:49:00.600 align:middle line:90% HAZHIR RAHMANDAD: OK, perfect. 00:49:00.600 --> 00:49:05.820 align:middle line:84% So is it clear for everybody what Kathy is doing here? 00:49:05.820 --> 00:49:08.440 align:middle line:84% Basically, she is accounting for the two formulations 00:49:08.440 --> 00:49:12.320 align:middle line:84% we discussed in Alban's model, where you either 00:49:12.320 --> 00:49:17.880 align:middle line:84% account for the stock adjustment in deciding your entry 00:49:17.880 --> 00:49:23.680 align:middle line:84% or replacement or desired stock values for the next phases 00:49:23.680 --> 00:49:24.380 align:middle line:90% or not. 00:49:24.380 --> 00:49:28.000 align:middle line:84% You just look at the-- so this is nice to think about the two 00:49:28.000 --> 00:49:30.340 align:middle line:84% explicitly and have a switch that says, 00:49:30.340 --> 00:49:33.780 align:middle line:84% I could look at it or not or have some intermediate value. 00:49:33.780 --> 00:49:39.440 align:middle line:84% So this is a good reflection of what you were thinking about. 00:49:39.440 --> 00:49:41.600 align:middle line:90% It works. 00:49:41.600 --> 00:49:48.800 align:middle line:84% As I said, I'm probably more towards not accounting for that. 00:49:48.800 --> 00:49:51.720 align:middle line:90% OK, so that's fine. 00:49:51.720 --> 00:49:54.740 align:middle line:84% But this expected loss rate-- go ahead. 00:49:54.740 --> 00:49:56.320 align:middle line:84% AUDIENCE: Not accounting for which. 00:49:56.320 --> 00:49:58.720 align:middle line:84% HAZHIR RAHMANDAD: Not accounting for the adjustment 00:49:58.720 --> 00:50:02.640 align:middle line:84% for drugs in market, that is, I don't know, turning on or off. 00:50:02.640 --> 00:50:06.200 align:middle line:84% But this formulation has some other challenges. 00:50:06.200 --> 00:50:11.240 align:middle line:84% So if you are having a desired supply line 00:50:11.240 --> 00:50:20.520 align:middle line:84% total that is coming from these four different outflows 00:50:20.520 --> 00:50:30.810 align:middle line:84% multiplied by total lag of three of these stages, 00:50:30.810 --> 00:50:32.050 align:middle line:90% how does it work? 00:50:32.050 --> 00:50:35.870 align:middle line:84% What is it exactly doing this desired supply line? 00:50:35.870 --> 00:50:38.930 align:middle line:84% Why should it be the same as the sum 00:50:38.930 --> 00:50:43.650 align:middle line:84% of desired value for the phase I, phase II, and phase III? 00:50:43.650 --> 00:50:45.350 align:middle line:90% Yes, why? 00:50:45.350 --> 00:50:46.310 align:middle line:90% Why would it be? 00:50:46.310 --> 00:50:50.670 align:middle line:90% 00:50:50.670 --> 00:50:54.210 align:middle line:84% Because the logic you are using or the assumption 00:50:54.210 --> 00:50:59.090 align:middle line:84% your model is making is that the desired supply line, which 00:50:59.090 --> 00:51:02.170 align:middle line:84% is the sum of desired in phase I, desired in phase II, desired 00:51:02.170 --> 00:51:10.490 align:middle line:84% in phase III, equals the outflow of the four stocks multiplied 00:51:10.490 --> 00:51:12.730 align:middle line:84% by this acquisition lag, which is 00:51:12.730 --> 00:51:17.450 align:middle line:84% the sum of the time in those three stocks. 00:51:17.450 --> 00:51:20.870 align:middle line:84% Why is that the right formulation? 00:51:20.870 --> 00:51:27.450 align:middle line:90% 00:51:27.450 --> 00:51:28.750 align:middle line:90% Which I think it is not. 00:51:28.750 --> 00:51:31.930 align:middle line:84% I don't think it actually works out. 00:51:31.930 --> 00:51:34.770 align:middle line:84% So this is basically, I don't know, 00:51:34.770 --> 00:51:37.130 align:middle line:84% some heuristic that came into your mind. 00:51:37.130 --> 00:51:38.530 align:middle line:84% The challenge with this heuristic 00:51:38.530 --> 00:51:40.238 align:middle line:84% is actually you're trying to do something 00:51:40.238 --> 00:51:44.490 align:middle line:84% much harder that is come up with a single total desired supply 00:51:44.490 --> 00:51:45.810 align:middle line:90% line. 00:51:45.810 --> 00:51:48.410 align:middle line:84% Getting to that without calculating 00:51:48.410 --> 00:51:52.170 align:middle line:84% the desired for phase I, II, and III is very hard. 00:51:52.170 --> 00:51:54.250 align:middle line:84% I mean, basically you have to calculate 00:51:54.250 --> 00:51:57.730 align:middle line:84% desired phase I, desired phase II, desired phase III, 00:51:57.730 --> 00:51:59.570 align:middle line:90% then add them up. 00:51:59.570 --> 00:52:01.290 align:middle line:90% You can't do it separately. 00:52:01.290 --> 00:52:04.665 align:middle line:84% And the desired values are the really challenging parts 00:52:04.665 --> 00:52:06.290 align:middle line:84% in this case because those are the ones 00:52:06.290 --> 00:52:08.490 align:middle line:90% you need also for equilibrium. 00:52:08.490 --> 00:52:10.970 align:middle line:84% So to calculate equilibrium, you need to put them 00:52:10.970 --> 00:52:12.230 align:middle line:90% at the desired value. 00:52:12.230 --> 00:52:14.930 align:middle line:84% The desired should be driven from the upstream 00:52:14.930 --> 00:52:20.010 align:middle line:84% from where you have the desired total drugs in the market. 00:52:20.010 --> 00:52:23.770 align:middle line:90% OK, so Alex. 00:52:23.770 --> 00:52:26.510 align:middle line:84% AUDIENCE: What is the issue with agglomerating them all together? 00:52:26.510 --> 00:52:29.850 align:middle line:84% Why do you need to consider every transitory stock 00:52:29.850 --> 00:52:30.450 align:middle line:90% separately? 00:52:30.450 --> 00:52:31.110 align:middle line:90% [INAUDIBLE] 00:52:31.110 --> 00:52:33.570 align:middle line:84% HAZHIR RAHMANDAD: You can't write the formulation for it. 00:52:33.570 --> 00:52:36.210 align:middle line:84% Now, if you wrote the formulation 00:52:36.210 --> 00:52:41.730 align:middle line:84% for it or in whatever way, combining them into one step 00:52:41.730 --> 00:52:45.570 align:middle line:84% and just looking at the sum of all of them 00:52:45.570 --> 00:52:48.310 align:middle line:84% versus the desired sum of all of them 00:52:48.310 --> 00:52:51.510 align:middle line:84% and dividing that by some time constant, is OK. 00:52:51.510 --> 00:52:55.570 align:middle line:84% There is nothing wrong with that conceptually. 00:52:55.570 --> 00:53:00.670 align:middle line:84% But to get to your desired total, 00:53:00.670 --> 00:53:05.250 align:middle line:84% you actually have to find the desired for every item. 00:53:05.250 --> 00:53:10.630 align:middle line:84% So that's where things don't work in this formulation. 00:53:10.630 --> 00:53:12.478 align:middle line:90% AUDIENCE: I think I figured out. 00:53:12.478 --> 00:53:14.770 align:middle line:84% HAZHIR RAHMANDAD: OK, we can check out your formulation 00:53:14.770 --> 00:53:16.650 align:middle line:90% as well. 00:53:16.650 --> 00:53:19.450 align:middle line:90% OK, so that's that. 00:53:19.450 --> 00:53:22.520 align:middle line:84% Then we have desired supply line. 00:53:22.520 --> 00:53:26.680 align:middle line:84% So you have adjustments for supply line. 00:53:26.680 --> 00:53:28.160 align:middle line:84% The rest is fairly straightforward. 00:53:28.160 --> 00:53:31.020 align:middle line:90% So that's replacement. 00:53:31.020 --> 00:53:35.120 align:middle line:84% So we had one request to look at [? Hassam's ?] model again, 00:53:35.120 --> 00:53:37.100 align:middle line:90% just to get-- 00:53:37.100 --> 00:53:40.860 align:middle line:84% this one, yes-- to get how the stock inflows work. 00:53:40.860 --> 00:53:49.460 align:middle line:84% And basically-- so initiation of drugs, 00:53:49.460 --> 00:53:53.740 align:middle line:84% that's the key formulation that we haven't looked at. 00:53:53.740 --> 00:53:56.660 align:middle line:90% Here is coming from a budget. 00:53:56.660 --> 00:54:01.140 align:middle line:84% And then the budget is for each phase. 00:54:01.140 --> 00:54:08.860 align:middle line:84% And the budget for each phase comes from a budget share. 00:54:08.860 --> 00:54:15.740 align:middle line:84% But it doesn't account for availability 00:54:15.740 --> 00:54:21.993 align:middle line:84% of drugs for phase-- so let's say I want to start phase III. 00:54:21.993 --> 00:54:23.660 align:middle line:84% AUDIENCE: You don't have any candidates. 00:54:23.660 --> 00:54:25.702 align:middle line:84% HAZHIR RAHMANDAD: And I don't have any candidate. 00:54:25.702 --> 00:54:27.620 align:middle line:84% Is that captured in this feedback loop? 00:54:27.620 --> 00:54:31.300 align:middle line:84% AUDIENCE: [INAUDIBLE] that version of them 00:54:31.300 --> 00:54:34.360 align:middle line:84% can start drugs for phase III, which is unrealistic. 00:54:34.360 --> 00:54:36.700 align:middle line:84% But the success rate would be zero. 00:54:36.700 --> 00:54:39.940 align:middle line:84% So I'm repacking the availability of good candidates 00:54:39.940 --> 00:54:40.960 align:middle line:90% and success rates. 00:54:40.960 --> 00:54:43.180 align:middle line:84% HAZHIR RAHMANDAD: So that's not generally a good way 00:54:43.180 --> 00:54:46.500 align:middle line:84% to do these things because it will-- you are basically saying, 00:54:46.500 --> 00:54:51.420 align:middle line:84% let me change the success rate, but let me start drugs. 00:54:51.420 --> 00:54:52.620 align:middle line:90% OK. 00:54:52.620 --> 00:54:58.500 align:middle line:84% And that's not how the real world works, basically. 00:54:58.500 --> 00:55:01.100 align:middle line:84% AUDIENCE: Shoestring budget when you start those? 00:55:01.100 --> 00:55:01.980 align:middle line:90% AUDIENCE: It does. 00:55:01.980 --> 00:55:02.980 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 00:55:02.980 --> 00:55:04.500 align:middle line:90% Part of it is that it does. 00:55:04.500 --> 00:55:07.580 align:middle line:84% I mean, you could always make additional auxiliary 00:55:07.580 --> 00:55:08.160 align:middle line:90% assumptions. 00:55:08.160 --> 00:55:10.940 align:middle line:84% I go and acquire a firm that has done phase II trials 00:55:10.940 --> 00:55:12.720 align:middle line:84% and now starting something in phase III. 00:55:12.720 --> 00:55:14.640 align:middle line:84% So you could come up with those explanations. 00:55:14.640 --> 00:55:17.040 align:middle line:84% But if you keep everything from your pipeline, 00:55:17.040 --> 00:55:19.900 align:middle line:84% you definitely need a feedback from drugs that 00:55:19.900 --> 00:55:23.900 align:middle line:90% have passed the previous phase. 00:55:23.900 --> 00:55:27.420 align:middle line:84% Then you have to define a maximum rate of starting 00:55:27.420 --> 00:55:30.740 align:middle line:84% new drugs based on a minimum time to start a trial 00:55:30.740 --> 00:55:34.000 align:middle line:84% and then compare that with what you can through the budget 00:55:34.000 --> 00:55:34.820 align:middle line:90% and start. 00:55:34.820 --> 00:55:36.695 align:middle line:84% AUDIENCE: I was formulating the success rate. 00:55:36.695 --> 00:55:37.862 align:middle line:90% So I just skipped that. 00:55:37.862 --> 00:55:38.820 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 00:55:38.820 --> 00:55:39.520 align:middle line:90% Yeah, anyway. 00:55:39.520 --> 00:55:44.000 align:middle line:84% So we could spend more time on this. 00:55:44.000 --> 00:55:45.540 align:middle line:90% But I think-- 00:55:45.540 --> 00:55:47.888 align:middle line:84% AUDIENCE: So drugs don't flow from one place to another? 00:55:47.888 --> 00:55:49.180 align:middle line:90% HAZHIR RAHMANDAD: They are not. 00:55:49.180 --> 00:55:52.460 align:middle line:84% In this model, it's actually there is no endogenous flow 00:55:52.460 --> 00:55:54.620 align:middle line:90% here. 00:55:54.620 --> 00:55:56.200 align:middle line:90% Yeah, that is confusing. 00:55:56.200 --> 00:55:59.940 align:middle line:84% And actually to do it right, you will need 00:55:59.940 --> 00:56:02.100 align:middle line:90% these shifting of subscripts. 00:56:02.100 --> 00:56:04.740 align:middle line:84% That is, you remember in the population 00:56:04.740 --> 00:56:08.500 align:middle line:84% aging things that we had the population of the previous age 00:56:08.500 --> 00:56:09.480 align:middle line:90% feeding into this. 00:56:09.480 --> 00:56:12.220 align:middle line:84% You would need that, and maybe you have it somewhere. 00:56:12.220 --> 00:56:15.980 align:middle line:84% Yeah, so you have seen examples of that shifting. 00:56:15.980 --> 00:56:20.270 align:middle line:84% You cannot have equations that only use the full subscript 00:56:20.270 --> 00:56:22.730 align:middle line:84% in them because there is a shifting. 00:56:22.730 --> 00:56:25.910 align:middle line:84% So phase I has a different decision rule because you 00:56:25.910 --> 00:56:30.030 align:middle line:84% can start a lot whereas phase II depends on how many phase 00:56:30.030 --> 00:56:37.030 align:middle line:84% I has passed and is in the menu for starting phase II. 00:56:37.030 --> 00:56:41.450 align:middle line:84% AUDIENCE: So there's no aging chain here? 00:56:41.450 --> 00:56:43.450 align:middle line:84% HAZHIR RAHMANDAD: There is no exact aging chain. 00:56:43.450 --> 00:56:46.470 align:middle line:84% I mean, for each phase, there is an aging chain, 00:56:46.470 --> 00:56:49.150 align:middle line:84% but there is not a continuous aging chain. 00:56:49.150 --> 00:56:50.930 align:middle line:84% AUDIENCE: You just approximate it, 00:56:50.930 --> 00:56:53.030 align:middle line:84% so to speak, by changing the success rate, 00:56:53.030 --> 00:56:57.830 align:middle line:84% where if there's zero in phase I, then you try to start-- 00:56:57.830 --> 00:57:00.750 align:middle line:84% but you try to start phase II, but none of the phase II 00:57:00.750 --> 00:57:01.870 align:middle line:90% that you start will-- 00:57:01.870 --> 00:57:03.090 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so this is not working. 00:57:03.090 --> 00:57:04.870 align:middle line:84% Basically, there is also the other problem 00:57:04.870 --> 00:57:06.703 align:middle line:84% that if you are starting something, at least 00:57:06.703 --> 00:57:12.310 align:middle line:84% you have to drain it out of the successful ones in that phase 00:57:12.310 --> 00:57:14.530 align:middle line:90% to get to this continuous aging. 00:57:14.530 --> 00:57:17.470 align:middle line:84% That is, if I'm starting a phase II, 00:57:17.470 --> 00:57:21.347 align:middle line:84% then the drug past trial phase I, 00:57:21.347 --> 00:57:22.930 align:middle line:84% I mean, you can keep it in that stock. 00:57:22.930 --> 00:57:24.270 align:middle line:90% You just call it-- 00:57:24.270 --> 00:57:28.150 align:middle line:84% yeah, but if you wanted to have the feedback, 00:57:28.150 --> 00:57:32.730 align:middle line:84% then you couldn't use those drugs that have passed phase I 00:57:32.730 --> 00:57:36.450 align:middle line:84% but have already started phase II to restart them. 00:57:36.450 --> 00:57:40.465 align:middle line:84% So you needed to drain those into a different stock. 00:57:40.465 --> 00:57:42.090 align:middle line:84% AUDIENCE: I am not following the logic. 00:57:42.090 --> 00:57:44.390 align:middle line:84% I don't want to be taking too much of time [INAUDIBLE]. 00:57:44.390 --> 00:57:45.890 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so the logic 00:57:45.890 --> 00:57:51.190 align:middle line:84% is that if you are starting phase II out of a drug 00:57:51.190 --> 00:57:53.950 align:middle line:84% that you have already passed in phase I, 00:57:53.950 --> 00:57:58.590 align:middle line:84% you want to drain that drug past phase I, 00:57:58.590 --> 00:58:03.670 align:middle line:84% either into a separate stock or into a cloud because, otherwise, 00:58:03.670 --> 00:58:06.970 align:middle line:84% next year, you want to start another phase II. 00:58:06.970 --> 00:58:11.910 align:middle line:84% You go and count how many you have in past phase I. 00:58:11.910 --> 00:58:14.270 align:middle line:84% AUDIENCE: The firm can actually do that, right? 00:58:14.270 --> 00:58:17.970 align:middle line:84% Can you start a phase II trial on that drug this year? 00:58:17.970 --> 00:58:18.728 align:middle line:90% Another one-- 00:58:18.728 --> 00:58:20.270 align:middle line:84% HAZHIR RAHMANDAD: But not infinitely. 00:58:20.270 --> 00:58:21.870 align:middle line:84% So, yes, you can have a parameter 00:58:21.870 --> 00:58:23.210 align:middle line:90% that says how many times. 00:58:23.210 --> 00:58:25.710 align:middle line:84% AUDIENCE: But so what I've done is that I've-- 00:58:25.710 --> 00:58:29.030 align:middle line:84% depending on how much initiation of phase II I have, 00:58:29.030 --> 00:58:31.990 align:middle line:84% I change the observation rate of phase I. 00:58:31.990 --> 00:58:36.430 align:middle line:84% So if I'm starting a lot of trials for phase II, the drug 00:58:36.430 --> 00:58:39.670 align:middle line:84% that I have in phase I of the past phase I, 00:58:39.670 --> 00:58:41.670 align:middle line:84% they will go obsolete more quickly? 00:58:41.670 --> 00:58:43.670 align:middle line:84% HAZHIR RAHMANDAD: It wouldn't work because there 00:58:43.670 --> 00:58:45.210 align:middle line:90% is a one-on-one thing. 00:58:45.210 --> 00:58:49.830 align:middle line:84% That is, each drug that you take from phase 00:58:49.830 --> 00:58:54.630 align:middle line:84% I is feeding into one drug for phase II. 00:58:54.630 --> 00:58:57.150 align:middle line:84% Now, you may go into the more complex case 00:58:57.150 --> 00:58:58.650 align:middle line:90% that I can do it five times. 00:58:58.650 --> 00:59:02.970 align:middle line:84% Then you have to drain it 0.2 of it or something. 00:59:02.970 --> 00:59:05.110 align:middle line:84% But with the time constant changes 00:59:05.110 --> 00:59:07.110 align:middle line:84% that change the obsoletion rate, you 00:59:07.110 --> 00:59:13.320 align:middle line:84% can't correctly account for, OK, how much of it I have drained 00:59:13.320 --> 00:59:15.700 align:middle line:84% and how much credit still I have. 00:59:15.700 --> 00:59:18.520 align:middle line:84% It wouldn't remain internally consistent. 00:59:18.520 --> 00:59:21.400 align:middle line:84% So that becomes a problem down the road. 00:59:21.400 --> 00:59:23.313 align:middle line:84% Let's not spend too much time on this. 00:59:23.313 --> 00:59:25.480 align:middle line:84% But I think that was a good conversation because you 00:59:25.480 --> 00:59:27.440 align:middle line:90% need to think about these-- 00:59:27.440 --> 00:59:32.960 align:middle line:84% biggest lesson for this here is follow the physics. 00:59:32.960 --> 00:59:38.420 align:middle line:84% Don't try to bring alternative ways of capturing a feedback, 00:59:38.420 --> 00:59:40.100 align:middle line:84% whether it is through obsoletion rate, 00:59:40.100 --> 00:59:43.280 align:middle line:84% whether it is through changing the success rate. 00:59:43.280 --> 00:59:45.040 align:middle line:90% Just follow the physics. 00:59:45.040 --> 00:59:46.720 align:middle line:90% Otherwise, it will blow up. 00:59:46.720 --> 00:59:49.400 align:middle line:90% OK, good. 00:59:49.400 --> 00:59:51.680 align:middle line:90% Who wants to look at-- 00:59:51.680 --> 00:59:55.720 align:middle line:90% wants us to look at their model? 00:59:55.720 --> 00:59:58.137 align:middle line:90% Do you want-- sure. 00:59:58.137 --> 00:59:59.720 align:middle line:84% AUDIENCE: I think it's pretty similar. 00:59:59.720 --> 01:00:00.888 align:middle line:90% It's the next one. 01:00:00.888 --> 01:00:02.180 align:middle line:90% HAZHIR RAHMANDAD: To the right. 01:00:02.180 --> 01:00:06.960 align:middle line:90% 01:00:06.960 --> 01:00:11.580 align:middle line:84% OK, so we have the same a time failure rate. 01:00:11.580 --> 01:00:13.400 align:middle line:84% So that's very similar to Kathy's. 01:00:13.400 --> 01:00:19.460 align:middle line:84% And then we have the initial values that are hard coded. 01:00:19.460 --> 01:00:21.960 align:middle line:84% So don't hard code initial values. 01:00:21.960 --> 01:00:24.140 align:middle line:84% Even if you're putting it into equilibrium, 01:00:24.140 --> 01:00:26.480 align:middle line:90% put a desired initial-- 01:00:26.480 --> 01:00:28.577 align:middle line:84% I mean, if you want to have a numerical value, 01:00:28.577 --> 01:00:30.160 align:middle line:84% put it initial because, otherwise, you 01:00:30.160 --> 01:00:32.460 align:middle line:84% have to come into this equation and change it. 01:00:32.460 --> 01:00:34.880 align:middle line:84% You can't change it quickly into your-- 01:00:34.880 --> 01:00:40.880 align:middle line:90% so that's generic suggestion. 01:00:40.880 --> 01:00:46.680 align:middle line:84% Then you have patent expiry, time on market. 01:00:46.680 --> 01:00:49.500 align:middle line:84% You have very similar idea here for-- 01:00:49.500 --> 01:00:54.000 align:middle line:90% 01:00:54.000 --> 01:00:56.940 align:middle line:84% no, actually, your desired annual revenue is exogenous. 01:00:56.940 --> 01:01:01.120 align:middle line:84% So it is happening from some initial value 01:01:01.120 --> 01:01:06.200 align:middle line:84% that you have hard coded here and with target growth rates. 01:01:06.200 --> 01:01:10.880 align:middle line:84% Then this gives you the target drugs with your revenue. 01:01:10.880 --> 01:01:12.380 align:middle line:90% You look at the gap. 01:01:12.380 --> 01:01:15.480 align:middle line:84% That's the adjustment for ordering that comes 01:01:15.480 --> 01:01:17.380 align:middle line:90% from drugs in market. 01:01:17.380 --> 01:01:20.440 align:middle line:90% 01:01:20.440 --> 01:01:25.880 align:middle line:84% So this, with a total success rate, 01:01:25.880 --> 01:01:30.360 align:middle line:90% gives you desired attempts. 01:01:30.360 --> 01:01:31.260 align:middle line:90% And then-- 01:01:31.260 --> 01:01:36.065 align:middle line:90% 01:01:36.065 --> 01:01:37.940 align:middle line:84% AUDIENCE: How does is the success rate impact 01:01:37.940 --> 01:01:40.840 align:middle line:90% the adjustment order? 01:01:40.840 --> 01:01:41.840 align:middle line:90% You divide it by-- 01:01:41.840 --> 01:01:43.857 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 01:01:43.857 --> 01:01:45.440 align:middle line:84% AUDIENCE: Originally, the success rate 01:01:45.440 --> 01:01:47.480 align:middle line:90% was just the percentage. 01:01:47.480 --> 01:01:51.240 align:middle line:84% And last minute, changed it to [INAUDIBLE] close out. 01:01:51.240 --> 01:01:53.120 align:middle line:90% I don't really know why. 01:01:53.120 --> 01:01:55.800 align:middle line:90% [INAUDIBLE] 01:01:55.800 --> 01:01:57.840 align:middle line:84% HAZHIR RAHMANDAD: So success rate, I think, 01:01:57.840 --> 01:02:02.120 align:middle line:84% parameter should be the right formulation because, 01:02:02.120 --> 01:02:06.430 align:middle line:84% yes, the flows here would make it a mess. 01:02:06.430 --> 01:02:07.550 align:middle line:90% You can't handle it. 01:02:07.550 --> 01:02:08.810 align:middle line:84% AUDIENCE: [INAUDIBLE] feel like the fail rates 01:02:08.810 --> 01:02:09.650 align:middle line:90% up there [INAUDIBLE]. 01:02:09.650 --> 01:02:10.608 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 01:02:10.608 --> 01:02:12.750 align:middle line:84% Yeah, the failure rates are the correct ones. 01:02:12.750 --> 01:02:14.210 align:middle line:90% They should be just-- 01:02:14.210 --> 01:02:18.050 align:middle line:84% well, so multiplied-- you should multiply the success rates 01:02:18.050 --> 01:02:19.910 align:middle line:90% to get the total success rate. 01:02:19.910 --> 01:02:21.988 align:middle line:90% So if you-- because they are-- 01:02:21.988 --> 01:02:24.530 align:middle line:84% AUDIENCE: Well, it used to be the multiplication of all the 1 01:02:24.530 --> 01:02:25.150 align:middle line:90% minus-- 01:02:25.150 --> 01:02:29.210 align:middle line:84% HAZHIR RAHMANDAD: Yes, that's correct, yeah. 01:02:29.210 --> 01:02:33.850 align:middle line:84% AUDIENCE: Yeah, my main issue is I just completely ignored time 01:02:33.850 --> 01:02:36.570 align:middle line:84% at some point because if there were 01:02:36.570 --> 01:02:42.050 align:middle line:84% optimizations to the path of getting the drugs to the phases, 01:02:42.050 --> 01:02:44.330 align:middle line:84% the drugs that are currently in markets patents 01:02:44.330 --> 01:02:46.390 align:middle line:84% are going to expire in two years or whatever. 01:02:46.390 --> 01:02:51.650 align:middle line:84% But these new drugs are going to be on the market for 18 years. 01:02:51.650 --> 01:02:54.330 align:middle line:84% Oh, yeah, the success [INAUDIBLE] because every time I 01:02:54.330 --> 01:02:57.530 align:middle line:84% wanted to try and do the effective entry on quality, 01:02:57.530 --> 01:02:59.750 align:middle line:84% but every time, I tried to make a formulation of it, 01:02:59.750 --> 01:03:01.445 align:middle line:84% it was a simultaneous formulation. 01:03:01.445 --> 01:03:03.070 align:middle line:84% And I couldn't figure out how to do it. 01:03:03.070 --> 01:03:05.850 align:middle line:84% I think I should just maybe stop [INAUDIBLE]. 01:03:05.850 --> 01:03:08.647 align:middle line:84% But, yeah, I have a lot of issues with [INAUDIBLE]. 01:03:08.647 --> 01:03:10.230 align:middle line:84% And then what you were saying earlier, 01:03:10.230 --> 01:03:13.290 align:middle line:84% which is the maintenance drug rate 01:03:13.290 --> 01:03:17.118 align:middle line:84% has to be correlated to the target group. 01:03:17.118 --> 01:03:18.410 align:middle line:90% I didn't know that [INAUDIBLE]. 01:03:18.410 --> 01:03:20.868 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so the growth is not captured here. 01:03:20.868 --> 01:03:24.610 align:middle line:84% But let's just track what is happening with the start rate 01:03:24.610 --> 01:03:25.730 align:middle line:90% right now. 01:03:25.730 --> 01:03:28.750 align:middle line:84% So quality, let's not worry about it. 01:03:28.750 --> 01:03:31.150 align:middle line:84% There is a max attempt based on budget. 01:03:31.150 --> 01:03:32.670 align:middle line:90% Let's not worry about it. 01:03:32.670 --> 01:03:36.910 align:middle line:84% So it is the desired attempts that is driving it. 01:03:36.910 --> 01:03:43.170 align:middle line:84% And it is coming from the patent expiration, which is important. 01:03:43.170 --> 01:03:45.530 align:middle line:84% There is this alternative drug thing, I don't know. 01:03:45.530 --> 01:03:46.430 align:middle line:90% Yeah, yeah. 01:03:46.430 --> 01:03:51.990 align:middle line:84% OK, so there is an expiration divided by the success rate. 01:03:51.990 --> 01:03:54.410 align:middle line:84% So that's the right formulation to get 01:03:54.410 --> 01:03:58.890 align:middle line:84% in the equilibrium without growth the number of new drugs 01:03:58.890 --> 01:03:59.950 align:middle line:90% that you start. 01:03:59.950 --> 01:04:01.130 align:middle line:90% So that's good. 01:04:01.130 --> 01:04:04.330 align:middle line:84% And then you have the adjustment based 01:04:04.330 --> 01:04:07.050 align:middle line:90% on the drugs in the market. 01:04:07.050 --> 01:04:08.470 align:middle line:90% That's also fine. 01:04:08.470 --> 01:04:12.090 align:middle line:90% 01:04:12.090 --> 01:04:15.370 align:middle line:90% Although, let me think. 01:04:15.370 --> 01:04:17.453 align:middle line:84% AUDIENCE: Is there no adjustment for the pipeline? 01:04:17.453 --> 01:04:20.037 align:middle line:84% HAZHIR RAHMANDAD: Yes, so there is no adjustment for pipeline. 01:04:20.037 --> 01:04:21.410 align:middle line:90% So that's missing, definitely. 01:04:21.410 --> 01:04:24.530 align:middle line:84% I'm also thinking whether the adjustment ordering here 01:04:24.530 --> 01:04:29.470 align:middle line:84% for this needs to be divided by the success rate. 01:04:29.470 --> 01:04:32.130 align:middle line:90% 01:04:32.130 --> 01:04:35.250 align:middle line:84% So right now, the role of this success rate division 01:04:35.250 --> 01:04:41.850 align:middle line:84% is basically making this time constant smaller, 01:04:41.850 --> 01:04:43.070 align:middle line:90% making it faster. 01:04:43.070 --> 01:04:44.630 align:middle line:90% You can look at the equation. 01:04:44.630 --> 01:04:47.850 align:middle line:84% It is the gap divided by success rate divided 01:04:47.850 --> 01:04:51.190 align:middle line:84% by time to market because time to market is a parameter. 01:04:51.190 --> 01:04:54.710 align:middle line:84% It is as if you are making that parameter shorter, smaller. 01:04:54.710 --> 01:04:58.650 align:middle line:90% 01:04:58.650 --> 01:05:01.460 align:middle line:84% Because this is a number between 0 and 1. 01:05:01.460 --> 01:05:05.980 align:middle line:84% So as such, it doesn't have a qualitative effect on-- 01:05:05.980 --> 01:05:08.780 align:middle line:84% so I'm not really following what exactly you 01:05:08.780 --> 01:05:11.820 align:middle line:84% wanted to do because the success rate is-- 01:05:11.820 --> 01:05:16.700 align:middle line:84% if you think it is impacting the desired level of the stock, 01:05:16.700 --> 01:05:22.160 align:middle line:84% it should be operating on the target draw queue, which is not, 01:05:22.160 --> 01:05:24.340 align:middle line:84% and which is fine because you don't want it to. 01:05:24.340 --> 01:05:27.600 align:middle line:84% Your target shouldn't be affected by the success rate. 01:05:27.600 --> 01:05:31.740 align:middle line:84% AUDIENCE: I think my idea is you have-- 01:05:31.740 --> 01:05:36.060 align:middle line:84% however, so target drug queue is, how many 01:05:36.060 --> 01:05:37.580 align:middle line:90% you need to be at this revenue? 01:05:37.580 --> 01:05:38.497 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:05:38.497 --> 01:05:41.040 align:middle line:84% AUDIENCE: And then the gap is, obviously, 01:05:41.040 --> 01:05:43.640 align:middle line:84% the difference between this target and the current drugs. 01:05:43.640 --> 01:05:45.620 align:middle line:84% And the reason I divided it by the success rate 01:05:45.620 --> 01:05:48.860 align:middle line:84% was the idea like, OK, well, if the gap between how many you 01:05:48.860 --> 01:05:54.040 align:middle line:84% want and how many there are is 10, the success rate is 10%, 01:05:54.040 --> 01:05:56.060 align:middle line:90% then you should have 100. 01:05:56.060 --> 01:05:58.923 align:middle line:84% So that was my idea of dividing by success rate 01:05:58.923 --> 01:06:00.340 align:middle line:84% because then you get like, OK, you 01:06:00.340 --> 01:06:05.740 align:middle line:84% need 100 drugs to be going in to the pipeline, 01:06:05.740 --> 01:06:07.722 align:middle line:84% and then you divide [INAUDIBLE] pipeline. 01:06:07.722 --> 01:06:10.180 align:middle line:84% HAZHIR RAHMANDAD: Yeah, but this is a little bit of a stock 01:06:10.180 --> 01:06:12.200 align:middle line:84% and flow confusion because, as you said, 01:06:12.200 --> 01:06:15.780 align:middle line:84% the time is missing because what is 100? 01:06:15.780 --> 01:06:19.300 align:middle line:84% Its per unit of time is the adjustment rate. 01:06:19.300 --> 01:06:22.435 align:middle line:84% So it is basically you're saying, I'm adjusting it faster. 01:06:22.435 --> 01:06:23.060 align:middle line:90% AUDIENCE: Yeah. 01:06:23.060 --> 01:06:26.780 align:middle line:84% HAZHIR RAHMANDAD: OK, so basically, this formulation 01:06:26.780 --> 01:06:28.940 align:middle line:84% works for adjusting the drugs in market 01:06:28.940 --> 01:06:31.940 align:middle line:84% with this caveat of what success rate really shouldn't 01:06:31.940 --> 01:06:34.180 align:middle line:90% come into this formulation. 01:06:34.180 --> 01:06:36.220 align:middle line:84% It is working fine for replacement 01:06:36.220 --> 01:06:39.520 align:middle line:84% of patent expiry under equilibrium conditions, 01:06:39.520 --> 01:06:41.200 align:middle line:90% but not in the general case. 01:06:41.200 --> 01:06:44.740 align:middle line:84% It doesn't have adjustments for P1, P2, and P3. 01:06:44.740 --> 01:06:47.300 align:middle line:90% So that's another challenge. 01:06:47.300 --> 01:06:51.180 align:middle line:84% But otherwise, it has the basics of the stock adjustment 01:06:51.180 --> 01:06:53.520 align:middle line:84% formulation we are familiar with. 01:06:53.520 --> 01:06:54.540 align:middle line:90% Good. 01:06:54.540 --> 01:06:57.580 align:middle line:84% AUDIENCE: So what is the issue with having a success 01:06:57.580 --> 01:06:58.860 align:middle line:90% rate in the adjustment order? 01:06:58.860 --> 01:07:00.460 align:middle line:84% Because I get that it essentially 01:07:00.460 --> 01:07:03.507 align:middle line:84% does the same thing here as the time to adjust, 01:07:03.507 --> 01:07:04.840 align:middle line:90% and it just makes you go faster. 01:07:04.840 --> 01:07:07.980 align:middle line:84% But I feel like, I mean, at least for me, it makes sense, 01:07:07.980 --> 01:07:08.920 align:middle line:90% exactly what you said. 01:07:08.920 --> 01:07:11.980 align:middle line:84% You want you want to be starting more drugs than you 01:07:11.980 --> 01:07:15.220 align:middle line:84% need in the end because the vast majority will fail. 01:07:15.220 --> 01:07:18.540 align:middle line:84% I guess, for me, personally, it just-- 01:07:18.540 --> 01:07:20.880 align:middle line:84% and I'm not in this space, so what does it matter? 01:07:20.880 --> 01:07:23.297 align:middle line:84% But when I'm formulating, it makes a lot more sense for me 01:07:23.297 --> 01:07:25.580 align:middle line:84% to think about what I need to start more [INAUDIBLE]. 01:07:25.580 --> 01:07:31.520 align:middle line:84% HAZHIR RAHMANDAD: Yeah, it's a good pushback. 01:07:31.520 --> 01:07:34.300 align:middle line:90% 01:07:34.300 --> 01:07:39.100 align:middle line:84% That is, the time to adjust can be 01:07:39.100 --> 01:07:42.400 align:middle line:84% thought of as having these two components. 01:07:42.400 --> 01:07:45.760 align:middle line:84% One is kind of how fast I want to close the gap. 01:07:45.760 --> 01:07:48.580 align:middle line:84% The other is if the gap is bigger, 01:07:48.580 --> 01:07:53.900 align:middle line:84% I need to start a lot more at the beginning. 01:07:53.900 --> 01:07:58.120 align:middle line:84% So why not just divide it by the success rate? 01:07:58.120 --> 01:07:59.240 align:middle line:90% Yeah, I buy that. 01:07:59.240 --> 01:08:03.640 align:middle line:84% So I take back my comment that you don't need this. 01:08:03.640 --> 01:08:07.380 align:middle line:84% I mean, it's OK not to have it, but there is conceptually 01:08:07.380 --> 01:08:08.900 align:middle line:90% a good reason to do it. 01:08:08.900 --> 01:08:11.600 align:middle line:84% And I think your explanation was aligned with that. 01:08:11.600 --> 01:08:14.620 align:middle line:90% OK, good. 01:08:14.620 --> 01:08:17.020 align:middle line:90% Let's see, who else? 01:08:17.020 --> 01:08:18.779 align:middle line:90% Volunteers? 01:08:18.779 --> 01:08:21.300 align:middle line:84% AUDIENCE: I'm sorry, just one more question about this. 01:08:21.300 --> 01:08:24.140 align:middle line:84% Isn't the [INAUDIBLE] adjustment to support supply line 01:08:24.140 --> 01:08:25.500 align:middle line:90% problematic? 01:08:25.500 --> 01:08:28.220 align:middle line:84% Because, I mean, just in the basic stock management-- 01:08:28.220 --> 01:08:30.020 align:middle line:84% if you don't adjust the supply line-- 01:08:30.020 --> 01:08:31.770 align:middle line:84% HAZHIR RAHMANDAD: Yeah, things don't work. 01:08:31.770 --> 01:08:34.040 align:middle line:84% So this doesn't have the adjustment. 01:08:34.040 --> 01:08:36.819 align:middle line:84% So this will not do all of the nice things 01:08:36.819 --> 01:08:39.420 align:middle line:84% that-- basically, it is ignoring the supply line. 01:08:39.420 --> 01:08:41.540 align:middle line:84% And therefore, it will create oscillations 01:08:41.540 --> 01:08:43.200 align:middle line:90% that you don't want to see. 01:08:43.200 --> 01:08:48.500 align:middle line:84% So, yes, this does suffer from that. 01:08:48.500 --> 01:08:49.620 align:middle line:90% Sure. 01:08:49.620 --> 01:08:54.890 align:middle line:84% OK, good so you have two views for input. 01:08:54.890 --> 01:08:56.229 align:middle line:90% That's nice. 01:08:56.229 --> 01:09:01.149 align:middle line:90% Let's go to the basics again. 01:09:01.149 --> 01:09:05.430 align:middle line:84% Stocks and flows are standard removal multiplied 01:09:05.430 --> 01:09:07.729 align:middle line:90% by success and 1 minus success. 01:09:07.729 --> 01:09:09.670 align:middle line:90% All of that is fine. 01:09:09.670 --> 01:09:11.689 align:middle line:84% You are using the same success fraction. 01:09:11.689 --> 01:09:12.290 align:middle line:90% That's OK. 01:09:12.290 --> 01:09:13.665 align:middle line:84% Conceptually, they are different. 01:09:13.665 --> 01:09:16.170 align:middle line:84% And in reality, they are also somewhat different. 01:09:16.170 --> 01:09:20.990 align:middle line:84% But they are close enough that you can also combine them. 01:09:20.990 --> 01:09:26.470 align:middle line:84% You have the desired stock from the desired annual revenue. 01:09:26.470 --> 01:09:28.330 align:middle line:84% And then you get the annual revenue. 01:09:28.330 --> 01:09:30.470 align:middle line:90% All of that is good. 01:09:30.470 --> 01:09:33.630 align:middle line:84% And we talked about this patent duration 01:09:33.630 --> 01:09:37.390 align:middle line:84% to account actually for all of these other times, 01:09:37.390 --> 01:09:39.330 align:middle line:84% nothing important here mathematically. 01:09:39.330 --> 01:09:43.350 align:middle line:90% This doesn't make a difference. 01:09:43.350 --> 01:09:46.510 align:middle line:84% OK, adjustment for drugs on market 01:09:46.510 --> 01:09:50.870 align:middle line:84% is desired stock, market adjustment time. 01:09:50.870 --> 01:09:54.950 align:middle line:84% And then you have expected expiration date. 01:09:54.950 --> 01:09:59.890 align:middle line:84% Rate that creates desired market advancement. 01:09:59.890 --> 01:10:02.690 align:middle line:90% So this is for equilibrium. 01:10:02.690 --> 01:10:07.230 align:middle line:84% So this is very similar to Alban's formulation, I think. 01:10:07.230 --> 01:10:11.230 align:middle line:84% And then that gives you the desired phase III. 01:10:11.230 --> 01:10:17.590 align:middle line:84% Good, and then the desired phase III goes into the initiation 01:10:17.590 --> 01:10:18.090 align:middle line:90% here. 01:10:18.090 --> 01:10:20.870 align:middle line:84% And the way you formulated the desired phase III, let's 01:10:20.870 --> 01:10:22.010 align:middle line:90% check that out. 01:10:22.010 --> 01:10:27.830 align:middle line:84% So it is desired market advancement, average timing P3 01:10:27.830 --> 01:10:29.850 align:middle line:90% divided by P3 success fraction. 01:10:29.850 --> 01:10:32.010 align:middle line:90% So that's good formulation. 01:10:32.010 --> 01:10:37.230 align:middle line:84% Does all you need to do for non-growth case. 01:10:37.230 --> 01:10:37.730 align:middle line:90% This-- 01:10:37.730 --> 01:10:38.813 align:middle line:90% AUDIENCE: This won't grow. 01:10:38.813 --> 01:10:39.630 align:middle line:90% Or it grows, but-- 01:10:39.630 --> 01:10:41.910 align:middle line:84% HAZHIR RAHMANDAD: Then there will be a steady state 01:10:41.910 --> 01:10:45.010 align:middle line:90% gap for the growth case. 01:10:45.010 --> 01:10:49.870 align:middle line:84% And then this then goes backwards. 01:10:49.870 --> 01:10:54.730 align:middle line:84% Very similar, I think, all of them will do the same idea. 01:10:54.730 --> 01:10:58.230 align:middle line:84% So you are also using Alban's version 01:10:58.230 --> 01:11:01.550 align:middle line:84% where what comes from the previous stages 01:11:01.550 --> 01:11:05.050 align:middle line:84% feeds into the desired levels of the stocks. 01:11:05.050 --> 01:11:10.410 align:middle line:84% So it can push them up and down notably 01:11:10.410 --> 01:11:13.830 align:middle line:84% as a result of that, which is, as I said, 01:11:13.830 --> 01:11:16.090 align:middle line:84% debatable whether that's the best formulation or not, 01:11:16.090 --> 01:11:19.590 align:middle line:90% but it's OK. 01:11:19.590 --> 01:11:26.150 align:middle line:84% And then let's see, I think it's all-- 01:11:26.150 --> 01:11:27.370 align:middle line:90% the rest is a standard. 01:11:27.370 --> 01:11:30.505 align:middle line:90% We have talked about the ideas. 01:11:30.505 --> 01:11:32.630 align:middle line:84% AUDIENCE: Yeah, I actually don't know if I have it. 01:11:32.630 --> 01:11:34.255 align:middle line:84% HAZHIR RAHMANDAD: So let's simulate it. 01:11:34.255 --> 01:11:35.570 align:middle line:90% We haven't simulated much yet. 01:11:35.570 --> 01:11:38.470 align:middle line:84% So this is actually a good time to start simulating. 01:11:38.470 --> 01:11:41.750 align:middle line:84% So this starts from equilibrium, great. 01:11:41.750 --> 01:11:44.790 align:middle line:90% And then we can-- 01:11:44.790 --> 01:11:45.570 align:middle line:90% what's that? 01:11:45.570 --> 01:11:47.535 align:middle line:84% AUDIENCE: [INAUDIBLE] has all the inputs. 01:11:47.535 --> 01:11:49.160 align:middle line:84% HAZHIR RAHMANDAD: Yeah, but another way 01:11:49.160 --> 01:11:54.820 align:middle line:84% is to just change the annual desired stock or annual revenue. 01:11:54.820 --> 01:11:57.700 align:middle line:90% So I'll just do this. 01:11:57.700 --> 01:12:01.120 align:middle line:90% 01:12:01.120 --> 01:12:04.920 align:middle line:84% So I'll say, let's do a step change. 01:12:04.920 --> 01:12:07.020 align:middle line:90% Go 20% off. 01:12:07.020 --> 01:12:20.160 align:middle line:90% 01:12:20.160 --> 01:12:22.840 align:middle line:84% So drugs in the market is the key thing 01:12:22.840 --> 01:12:26.960 align:middle line:84% because you want that to be stable. 01:12:26.960 --> 01:12:29.520 align:middle line:84% Now, this does create oscillations 01:12:29.520 --> 01:12:32.720 align:middle line:90% for drugs in market. 01:12:32.720 --> 01:12:37.480 align:middle line:90% And part of it is-- 01:12:37.480 --> 01:12:44.120 align:middle line:84% so if we don't adjust the market as fast, it actually helps. 01:12:44.120 --> 01:12:46.320 align:middle line:90% So this is one of those places. 01:12:46.320 --> 01:12:47.160 align:middle line:90% Is it visible? 01:12:47.160 --> 01:12:50.080 align:middle line:90% Or is it too small? 01:12:50.080 --> 01:12:56.880 align:middle line:84% So you see, if we go smaller on this market adjustment time, 01:12:56.880 --> 01:13:01.860 align:middle line:84% we get into a full-fledged undamped oscillations. 01:13:01.860 --> 01:13:04.440 align:middle line:84% And as soon as we increase that a little bit, 01:13:04.440 --> 01:13:07.840 align:middle line:90% things become pretty reasonable. 01:13:07.840 --> 01:13:11.000 align:middle line:84% So I mean, you still see the oscillations 01:13:11.000 --> 01:13:12.740 align:middle line:90% back there, but much smaller. 01:13:12.740 --> 01:13:15.120 align:middle line:84% So can anybody come up with a hypothesis 01:13:15.120 --> 01:13:17.660 align:middle line:90% for what is happening here? 01:13:17.660 --> 01:13:22.160 align:middle line:84% So we have full adjustment for the supply line. 01:13:22.160 --> 01:13:25.480 align:middle line:84% So in that sense, we are not ignoring the supply line. 01:13:25.480 --> 01:13:28.380 align:middle line:84% And we are doing it with decent formulations all along. 01:13:28.380 --> 01:13:40.640 align:middle line:84% Why do you get cases where you still get a lot of oscillation? 01:13:40.640 --> 01:13:41.240 align:middle line:90% Alexander. 01:13:41.240 --> 01:13:44.360 align:middle line:84% AUDIENCE: What is the adjustment time for the supply line? 01:13:44.360 --> 01:13:50.120 align:middle line:84% HAZHIR RAHMANDAD: So adjustments times are 2. 01:13:50.120 --> 01:13:52.560 align:middle line:90% So they're all 2, I think. 01:13:52.560 --> 01:13:54.200 align:middle line:84% AUDIENCE: I have a hyperparameter. 01:13:54.200 --> 01:13:56.220 align:middle line:84% HAZHIR RAHMANDAD: Yes, that is adjusting. 01:13:56.220 --> 01:14:01.420 align:middle line:90% But any hypothesis? 01:14:01.420 --> 01:14:04.760 align:middle line:90% 01:14:04.760 --> 01:14:10.080 align:middle line:84% AUDIENCE: Oh, [INAUDIBLE] to a short-term disequilibrium. 01:14:10.080 --> 01:14:14.120 align:middle line:84% HAZHIR RAHMANDAD: Can you, can you speak up again, Alban? 01:14:14.120 --> 01:14:18.080 align:middle line:84% AUDIENCE: You overreact to a short-term disequilibrium? 01:14:18.080 --> 01:14:20.240 align:middle line:84% HAZHIR RAHMANDAD: Yes, how do you overreact 01:14:20.240 --> 01:14:23.800 align:middle line:90% to a short-term disequilibrium? 01:14:23.800 --> 01:14:27.360 align:middle line:84% AUDIENCE: Because your adjustment time is too small. 01:14:27.360 --> 01:14:29.440 align:middle line:90% The timescale is too small. 01:14:29.440 --> 01:14:32.360 align:middle line:84% HAZHIR RAHMANDAD: So this is actually 01:14:32.360 --> 01:14:36.600 align:middle line:84% where the formulation issue that I mentioned 01:14:36.600 --> 01:14:39.880 align:middle line:90% is really creating its problem. 01:14:39.880 --> 01:14:45.450 align:middle line:84% So if you're adjusting the next stock, desired level 01:14:45.450 --> 01:14:49.890 align:middle line:84% of the next stock, based on adjustment in the current stock, 01:14:49.890 --> 01:14:54.550 align:middle line:84% now, if the adjustment in the current stock is large, 01:14:54.550 --> 01:14:57.050 align:middle line:84% now it requires, even a larger adjustment 01:14:57.050 --> 01:15:00.170 align:middle line:84% in the previous stock, and that will 01:15:00.170 --> 01:15:03.970 align:middle line:84% require even a larger adjustment in the next one and so on. 01:15:03.970 --> 01:15:07.610 align:middle line:84% So it creates this cascade of adjustments 01:15:07.610 --> 01:15:11.330 align:middle line:84% that, under some time constants, for these adjustments, 01:15:11.330 --> 01:15:17.890 align:middle line:84% can actually create their own oscillatory mode of behavior. 01:15:17.890 --> 01:15:24.530 align:middle line:84% So my pretty strong guess is that they will go away 01:15:24.530 --> 01:15:29.810 align:middle line:84% if you didn't have this formulation that adds up 01:15:29.810 --> 01:15:34.570 align:middle line:84% the desired for replacement with the desired changes 01:15:34.570 --> 01:15:38.730 align:middle line:90% in each stage for the stock. 01:15:38.730 --> 01:15:40.890 align:middle line:84% So this is actually a good example 01:15:40.890 --> 01:15:43.370 align:middle line:90% of where the two formulations-- 01:15:43.370 --> 01:15:46.170 align:middle line:84% and Kathy had the two extremes on a switch 01:15:46.170 --> 01:15:47.310 align:middle line:90% that you could play with. 01:15:47.310 --> 01:15:49.810 align:middle line:84% We don't have a switch here, so it's a little bit more work 01:15:49.810 --> 01:15:52.390 align:middle line:84% to get it to see that difference. 01:15:52.390 --> 01:15:55.810 align:middle line:90% But that's the idea. 01:15:55.810 --> 01:16:00.195 align:middle line:84% AUDIENCE: Does it depend-- well, I asked about the supply line 01:16:00.195 --> 01:16:01.570 align:middle line:84% adjustment because it seems like, 01:16:01.570 --> 01:16:06.170 align:middle line:84% when you go over it, when you go above 2, then the oscillations 01:16:06.170 --> 01:16:08.810 align:middle line:90% get damped. 01:16:08.810 --> 01:16:11.560 align:middle line:84% So like it just seems odd but in real-- 01:16:11.560 --> 01:16:13.310 align:middle line:84% And that's not how Jason parameterized it. 01:16:13.310 --> 01:16:16.210 align:middle line:84% So it would just seem odd that in real life 01:16:16.210 --> 01:16:18.192 align:middle line:90% you're trying to adjust your-- 01:16:18.192 --> 01:16:20.150 align:middle line:84% well, I guess that's what happens in real life. 01:16:20.150 --> 01:16:23.610 align:middle line:84% And that's the whole point of the growing supply line. 01:16:23.610 --> 01:16:27.010 align:middle line:84% You're trying to change the drugs on the market really 01:16:27.010 --> 01:16:29.130 align:middle line:84% quickly, but you're not changing how many drugs 01:16:29.130 --> 01:16:33.330 align:middle line:90% you have in supply as quickly. 01:16:33.330 --> 01:16:36.168 align:middle line:84% Because when you had the oscillations 01:16:36.168 --> 01:16:38.210 align:middle line:84% for the drugs in the market [INAUDIBLE] sometimes 01:16:38.210 --> 01:16:42.370 align:middle line:84% one but the adjustment for the phases was twice as long. 01:16:42.370 --> 01:16:43.810 align:middle line:90% It was two years. 01:16:43.810 --> 01:16:47.050 align:middle line:90% So it just seems-- 01:16:47.050 --> 01:16:48.690 align:middle line:90% isn't that part of it as well? 01:16:48.690 --> 01:16:51.293 align:middle line:84% It's the balance of the adjustment times for the-- 01:16:51.293 --> 01:16:53.210 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so the real difference 01:16:53.210 --> 01:16:57.410 align:middle line:84% is that we are correcting two different-- 01:16:57.410 --> 01:16:59.110 align:middle line:90% through two different channels. 01:16:59.110 --> 01:17:02.530 align:middle line:84% One is the channel for replacement 01:17:02.530 --> 01:17:05.130 align:middle line:84% that needs to be corrected across all 01:17:05.130 --> 01:17:08.610 align:middle line:84% of the intermediates' stocks so that they 01:17:08.610 --> 01:17:13.290 align:middle line:84% are consistent with our ultimate outflow. 01:17:13.290 --> 01:17:16.810 align:middle line:84% The other is we are adding another correction that 01:17:16.810 --> 01:17:20.170 align:middle line:84% is saying, all these intermediate stocks 01:17:20.170 --> 01:17:24.970 align:middle line:84% need to go up and down to also adjust 01:17:24.970 --> 01:17:29.913 align:middle line:84% for the adjustment of the upstream stocks. 01:17:29.913 --> 01:17:31.330 align:middle line:84% AUDIENCE: So in this case, so just 01:17:31.330 --> 01:17:36.130 align:middle line:84% to be extremely operational, the desired phase III in this case 01:17:36.130 --> 01:17:39.740 align:middle line:84% should just be the expected expiration date multiplied 01:17:39.740 --> 01:17:42.002 align:middle line:90% by the, whatever, the time. 01:17:42.002 --> 01:17:43.960 align:middle line:84% HAZHIR RAHMANDAD: Yes, divided by success rate. 01:17:43.960 --> 01:17:45.560 align:middle line:84% AUDIENCE: And then it's the same for all the-- 01:17:45.560 --> 01:17:47.310 align:middle line:84% HAZHIR RAHMANDAD: --for all the next ones. 01:17:47.310 --> 01:17:49.280 align:middle line:90% In fact-- yes, exactly. 01:17:49.280 --> 01:17:50.860 align:middle line:90% That's it. 01:17:50.860 --> 01:17:53.140 align:middle line:90% And it is also. 01:17:53.140 --> 01:17:55.820 align:middle line:84% Yes, it could be the expiration date. 01:17:55.820 --> 01:18:01.100 align:middle line:84% But this is another important conceptual difference. 01:18:01.100 --> 01:18:04.580 align:middle line:84% That is, better solution is not getting it 01:18:04.580 --> 01:18:08.580 align:middle line:84% from the patent expiration date, but get it 01:18:08.580 --> 01:18:15.460 align:middle line:84% from the desired stock of desired drugs on market 01:18:15.460 --> 01:18:21.500 align:middle line:90% divided by the patent duration. 01:18:21.500 --> 01:18:22.600 align:middle line:90% You see the difference? 01:18:22.600 --> 01:18:23.100 align:middle line:90% So-- 01:18:23.100 --> 01:18:24.207 align:middle line:90% AUDIENCE: Yeah, instead-- 01:18:24.207 --> 01:18:26.540 align:middle line:84% HAZHIR RAHMANDAD: Yes, because this is the current rate, 01:18:26.540 --> 01:18:28.500 align:middle line:90% and it is not the desired rate. 01:18:28.500 --> 01:18:31.300 align:middle line:84% So it will wait for that stock to be 01:18:31.300 --> 01:18:34.120 align:middle line:90% adjusted to get it correctly. 01:18:34.120 --> 01:18:37.380 align:middle line:90% Is that clear? 01:18:37.380 --> 01:18:43.220 align:middle line:84% AUDIENCE: So just to summarize, Alexander's point 01:18:43.220 --> 01:18:46.820 align:middle line:84% was those desired levels, each phase 01:18:46.820 --> 01:18:51.260 align:middle line:84% should not depend on the desired level for the prior phase. 01:18:51.260 --> 01:18:54.560 align:middle line:84% This way you avoid that accumulating. 01:18:54.560 --> 01:18:56.140 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:18:56.140 --> 01:18:58.460 align:middle line:84% AUDIENCE: I think it's more isolated to each. 01:18:58.460 --> 01:19:00.180 align:middle line:84% HAZHIR RAHMANDAD: Yes, yes, exactly. 01:19:00.180 --> 01:19:01.680 align:middle line:84% AUDIENCE: They don't see each other. 01:19:01.680 --> 01:19:03.460 align:middle line:84% HAZHIR RAHMANDAD: They don't see each other. 01:19:03.460 --> 01:19:03.960 align:middle line:90% Yeah. 01:19:03.960 --> 01:19:06.500 align:middle line:90% 01:19:06.500 --> 01:19:08.800 align:middle line:84% AUDIENCE: So the desired for phase II, for example, 01:19:08.800 --> 01:19:11.800 align:middle line:90% is that case. 01:19:11.800 --> 01:19:16.622 align:middle line:84% It's just based off of the failure rate for phase III? 01:19:16.622 --> 01:19:18.080 align:middle line:84% HAZHIR RAHMANDAD: Not failure rate. 01:19:18.080 --> 01:19:22.540 align:middle line:84% You want it to be based on the desired replacement rate 01:19:22.540 --> 01:19:24.040 align:middle line:90% that you calculated. 01:19:24.040 --> 01:19:27.820 align:middle line:84% So here, let's say this is the desired expiration 01:19:27.820 --> 01:19:30.000 align:middle line:90% rate, not the expected. 01:19:30.000 --> 01:19:34.620 align:middle line:84% It is the desired based on the desired stock. 01:19:34.620 --> 01:19:38.300 align:middle line:84% Then you use that desired expiration rate to calculate 01:19:38.300 --> 01:19:41.100 align:middle line:90% desired market advancement. 01:19:41.100 --> 01:19:42.000 align:middle line:90% That's fine. 01:19:42.000 --> 01:19:44.740 align:middle line:84% You don't add this adjustment for drugs on market 01:19:44.740 --> 01:19:46.380 align:middle line:90% into market advancement. 01:19:46.380 --> 01:19:51.040 align:middle line:84% Then this desired advancement goes into the next one. 01:19:51.040 --> 01:19:53.280 align:middle line:84% You just don't add this adjustment for phase III. 01:19:53.280 --> 01:19:55.160 align:middle line:84% So all of the equations remain the same, 01:19:55.160 --> 01:19:57.180 align:middle line:84% except that these adjustments don't 01:19:57.180 --> 01:20:00.580 align:middle line:90% come into this desired thingy. 01:20:00.580 --> 01:20:04.100 align:middle line:84% And then, at the end, you add all of those adjustments 01:20:04.100 --> 01:20:08.900 align:middle line:84% into a separate component that goes into the development start 01:20:08.900 --> 01:20:09.795 align:middle line:90% rate. 01:20:09.795 --> 01:20:11.420 align:middle line:84% So right now the development start rate 01:20:11.420 --> 01:20:16.680 align:middle line:84% is max of 0 and this desired DSR so that it doesn't go 0. 01:20:16.680 --> 01:20:18.220 align:middle line:90% That's good. 01:20:18.220 --> 01:20:20.180 align:middle line:84% Then, in this alternative, you would 01:20:20.180 --> 01:20:24.820 align:middle line:84% have this desired DSR plus all of those stock adjustments. 01:20:24.820 --> 01:20:27.140 align:middle line:84% And now going back to your formulation, 01:20:27.140 --> 01:20:30.460 align:middle line:84% we could, for those, incorporate those success rates 01:20:30.460 --> 01:20:32.850 align:middle line:90% as well to speed that up. 01:20:32.850 --> 01:20:36.265 align:middle line:90% 01:20:36.265 --> 01:20:36.890 align:middle line:90% AUDIENCE: Wait. 01:20:36.890 --> 01:20:39.365 align:middle line:84% So wait, I thought you had to include the success 01:20:39.365 --> 01:20:41.490 align:middle line:84% rates at this point because I don't see where the-- 01:20:41.490 --> 01:20:43.450 align:middle line:84% HAZHIR RAHMANDAD: So the success rates are incorporated. 01:20:43.450 --> 01:20:45.910 align:middle line:84% So the way they are incorporated is that, at each step, 01:20:45.910 --> 01:20:48.390 align:middle line:84% the desired advanced to the next phase 01:20:48.390 --> 01:20:51.445 align:middle line:84% is getting feedback from the success rate. 01:20:51.445 --> 01:20:53.570 align:middle line:84% AUDIENCE: Yeah, I'm adding in the expected failure. 01:20:53.570 --> 01:20:55.028 align:middle line:84% HAZHIR RAHMANDAD: Yes, it is coming 01:20:55.028 --> 01:20:56.530 align:middle line:90% from the expected failure. 01:20:56.530 --> 01:20:59.910 align:middle line:90% 01:20:59.910 --> 01:21:01.730 align:middle line:90% There is expected failure. 01:21:01.730 --> 01:21:03.190 align:middle line:90% Yes, this is the expected. 01:21:03.190 --> 01:21:05.250 align:middle line:90% But this is the problem. 01:21:05.250 --> 01:21:06.630 align:middle line:90% This is another problem. 01:21:06.630 --> 01:21:15.590 align:middle line:84% So this should not be getting input from the expected P3-- 01:21:15.590 --> 01:21:19.030 align:middle line:84% OK, let me see what's the equation here, sorry. 01:21:19.030 --> 01:21:24.670 align:middle line:84% First of all, why does it have max 0 here? 01:21:24.670 --> 01:21:26.270 align:middle line:90% AUDIENCE: Can't go backwards. 01:21:26.270 --> 01:21:28.110 align:middle line:90% Or you can't-- 01:21:28.110 --> 01:21:31.710 align:middle line:84% HAZHIR RAHMANDAD: You're not yet affecting any flow. 01:21:31.710 --> 01:21:37.208 align:middle line:84% Why do you impose the max 0 at every step? 01:21:37.208 --> 01:21:39.250 align:middle line:84% AUDIENCE: What do you mean you're not affecting-- 01:21:39.250 --> 01:21:41.990 align:middle line:90% 01:21:41.990 --> 01:21:42.870 align:middle line:90% I see. 01:21:42.870 --> 01:21:43.390 align:middle line:90% Because-- 01:21:43.390 --> 01:21:48.147 align:middle line:90% 01:21:48.147 --> 01:21:50.730 align:middle line:84% HAZHIR RAHMANDAD: So you have actually three different things. 01:21:50.730 --> 01:21:54.270 align:middle line:84% So you have the expected P3 failure. 01:21:54.270 --> 01:21:57.030 align:middle line:84% You have desired market advancement. 01:21:57.030 --> 01:22:00.190 align:middle line:84% And then you have the adjustment for phase III. 01:22:00.190 --> 01:22:00.990 align:middle line:90% I see. 01:22:00.990 --> 01:22:03.910 align:middle line:84% OK, so the way Jason is capturing it here 01:22:03.910 --> 01:22:06.230 align:middle line:84% is that he's capturing the failure 01:22:06.230 --> 01:22:08.490 align:middle line:90% rate inside this formulation. 01:22:08.490 --> 01:22:10.970 align:middle line:84% So he's saying, OK, there is the-- 01:22:10.970 --> 01:22:13.050 align:middle line:84% sorry, leave aside adjustment for phase III. 01:22:13.050 --> 01:22:15.630 align:middle line:90% You could throw this out. 01:22:15.630 --> 01:22:18.510 align:middle line:84% You have desired market advancement 01:22:18.510 --> 01:22:20.670 align:middle line:90% which is the on flow. 01:22:20.670 --> 01:22:24.710 align:middle line:84% And then you have expected failure phase III 01:22:24.710 --> 01:22:27.110 align:middle line:84% which is another flow, which is going out. 01:22:27.110 --> 01:22:31.430 align:middle line:84% But note that there is a little bit of an internal inconsistency 01:22:31.430 --> 01:22:33.310 align:middle line:90% between these two flows. 01:22:33.310 --> 01:22:39.830 align:middle line:84% The second one is coming from your ultimate expectation 01:22:39.830 --> 01:22:45.110 align:middle line:84% of how many things are going to be expiring. 01:22:45.110 --> 01:22:47.670 align:middle line:84% This desired market advancement is 01:22:47.670 --> 01:22:55.990 align:middle line:84% coming from the current level of the stock being failed-- 01:22:55.990 --> 01:22:59.950 align:middle line:84% stock going into the failure rate. 01:22:59.950 --> 01:23:02.110 align:middle line:84% AUDIENCE: They're both coming from-- 01:23:02.110 --> 01:23:04.190 align:middle line:84% HAZHIR RAHMANDAD: This expected P3 failure 01:23:04.190 --> 01:23:06.170 align:middle line:90% is coming from the next-- 01:23:06.170 --> 01:23:09.590 align:middle line:90% 01:23:09.590 --> 01:23:11.430 align:middle line:84% sorry, the desired market advancement 01:23:11.430 --> 01:23:13.470 align:middle line:90% is coming from the next stage. 01:23:13.470 --> 01:23:14.110 align:middle line:90% AUDIENCE: Yes. 01:23:14.110 --> 01:23:14.650 align:middle line:90% HAZHIR RAHMANDAD: OK. 01:23:14.650 --> 01:23:16.650 align:middle line:84% And in fact, with the correct formulation, 01:23:16.650 --> 01:23:19.030 align:middle line:84% it wouldn't be coming even from patent expiration. 01:23:19.030 --> 01:23:22.150 align:middle line:84% It would come from the desired expiration rate. 01:23:22.150 --> 01:23:25.090 align:middle line:84% So this is anchored into your ultimate goal. 01:23:25.090 --> 01:23:26.680 align:middle line:90% That's good. 01:23:26.680 --> 01:23:29.480 align:middle line:84% But here, you are combining this component 01:23:29.480 --> 01:23:31.520 align:middle line:84% that is anchored to your ultimate goal 01:23:31.520 --> 01:23:33.280 align:middle line:84% with a component that is anchored 01:23:33.280 --> 01:23:35.520 align:middle line:90% in your current level of stock. 01:23:35.520 --> 01:23:38.720 align:middle line:84% So if my current level of stock here is 0, 01:23:38.720 --> 01:23:41.640 align:middle line:84% and therefore I have no phase III failure because 01:23:41.640 --> 01:23:44.760 align:middle line:84% of this equilibrium dynamics, I'm 01:23:44.760 --> 01:23:50.280 align:middle line:84% going to affect my replacement rate badly. 01:23:50.280 --> 01:23:54.440 align:middle line:84% That is, I'm going to under-replace. 01:23:54.440 --> 01:23:56.220 align:middle line:84% And you don't want that to happen. 01:23:56.220 --> 01:23:59.500 align:middle line:84% In fact, you actually want to increase-- 01:23:59.500 --> 01:24:00.000 align:middle line:90% so-- 01:24:00.000 --> 01:24:01.360 align:middle line:84% AUDIENCE: Why you get that [INAUDIBLE]. 01:24:01.360 --> 01:24:03.610 align:middle line:84% HAZHIR RAHMANDAD: Yes, so this might be another reason 01:24:03.610 --> 01:24:05.500 align:middle line:90% for the oscillatory modes. 01:24:05.500 --> 01:24:08.760 align:middle line:84% You have this built-in bad responses 01:24:08.760 --> 01:24:10.980 align:middle line:84% because they don't account for your ultimate goal. 01:24:10.980 --> 01:24:14.720 align:middle line:84% They are looking at what is currently being exited and only 01:24:14.720 --> 01:24:16.400 align:middle line:90% replacing that much. 01:24:16.400 --> 01:24:20.560 align:middle line:84% So the right way is to get your desired market advancement. 01:24:20.560 --> 01:24:24.440 align:middle line:84% Divide that by your success rate for this phase. 01:24:24.440 --> 01:24:27.800 align:middle line:84% So when you divide that by your success rate for this phase, 01:24:27.800 --> 01:24:30.960 align:middle line:84% you're accounting for the desired level, 01:24:30.960 --> 01:24:33.840 align:middle line:84% and you're expanding for the failure rate. 01:24:33.840 --> 01:24:36.500 align:middle line:84% Now, in equilibrium, they both give the right answer. 01:24:36.500 --> 01:24:38.280 align:middle line:84% And that's why you didn't detect it 01:24:38.280 --> 01:24:40.840 align:middle line:84% when you were doing the equilibrium analysis. 01:24:40.840 --> 01:24:45.300 align:middle line:84% But these oscillatory modes are coming out of these two issues. 01:24:45.300 --> 01:24:47.600 align:middle line:84% I'm not sure which one is more important. 01:24:47.600 --> 01:24:48.600 align:middle line:90% You actually need-- 01:24:48.600 --> 01:24:50.600 align:middle line:84% AUDIENCE: [INAUDIBLE] by the success rate. 01:24:50.600 --> 01:24:55.160 align:middle line:84% HAZHIR RAHMANDAD: Yeah, would resolve the issue. 01:24:55.160 --> 01:24:58.520 align:middle line:90% AUDIENCE: So that would-- 01:24:58.520 --> 01:25:01.560 align:middle line:84% so you would divide by the success rate for the desired P3 01:25:01.560 --> 01:25:02.880 align:middle line:90% advancement? 01:25:02.880 --> 01:25:07.500 align:middle line:84% HAZHIR RAHMANDAD: Yes, I would divide by success rate for P3. 01:25:07.500 --> 01:25:08.000 align:middle line:90% Yes. 01:25:08.000 --> 01:25:08.920 align:middle line:90% AUDIENCE: So for the-- 01:25:08.920 --> 01:25:09.680 align:middle line:90% OK. 01:25:09.680 --> 01:25:10.440 align:middle line:90% And then-- 01:25:10.440 --> 01:25:12.107 align:middle line:84% HAZHIR RAHMANDAD: And then the next one, 01:25:12.107 --> 01:25:14.460 align:middle line:84% desired success rate for P2 and so on. 01:25:14.460 --> 01:25:16.980 align:middle line:84% AUDIENCE: And then that's all you do going down the chain. 01:25:16.980 --> 01:25:17.560 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:25:17.560 --> 01:25:18.900 align:middle line:90% AUDIENCE: OK, because then-- 01:25:18.900 --> 01:25:19.400 align:middle line:90% I see. 01:25:19.400 --> 01:25:20.920 align:middle line:84% HAZHIR RAHMANDAD: This is without growth. 01:25:20.920 --> 01:25:22.180 align:middle line:90% We should get to the growth. 01:25:22.180 --> 01:25:25.880 align:middle line:84% But I think it's a good time to take a break 01:25:25.880 --> 01:25:28.800 align:middle line:84% and look at the growth after we come back. 01:25:28.800 --> 01:25:29.760 align:middle line:90% Yeah, go ahead. 01:25:29.760 --> 01:25:32.320 align:middle line:84% AUDIENCE: And then the initial value of the mineral stocks 01:25:32.320 --> 01:25:33.482 align:middle line:90% would be the desire. 01:25:33.482 --> 01:25:35.440 align:middle line:84% HAZHIR RAHMANDAD: So the desired phase IIs that 01:25:35.440 --> 01:25:37.180 align:middle line:90% are being calculated are good. 01:25:37.180 --> 01:25:42.480 align:middle line:84% Once you have this desired advancement, you just get that. 01:25:42.480 --> 01:25:47.980 align:middle line:84% And yeah, P3 advancement should give you your desired two. 01:25:47.980 --> 01:25:49.920 align:middle line:84% You just multiply that by the time constant 01:25:49.920 --> 01:25:52.060 align:middle line:90% divided by P2 success fraction. 01:25:52.060 --> 01:25:55.740 align:middle line:84% And you can do it for every single one. 01:25:55.740 --> 01:25:56.240 align:middle line:90% Yes. 01:25:56.240 --> 01:25:59.132 align:middle line:90% 01:25:59.132 --> 01:26:03.080 align:middle line:84% AUDIENCE: Wait, sorry, how is that-- 01:26:03.080 --> 01:26:06.160 align:middle line:90% so for phase I-- 01:26:06.160 --> 01:26:07.100 align:middle line:90% oh, I see, I see. 01:26:07.100 --> 01:26:08.933 align:middle line:84% HAZHIR RAHMANDAD: Let's look at the phase I. 01:26:08.933 --> 01:26:14.160 align:middle line:84% The desired phase I is coming from desired P2 advancement 01:26:14.160 --> 01:26:17.880 align:middle line:90% times the average time in P1. 01:26:17.880 --> 01:26:22.450 align:middle line:84% So that is the Little's Law, except that you 01:26:22.450 --> 01:26:26.110 align:middle line:84% need to expand it for the fraction that fails. 01:26:26.110 --> 01:26:28.610 align:middle line:90% AUDIENCE: But then it's not-- 01:26:28.610 --> 01:26:32.130 align:middle line:84% but the desired levels aren't changing any of the flows. 01:26:32.130 --> 01:26:33.970 align:middle line:84% HAZHIR RAHMANDAD: The desired levels are not 01:26:33.970 --> 01:26:38.250 align:middle line:90% changing these flows yet. 01:26:38.250 --> 01:26:39.510 align:middle line:90% They will be added. 01:26:39.510 --> 01:26:43.250 align:middle line:84% So all of these adjustments need to be added together 01:26:43.250 --> 01:26:46.530 align:middle line:84% as a total stock adjustment that would 01:26:46.530 --> 01:26:48.482 align:middle line:90% be added to this desired DSR. 01:26:48.482 --> 01:26:50.690 align:middle line:84% AUDIENCE: Well, no, you were saying that we shouldn't 01:26:50.690 --> 01:26:52.330 align:middle line:90% add the adjustments because-- 01:26:52.330 --> 01:26:54.663 align:middle line:84% HAZHIR RAHMANDAD: No, no, I was saying, at the very end, 01:26:54.663 --> 01:26:55.943 align:middle line:90% they should be added. 01:26:55.943 --> 01:26:56.690 align:middle line:84% AUDIENCE: They don't need to be-- 01:26:56.690 --> 01:26:58.065 align:middle line:84% HAZHIR RAHMANDAD: They don't need 01:26:58.065 --> 01:27:00.370 align:middle line:84% to be added in the intermediate steps. 01:27:00.370 --> 01:27:03.870 align:middle line:84% In the intermediate steps, they'll mess things up, 01:27:03.870 --> 01:27:04.990 align:middle line:90% but they are important. 01:27:04.990 --> 01:27:08.030 align:middle line:84% You do want to adjust for those stocks. 01:27:08.030 --> 01:27:10.850 align:middle line:84% So they will-- I'll show you a version that 01:27:10.850 --> 01:27:12.750 align:middle line:90% has that when we come back. 01:27:12.750 --> 01:27:13.810 align:middle line:90% OK? 01:27:13.810 --> 01:27:15.310 align:middle line:90% Good, let's take 10 minutes. 01:27:15.310 --> 01:27:18.970 align:middle line:90% 01:27:18.970 --> 01:27:21.170 align:middle line:84% Let's look at what you have here. 01:27:21.170 --> 01:27:24.450 align:middle line:84% Let's not go through the last year thing. 01:27:24.450 --> 01:27:25.993 align:middle line:90% It's traumatic. 01:27:25.993 --> 01:27:27.410 align:middle line:84% AUDIENCE: Well, well, I bring it-- 01:27:27.410 --> 01:27:29.590 align:middle line:84% I bring it up because I think [INAUDIBLE] 01:27:29.590 --> 01:27:32.490 align:middle line:84% able to put it in equilibrium just by treating 01:27:32.490 --> 01:27:34.520 align:middle line:90% all the stocks together. 01:27:34.520 --> 01:27:36.770 align:middle line:84% HAZHIR RAHMANDAD: Ah, so because this one doesn't have 01:27:36.770 --> 01:27:38.010 align:middle line:90% equilibrium, you're saying. 01:27:38.010 --> 01:27:40.030 align:middle line:84% AUDIENCE: Yeah, this doesn't-- this one doesn't go to the-- 01:27:40.030 --> 01:27:41.530 align:middle line:84% HAZHIR RAHMANDAD: Yeah, but I think, 01:27:41.530 --> 01:27:44.970 align:middle line:84% last year, we weren't holding you for exponential growth 01:27:44.970 --> 01:27:46.230 align:middle line:90% trajectory either. 01:27:46.230 --> 01:27:46.930 align:middle line:84% AUDIENCE: So I don't-- yeah, yeah. 01:27:46.930 --> 01:27:48.805 align:middle line:84% And I don't do the exponential growth either. 01:27:48.805 --> 01:27:51.210 align:middle line:84% But I'm just saying that, unlike the cascading one, which 01:27:51.210 --> 01:27:52.918 align:middle line:84% is successful in [INAUDIBLE] equilibrium, 01:27:52.918 --> 01:27:55.208 align:middle line:90% it was a lot more complicated. 01:27:55.208 --> 01:27:57.250 align:middle line:84% But I just thought it might be instructive to see 01:27:57.250 --> 01:27:59.310 align:middle line:84% how I did it by putting them all together 01:27:59.310 --> 01:28:00.690 align:middle line:90% and those two [INAUDIBLE]. 01:28:00.690 --> 01:28:03.430 align:middle line:84% HAZHIR RAHMANDAD: OK, so maybe I'll check that as well. 01:28:03.430 --> 01:28:04.910 align:middle line:90% You have it on the folder. 01:28:04.910 --> 01:28:05.410 align:middle line:90% OK. 01:28:05.410 --> 01:28:06.785 align:middle line:84% AUDIENCE: Just like D2 generally. 01:28:06.785 --> 01:28:08.090 align:middle line:90% HAZHIR RAHMANDAD: I see, I see. 01:28:08.090 --> 01:28:12.090 align:middle line:84% So let's then take a quick look at this one 01:28:12.090 --> 01:28:14.310 align:middle line:84% and then maybe look at the other one. 01:28:14.310 --> 01:28:16.430 align:middle line:90% So this is simulating as well. 01:28:16.430 --> 01:28:20.890 align:middle line:84% So again, basic backbone, the same as before. 01:28:20.890 --> 01:28:25.290 align:middle line:90% You have the drug expiry. 01:28:25.290 --> 01:28:30.090 align:middle line:84% That is being added to adjustment 01:28:30.090 --> 01:28:34.010 align:middle line:84% for drugs in the market to create these desired drug 01:28:34.010 --> 01:28:41.470 align:middle line:84% development rate, which then is-- 01:28:41.470 --> 01:28:45.793 align:middle line:90% 01:28:45.793 --> 01:28:48.210 align:middle line:84% AUDIENCE: So I tried to treat all the drugs in development 01:28:48.210 --> 01:28:50.330 align:middle line:84% as a single stock, which I realized 01:28:50.330 --> 01:28:53.690 align:middle line:84% without a lot of subtleties doesn't work 01:28:53.690 --> 01:28:55.770 align:middle line:84% and which is why this model doesn't go-- 01:28:55.770 --> 01:28:57.470 align:middle line:90% it goes into a steady state. 01:28:57.470 --> 01:29:01.930 align:middle line:84% But it doesn't reach the desired level of drugs. 01:29:01.930 --> 01:29:04.090 align:middle line:84% So the desired total number of drugs 01:29:04.090 --> 01:29:07.170 align:middle line:84% is just the desired development rate times the time 01:29:07.170 --> 01:29:09.790 align:middle line:90% to develop the drugs. 01:29:09.790 --> 01:29:12.730 align:middle line:90% 01:29:12.730 --> 01:29:15.620 align:middle line:84% HAZHIR RAHMANDAD: Desired total drugs in development, 01:29:15.620 --> 01:29:24.020 align:middle line:84% so drugs in development requires accounting for the failure rates 01:29:24.020 --> 01:29:25.500 align:middle line:90% to do it right. 01:29:25.500 --> 01:29:28.780 align:middle line:90% So just looking at the-- 01:29:28.780 --> 01:29:32.180 align:middle line:84% so you can't get the desired total drugs in development 01:29:32.180 --> 01:29:35.780 align:middle line:84% by multiplying desired drug development 01:29:35.780 --> 01:29:39.220 align:middle line:90% rate and time to develop drugs. 01:29:39.220 --> 01:29:40.913 align:middle line:84% AUDIENCE: So I try to do it-- so again, 01:29:40.913 --> 01:29:43.080 align:middle line:84% I don't think I did it successfully in this version, 01:29:43.080 --> 01:29:44.760 align:middle line:84% but I tried [INAUDIBLE] later on, 01:29:44.760 --> 01:29:47.700 align:middle line:84% which I call the drug start rate with buffer. 01:29:47.700 --> 01:29:53.703 align:middle line:84% And then, there, that accounts for the failure rate. 01:29:53.703 --> 01:29:54.620 align:middle line:90% HAZHIR RAHMANDAD: Oof. 01:29:54.620 --> 01:29:58.220 align:middle line:90% 01:29:58.220 --> 01:29:58.760 align:middle line:90% OK. 01:29:58.760 --> 01:30:04.560 align:middle line:84% So wouldn't work well because if you 01:30:04.560 --> 01:30:07.923 align:middle line:84% are trying to adjust the stocks, you need to adjust the stocks. 01:30:07.923 --> 01:30:09.340 align:middle line:84% Otherwise, you are doing something 01:30:09.340 --> 01:30:13.080 align:middle line:84% that is hard to conceptually know what exactly it is. 01:30:13.080 --> 01:30:16.220 align:middle line:84% Yes, it adjusts for something, but it is not exactly 01:30:16.220 --> 01:30:21.980 align:middle line:84% doing the adjustment for stocks that you want it to do. 01:30:21.980 --> 01:30:28.220 align:middle line:84% And then you are adding the failure rates, 01:30:28.220 --> 01:30:30.240 align:middle line:90% which is similar to-- 01:30:30.240 --> 01:30:34.780 align:middle line:90% 01:30:34.780 --> 01:30:36.640 align:middle line:84% OK, this is a complex formulation. 01:30:36.640 --> 01:30:38.900 align:middle line:90% Let's see. 01:30:38.900 --> 01:30:42.700 align:middle line:84% AUDIENCE: So what this is is the first term is you-- 01:30:42.700 --> 01:30:45.467 align:middle line:84% I'm taking into account the failure rates. 01:30:45.467 --> 01:30:47.300 align:middle line:84% It does the same thing as taking [INAUDIBLE] 01:30:47.300 --> 01:30:50.020 align:middle line:84% out the failure rates when I determine the desired drug 01:30:50.020 --> 01:30:52.900 align:middle line:84% development rate and the desired number of drugs in development. 01:30:52.900 --> 01:30:55.360 align:middle line:84% And then my thought was like, OK, 01:30:55.360 --> 01:30:59.060 align:middle line:84% you want to replace the drugs that are failing, 01:30:59.060 --> 01:31:02.500 align:middle line:84% but you want to take into account the fact that there are 01:31:02.500 --> 01:31:03.840 align:middle line:90% failure rates along the way. 01:31:03.840 --> 01:31:06.940 align:middle line:84% So to replace the stage 1 drugs that are failing-- 01:31:06.940 --> 01:31:11.260 align:middle line:84% HAZHIR RAHMANDAD: OK, just so fraction succeeding development 01:31:11.260 --> 01:31:14.475 align:middle line:84% is the multiplication of the three success rates? 01:31:14.475 --> 01:31:15.100 align:middle line:90% AUDIENCE: Yeah. 01:31:15.100 --> 01:31:18.700 align:middle line:84% HAZHIR RAHMANDAD: OK, so indicated drug start rate, 01:31:18.700 --> 01:31:21.020 align:middle line:90% what is that? 01:31:21.020 --> 01:31:26.260 align:middle line:84% So indicated drug started was the total 01:31:26.260 --> 01:31:28.640 align:middle line:90% coming from two factors. 01:31:28.640 --> 01:31:32.120 align:middle line:84% One was the stock adjustment thingy that is not quite right, 01:31:32.120 --> 01:31:34.020 align:middle line:90% but let's put that aside. 01:31:34.020 --> 01:31:38.220 align:middle line:90% Then there is this the-- 01:31:38.220 --> 01:31:42.500 align:middle line:90% there is the replacement. 01:31:42.500 --> 01:31:44.700 align:middle line:84% And then there is the drug adjustment 01:31:44.700 --> 01:31:46.540 align:middle line:90% for the drugs in the market. 01:31:46.540 --> 01:31:49.800 align:middle line:84% So in the case that you have only the replacement, 01:31:49.800 --> 01:31:54.180 align:middle line:84% the simplest case, in the indicated drug start rate, 01:31:54.180 --> 01:31:59.380 align:middle line:84% dividing that by the total success rate 01:31:59.380 --> 01:32:03.260 align:middle line:84% gives you a good anchor for the drug start rate, 01:32:03.260 --> 01:32:05.620 align:middle line:90% without accounting for growth. 01:32:05.620 --> 01:32:09.140 align:middle line:84% If you account for growth, things will not work well. 01:32:09.140 --> 01:32:13.600 align:middle line:84% And we had that formulation, I think, in your case. 01:32:13.600 --> 01:32:15.580 align:middle line:84% In a couple other cases, we had that. 01:32:15.580 --> 01:32:18.220 align:middle line:90% In [? Oriana's ?] case as well. 01:32:18.220 --> 01:32:23.820 align:middle line:84% Then you are adding these drug failure rates 01:32:23.820 --> 01:32:28.580 align:middle line:90% to that total start rate. 01:32:28.580 --> 01:32:32.180 align:middle line:84% Those drug failure rates are an alternative way 01:32:32.180 --> 01:32:34.420 align:middle line:84% of accounting for failures, which 01:32:34.420 --> 01:32:37.060 align:middle line:84% I think Kathy was using by looking 01:32:37.060 --> 01:32:42.340 align:middle line:84% at the sum of all of the failure rates and some of-- 01:32:42.340 --> 01:32:44.820 align:middle line:84% and the drugs with expiring patterns. 01:32:44.820 --> 01:32:47.540 align:middle line:84% If you add all of those four together, 01:32:47.540 --> 01:32:50.440 align:middle line:84% that's the net outflow from the system. 01:32:50.440 --> 01:32:51.880 align:middle line:90% You restart that much. 01:32:51.880 --> 01:32:54.500 align:middle line:84% You keep the system in equilibrium. 01:32:54.500 --> 01:32:57.240 align:middle line:84% So then that would be another way to capture it. 01:32:57.240 --> 01:33:00.060 align:middle line:84% Here, you are really combining the two together 01:33:00.060 --> 01:33:02.480 align:middle line:84% in a way that is not fully consistent as well. 01:33:02.480 --> 01:33:04.100 align:middle line:84% You have all these stock adjustments 01:33:04.100 --> 01:33:05.587 align:middle line:90% that are not quite right. 01:33:05.587 --> 01:33:06.920 align:middle line:90% I mean, the first part is right. 01:33:06.920 --> 01:33:10.950 align:middle line:84% The second part, as we went through Kathy's example, 01:33:10.950 --> 01:33:12.350 align:middle line:90% doesn't quite work. 01:33:12.350 --> 01:33:14.950 align:middle line:84% So this is not going to work, even 01:33:14.950 --> 01:33:18.310 align:middle line:84% for the normal getting to what you want 01:33:18.310 --> 01:33:22.430 align:middle line:90% to have in the desired stocks. 01:33:22.430 --> 01:33:24.390 align:middle line:84% Let's open the other one that you 01:33:24.390 --> 01:33:28.570 align:middle line:84% said has some additional features we may want to look at. 01:33:28.570 --> 01:33:32.710 align:middle line:90% So this is the general version. 01:33:32.710 --> 01:33:35.470 align:middle line:84% AUDIENCE: Yeah, so the basic idea is the same. 01:33:35.470 --> 01:33:36.370 align:middle line:90% I just built on it. 01:33:36.370 --> 01:33:37.590 align:middle line:84% And there's a bunch of other stuff that 01:33:37.590 --> 01:33:39.465 align:middle line:84% was taken from the other [INAUDIBLE] question 01:33:39.465 --> 01:33:42.750 align:middle line:84% that isn't pertinent here, like the cancellation 01:33:42.750 --> 01:33:43.830 align:middle line:90% and things like that. 01:33:43.830 --> 01:33:45.178 align:middle line:90% That's 0, I think. 01:33:45.178 --> 01:33:47.470 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so the cancellation is actually 01:33:47.470 --> 01:33:49.090 align:middle line:90% an important consideration. 01:33:49.090 --> 01:33:51.910 align:middle line:84% That is, in all of our conversations, 01:33:51.910 --> 01:33:55.430 align:middle line:84% we have assumed the only way to get rid 01:33:55.430 --> 01:33:59.350 align:middle line:84% of a drug is wait for it to flow out of the system 01:33:59.350 --> 01:34:01.230 align:middle line:90% or down through failure. 01:34:01.230 --> 01:34:03.850 align:middle line:84% But it is actually very easy to cancel things. 01:34:03.850 --> 01:34:07.670 align:middle line:84% So that is a very conceptually important thing 01:34:07.670 --> 01:34:11.350 align:middle line:84% that we are skipping, we are ignoring here, just 01:34:11.350 --> 01:34:13.270 align:middle line:90% to keep things simple. 01:34:13.270 --> 01:34:17.230 align:middle line:84% Now, it doesn't kick in in a situation that you are growing, 01:34:17.230 --> 01:34:21.090 align:middle line:84% and you don't have big misalignments in your stocks. 01:34:21.090 --> 01:34:22.650 align:middle line:84% It doesn't become that important. 01:34:22.650 --> 01:34:26.690 align:middle line:84% But if you want to reduce your pipeline for whatever reason, 01:34:26.690 --> 01:34:29.670 align:middle line:84% you're just exiting market because the world is finishing 01:34:29.670 --> 01:34:36.350 align:middle line:84% or something, you can use the exit rates cancellations more 01:34:36.350 --> 01:34:37.210 align:middle line:90% explicitly. 01:34:37.210 --> 01:34:39.970 align:middle line:84% Or if you have too much in any of your stages, you can do it. 01:34:39.970 --> 01:34:43.510 align:middle line:84% So, OK, that's just something that we are ignoring. 01:34:43.510 --> 01:34:49.650 align:middle line:84% Now, here, again, the basics are pretty much the same. 01:34:49.650 --> 01:34:52.630 align:middle line:90% You have the time to develop. 01:34:52.630 --> 01:34:58.290 align:middle line:84% So tell me, what was the equilibrium setup here? 01:34:58.290 --> 01:35:01.330 align:middle line:90% 01:35:01.330 --> 01:35:03.830 align:middle line:84% AUDIENCE: Yeah, it's been a while since I've looked at this. 01:35:03.830 --> 01:35:05.247 align:middle line:84% HAZHIR RAHMANDAD: Yes, OK, so this 01:35:05.247 --> 01:35:12.030 align:middle line:84% is initial successful drugs in trial divided by 3 01:35:12.030 --> 01:35:13.070 align:middle line:90% It shows succ-- 01:35:13.070 --> 01:35:18.070 align:middle line:90% 01:35:18.070 --> 01:35:21.270 align:middle line:84% So this is I'm not sure if it would 01:35:21.270 --> 01:35:27.230 align:middle line:84% do the trick for the equilibrium either because-- 01:35:27.230 --> 01:35:29.110 align:middle line:84% AUDIENCE: So it might not be-- yeah, 01:35:29.110 --> 01:35:32.832 align:middle line:84% it might not be initialized in equilibrium. 01:35:32.832 --> 01:35:34.290 align:middle line:84% That wasn't what I was looking for. 01:35:34.290 --> 01:35:36.165 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so the initialization 01:35:36.165 --> 01:35:39.330 align:middle line:84% in equilibrium, it probably wouldn't work that well. 01:35:39.330 --> 01:35:41.890 align:middle line:84% And then there is that stock adjustment question. 01:35:41.890 --> 01:35:46.490 align:middle line:84% That is, OK, how do you correct for these different stocks? 01:35:46.490 --> 01:35:49.930 align:middle line:84% You have it in the drugs in development adjustment. 01:35:49.930 --> 01:35:53.230 align:middle line:90% You are adding them up. 01:35:53.230 --> 01:35:55.230 align:middle line:90% Let's look at that. 01:35:55.230 --> 01:35:59.310 align:middle line:84% AUDIENCE: Yeah, I think this is a relatively-- 01:35:59.310 --> 01:36:01.750 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so you are looking at each 01:36:01.750 --> 01:36:03.257 align:middle line:90% with a-- compared to a desire. 01:36:03.257 --> 01:36:04.840 align:middle line:84% So this is what we discussed, that you 01:36:04.840 --> 01:36:08.240 align:middle line:84% want to have separate desired ones for each stage. 01:36:08.240 --> 01:36:13.560 align:middle line:84% And you look at the gap between the desired and actual for each 01:36:13.560 --> 01:36:14.585 align:middle line:90% and correct for that. 01:36:14.585 --> 01:36:15.960 align:middle line:84% So then there is the question of, 01:36:15.960 --> 01:36:18.480 align:middle line:84% what is the desired for each of these? 01:36:18.480 --> 01:36:24.520 align:middle line:90% So then you have desired-- 01:36:24.520 --> 01:36:25.700 align:middle line:90% where is desired? 01:36:25.700 --> 01:36:27.180 align:middle line:90% Middle stage drugs. 01:36:27.180 --> 01:36:29.000 align:middle line:90% No. 01:36:29.000 --> 01:36:30.730 align:middle line:90% AUDIENCE: One to the right. 01:36:30.730 --> 01:36:33.720 align:middle line:84% HAZHIR RAHMANDAD: Right of desired drugs in development. 01:36:33.720 --> 01:36:37.202 align:middle line:84% AUDIENCE: It's essentially equal to the indicated. 01:36:37.202 --> 01:36:39.160 align:middle line:84% Again, because of the other parts of the model, 01:36:39.160 --> 01:36:42.340 align:middle line:84% there was a consideration of [INAUDIBLE] budget, 01:36:42.340 --> 01:36:44.000 align:middle line:90% which I don't mean to-- 01:36:44.000 --> 01:36:47.200 align:middle line:84% HAZHIR RAHMANDAD: So this needs us to understand a little bit 01:36:47.200 --> 01:36:48.500 align:middle line:90% more about what was happening. 01:36:48.500 --> 01:36:49.740 align:middle line:90% I don't remember the details. 01:36:49.740 --> 01:36:51.180 align:middle line:84% AUDIENCE: So it's not supposed to be a constraint. 01:36:51.180 --> 01:36:52.972 align:middle line:84% It's supposed to be equal to the indicated. 01:36:52.972 --> 01:36:57.160 align:middle line:90% And the indicated-- yeah. 01:36:57.160 --> 01:36:59.400 align:middle line:84% HAZHIR RAHMANDAD: And indicated is the total-- 01:36:59.400 --> 01:37:04.122 align:middle line:90% 01:37:04.122 --> 01:37:05.100 align:middle line:90% ah, interesting. 01:37:05.100 --> 01:37:07.560 align:middle line:84% So you have this likelihood that is 01:37:07.560 --> 01:37:09.520 align:middle line:84% trying to adjust across all of them 01:37:09.520 --> 01:37:13.900 align:middle line:84% and give you a single desired value for each step. 01:37:13.900 --> 01:37:17.040 align:middle line:90% 01:37:17.040 --> 01:37:19.840 align:middle line:84% AUDIENCE: And it's quite complex. 01:37:19.840 --> 01:37:21.480 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 01:37:21.480 --> 01:37:25.280 align:middle line:84% OK, so I'm not going to dig deeper into this 01:37:25.280 --> 01:37:28.200 align:middle line:84% because it will take us too long to figure out 01:37:28.200 --> 01:37:29.620 align:middle line:90% what exactly works here. 01:37:29.620 --> 01:37:32.700 align:middle line:84% But it's not the cleanest way of doing it. 01:37:32.700 --> 01:37:34.800 align:middle line:84% So you need separate desired values 01:37:34.800 --> 01:37:36.800 align:middle line:90% for each stock that accounts. 01:37:36.800 --> 01:37:42.080 align:middle line:84% And this one also wouldn't do the growth dynamics. 01:37:42.080 --> 01:37:44.820 align:middle line:90% OK, other volunteers? 01:37:44.820 --> 01:37:48.160 align:middle line:90% 01:37:48.160 --> 01:37:54.840 align:middle line:84% Let's then just go and see who we haven't checked out. 01:37:54.840 --> 01:38:00.400 align:middle line:84% Jason we looked at, which is this one. 01:38:00.400 --> 01:38:03.040 align:middle line:90% This is Ross. 01:38:03.040 --> 01:38:11.800 align:middle line:84% OK, so Ross's model has the basic backbone with the start 01:38:11.800 --> 01:38:16.440 align:middle line:90% and failures, revenue. 01:38:16.440 --> 01:38:19.640 align:middle line:84% Then you have the desired revenue 01:38:19.640 --> 01:38:24.920 align:middle line:90% that is based on a growth rate. 01:38:24.920 --> 01:38:27.820 align:middle line:90% That gives you desired drugs. 01:38:27.820 --> 01:38:30.680 align:middle line:90% 01:38:30.680 --> 01:38:36.760 align:middle line:84% And then desired drugs, let me make it a little bit bigger 01:38:36.760 --> 01:38:38.820 align:middle line:84% so that we can see things a bit better. 01:38:38.820 --> 01:38:43.680 align:middle line:90% 01:38:43.680 --> 01:38:45.740 align:middle line:90% OK, desired drugs. 01:38:45.740 --> 01:38:51.480 align:middle line:90% 01:38:51.480 --> 01:38:56.400 align:middle line:84% OK, I need to go here and see what is happening in project. 01:38:56.400 --> 01:39:01.210 align:middle line:84% Start rate because it's a bit more complex. 01:39:01.210 --> 01:39:06.690 align:middle line:84% Desired patented drugs at t plus capital T 01:39:06.690 --> 01:39:13.370 align:middle line:84% multiplied by desired growth rate plus 1 over patent time 01:39:13.370 --> 01:39:18.390 align:middle line:84% divided by drug success probability. 01:39:18.390 --> 01:39:23.450 align:middle line:90% 01:39:23.450 --> 01:39:25.630 align:middle line:84% Ross, can you tell us what's happening here? 01:39:25.630 --> 01:39:27.450 align:middle line:90% What's the logic behind them? 01:39:27.450 --> 01:39:28.690 align:middle line:90% AUDIENCE: Oh, there were-- 01:39:28.690 --> 01:39:32.090 align:middle line:84% I don't think I dealt with the stock thing before, 01:39:32.090 --> 01:39:36.890 align:middle line:84% so I was trying to look at the outflow from the total system 01:39:36.890 --> 01:39:39.930 align:middle line:90% and then needed the growth part. 01:39:39.930 --> 01:39:42.930 align:middle line:84% I try to replace it in the beginning with the time 01:39:42.930 --> 01:39:45.050 align:middle line:84% difference between the whole pipe. 01:39:45.050 --> 01:39:45.985 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:39:45.985 --> 01:39:47.110 align:middle line:90% So all of that makes sense. 01:39:47.110 --> 01:39:49.810 align:middle line:84% So division by drug success probability, I think, 01:39:49.810 --> 01:39:52.870 align:middle line:84% is the part for accounting for failure rates. 01:39:52.870 --> 01:39:55.550 align:middle line:90% So that makes sense. 01:39:55.550 --> 01:40:00.290 align:middle line:84% The desired patented drugs at time t plus capital T 01:40:00.290 --> 01:40:01.970 align:middle line:90% is, I guess-- 01:40:01.970 --> 01:40:05.450 align:middle line:84% AUDIENCE: Average time spent in the pipeline. 01:40:05.450 --> 01:40:08.390 align:middle line:84% HAZHIR RAHMANDAD: Yes, but desired patented drugs, 01:40:08.390 --> 01:40:12.090 align:middle line:84% this sounds like in the units of drugs. 01:40:12.090 --> 01:40:15.010 align:middle line:90% Yes. 01:40:15.010 --> 01:40:18.930 align:middle line:84% So this is like the stock that you want to have. 01:40:18.930 --> 01:40:23.170 align:middle line:90% Then you get that stock. 01:40:23.170 --> 01:40:32.030 align:middle line:84% You multiply that by growth rate plus 1 over patent life. 01:40:32.030 --> 01:40:33.090 align:middle line:90% What is this? 01:40:33.090 --> 01:40:34.512 align:middle line:90% This part I can't follow. 01:40:34.512 --> 01:40:35.470 align:middle line:90% What is happening here? 01:40:35.470 --> 01:40:37.810 align:middle line:84% Can you tell us what you were thinking to do? 01:40:37.810 --> 01:40:40.330 align:middle line:90% AUDIENCE: To add for the growth. 01:40:40.330 --> 01:40:43.302 align:middle line:84% And then the second part is to replace the outflow 01:40:43.302 --> 01:40:44.010 align:middle line:90% from the patent-- 01:40:44.010 --> 01:40:47.928 align:middle line:84% HAZHIR RAHMANDAD: Yes, so 1 over patent life is good for outflow. 01:40:47.928 --> 01:40:49.470 align:middle line:84% That basically gives you the outflow. 01:40:49.470 --> 01:40:52.310 align:middle line:84% So if you didn't have the desired growth rate here. 01:40:52.310 --> 01:40:55.690 align:middle line:84% I could follow this for the equilibrium condition. 01:40:55.690 --> 01:41:03.290 align:middle line:84% Then you have this desired growth rate being added to it. 01:41:03.290 --> 01:41:06.930 align:middle line:84% And the units work because growth rate 01:41:06.930 --> 01:41:11.850 align:middle line:90% is 1 over unit of time. 01:41:11.850 --> 01:41:14.970 align:middle line:84% But I'm not just following the conceptually 01:41:14.970 --> 01:41:18.730 align:middle line:90% what is happening here. 01:41:18.730 --> 01:41:21.890 align:middle line:84% Because that growth rate multiplied 01:41:21.890 --> 01:41:30.090 align:middle line:84% by the stock of desired patented drugs, what is it telling us? 01:41:30.090 --> 01:41:39.170 align:middle line:84% It tells us, what's the rate of growth in this stock 01:41:39.170 --> 01:41:42.490 align:middle line:90% that we want to see? 01:41:42.490 --> 01:41:44.570 align:middle line:90% So it would be the net flow. 01:41:44.570 --> 01:41:48.610 align:middle line:84% So that would be the net flow for the stock. 01:41:48.610 --> 01:41:53.540 align:middle line:84% So you are saying I'm adding the net flow for it 01:41:53.540 --> 01:42:03.780 align:middle line:84% to be able to grow to what is the outflow, which 01:42:03.780 --> 01:42:07.060 align:middle line:90% is 1 over patent time. 01:42:07.060 --> 01:42:13.140 align:middle line:84% So that becomes the net inflow that 01:42:13.140 --> 01:42:19.500 align:middle line:84% should go into it to get the outflow that allows us to grow. 01:42:19.500 --> 01:42:22.220 align:middle line:90% OK, that makes sense. 01:42:22.220 --> 01:42:27.380 align:middle line:84% Then to get that net inflow, you need to also divide it 01:42:27.380 --> 01:42:29.600 align:middle line:90% by drug success probability. 01:42:29.600 --> 01:42:32.740 align:middle line:90% 01:42:32.740 --> 01:42:36.200 align:middle line:90% So that part works fine. 01:42:36.200 --> 01:42:44.260 align:middle line:90% 01:42:44.260 --> 01:42:45.540 align:middle line:90% AUDIENCE: I simulated. 01:42:45.540 --> 01:42:49.422 align:middle line:84% Then it gets less and less accurate as-- 01:42:49.422 --> 01:42:50.880 align:middle line:84% HAZHIR RAHMANDAD: As the time goes. 01:42:50.880 --> 01:42:51.505 align:middle line:90% AUDIENCE: Yeah. 01:42:51.505 --> 01:42:53.940 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so it is missing something. 01:42:53.940 --> 01:42:56.640 align:middle line:84% I'll show you some example that has this. 01:42:56.640 --> 01:42:58.800 align:middle line:90% But this is an interesting-- 01:42:58.800 --> 01:43:01.800 align:middle line:84% you had a good piece of idea for capturing the growth. 01:43:01.800 --> 01:43:08.780 align:middle line:84% That is, you want the inflow minus outflow for the last stock 01:43:08.780 --> 01:43:11.540 align:middle line:90% to be the growing-- 01:43:11.540 --> 01:43:14.600 align:middle line:84% I mean, to be the net growth rate for that stock. 01:43:14.600 --> 01:43:18.380 align:middle line:84% And the net growth rate is your desired growth rate 01:43:18.380 --> 01:43:19.880 align:middle line:90% multiplied by the stock. 01:43:19.880 --> 01:43:24.100 align:middle line:84% So this is actually giving you an indication 01:43:24.100 --> 01:43:26.820 align:middle line:84% of the growth-- what you need to adjust 01:43:26.820 --> 01:43:29.140 align:middle line:90% to be able to actually grow. 01:43:29.140 --> 01:43:32.900 align:middle line:84% But that indication alone is not going to do the job for you 01:43:32.900 --> 01:43:33.700 align:middle line:90% here. 01:43:33.700 --> 01:43:35.620 align:middle line:84% It needs to be kind of incorporated 01:43:35.620 --> 01:43:43.380 align:middle line:84% more structurally into the steps of the process. 01:43:43.380 --> 01:43:47.040 align:middle line:84% And of course, you don't have stock adjustment parts. 01:43:47.040 --> 01:43:49.873 align:middle line:84% So for those intermediate stocks, there is no adjustment. 01:43:49.873 --> 01:43:52.040 align:middle line:84% Even for the patented drugs, there is no adjustment. 01:43:52.040 --> 01:43:55.560 align:middle line:84% So that will create another issue. 01:43:55.560 --> 01:43:59.960 align:middle line:84% Then the equilibrium initialization is not happening. 01:43:59.960 --> 01:44:04.720 align:middle line:84% So those are things that we already talked about. 01:44:04.720 --> 01:44:06.140 align:middle line:90% So you know, good. 01:44:06.140 --> 01:44:12.100 align:middle line:84% I think that idea, we'll use it in a few minutes. 01:44:12.100 --> 01:44:13.020 align:middle line:90% Let's see. 01:44:13.020 --> 01:44:17.500 align:middle line:90% We have looked at Ross's. 01:44:17.500 --> 01:44:20.540 align:middle line:90% Alban's we have looked at. 01:44:20.540 --> 01:44:22.940 align:middle line:90% [? Oriana ?] we have looked at. 01:44:22.940 --> 01:44:27.780 align:middle line:84% [INAUDIBLE], OK, let's look at this one. 01:44:27.780 --> 01:44:33.260 align:middle line:84% So again, basic structure, we are in agreement. 01:44:33.260 --> 01:44:36.080 align:middle line:84% Then to look at what is happening, 01:44:36.080 --> 01:44:38.440 align:middle line:84% we have adjustments for different phases. 01:44:38.440 --> 01:44:40.960 align:middle line:84% So you have desired phase I, phase II, phase III. 01:44:40.960 --> 01:44:43.260 align:middle line:84% You have these adjustments, and then you 01:44:43.260 --> 01:44:50.910 align:middle line:84% have the desired numbers entering the market that 01:44:50.910 --> 01:44:55.630 align:middle line:84% is coming from desired number of patented drugs in the market 01:44:55.630 --> 01:44:58.830 align:middle line:84% compared to the desired patent plus-- 01:44:58.830 --> 01:45:03.030 align:middle line:84% so this is the adjustment for this stock and expected patent 01:45:03.030 --> 01:45:04.950 align:middle line:90% expirations. 01:45:04.950 --> 01:45:09.210 align:middle line:84% So let's take a look at this formulation. 01:45:09.210 --> 01:45:12.910 align:middle line:90% 01:45:12.910 --> 01:45:16.830 align:middle line:84% So this is basically the standard replacement 01:45:16.830 --> 01:45:21.310 align:middle line:84% plus adjustment for the final stock that we have seen. 01:45:21.310 --> 01:45:26.670 align:middle line:84% And that works fine with the caveat 01:45:26.670 --> 01:45:29.630 align:middle line:84% that this is not the desired number of molecules 01:45:29.630 --> 01:45:30.890 align:middle line:90% entering the market. 01:45:30.890 --> 01:45:33.430 align:middle line:84% This is the number that is exiting and needs 01:45:33.430 --> 01:45:34.450 align:middle line:90% to be replaced. 01:45:34.450 --> 01:45:38.470 align:middle line:84% But to get to the desired that gets into the market, what 01:45:38.470 --> 01:45:41.350 align:middle line:90% do we need? 01:45:41.350 --> 01:45:43.950 align:middle line:90% What correction do we need? 01:45:43.950 --> 01:45:49.310 align:middle line:84% AUDIENCE: [INAUDIBLE] It doesn't for the supply. 01:45:49.310 --> 01:45:51.870 align:middle line:84% HAZHIR RAHMANDAD: So that you are adding later. 01:45:51.870 --> 01:45:53.870 align:middle line:84% AUDIENCE: You need this growth after the-- 01:45:53.870 --> 01:45:55.910 align:middle line:84% HAZHIR RAHMANDAD: And let's forget about growth. 01:45:55.910 --> 01:45:59.550 align:middle line:84% The growth factor, yes, is missing, but that's not-- it 01:45:59.550 --> 01:46:03.630 align:middle line:90% needs something more basic. 01:46:03.630 --> 01:46:05.490 align:middle line:84% Yeah, the success rates are missing. 01:46:05.490 --> 01:46:09.590 align:middle line:84% So if only 10% are succeeding, you 01:46:09.590 --> 01:46:15.430 align:middle line:84% need to multiply the exit rate of the drug getting out of-- 01:46:15.430 --> 01:46:23.670 align:middle line:84% expiring by 10 to start enough to get to replace 01:46:23.670 --> 01:46:25.990 align:middle line:90% the 10 that are expiring. 01:46:25.990 --> 01:46:28.132 align:middle line:84% AUDIENCE: I incorporated the success rates-- 01:46:28.132 --> 01:46:29.590 align:middle line:84% HAZHIR RAHMANDAD: In the last step? 01:46:29.590 --> 01:46:30.170 align:middle line:90% Ah, OK. 01:46:30.170 --> 01:46:33.950 align:middle line:84% AUDIENCE: --calculating the desired values for the stocks. 01:46:33.950 --> 01:46:38.526 align:middle line:84% HAZHIR RAHMANDAD: So desired values for the stocks-- 01:46:38.526 --> 01:46:40.765 align:middle line:90% AUDIENCE: I think it's up, up. 01:46:40.765 --> 01:46:41.890 align:middle line:90% HAZHIR RAHMANDAD: OK, good. 01:46:41.890 --> 01:46:43.250 align:middle line:90% So we'll get to that. 01:46:43.250 --> 01:46:44.930 align:middle line:90% But that is not enough. 01:46:44.930 --> 01:46:48.150 align:middle line:84% So even if the desired values are correctly 01:46:48.150 --> 01:46:51.750 align:middle line:84% accounting for that, the replacement-- so in equilibrium, 01:46:51.750 --> 01:46:55.030 align:middle line:84% the desired stocks will have their desired values. 01:46:55.030 --> 01:46:57.990 align:middle line:84% So all that is happening is the replacement. 01:46:57.990 --> 01:47:01.450 align:middle line:84% OK, the replacement, for every 10 that is going out, 01:47:01.450 --> 01:47:03.350 align:middle line:90% you need to start 100. 01:47:03.350 --> 01:47:07.150 align:middle line:84% That is not yet in the formulation. 01:47:07.150 --> 01:47:09.710 align:middle line:90% So that needs to be there. 01:47:09.710 --> 01:47:13.250 align:middle line:84% Then we can look at the desired values which are very important. 01:47:13.250 --> 01:47:15.870 align:middle line:84% So the first one is easy because that is coming directly 01:47:15.870 --> 01:47:19.030 align:middle line:90% from desired revenue. 01:47:19.030 --> 01:47:26.830 align:middle line:84% Then the desired phase III trials or-- 01:47:26.830 --> 01:47:31.590 align:middle line:84% yes, phase III trials, it's getting the input 01:47:31.590 --> 01:47:33.610 align:middle line:84% from the expected patent expiration. 01:47:33.610 --> 01:47:36.390 align:middle line:84% So that's the ultimate goal, which is good. 01:47:36.390 --> 01:47:41.040 align:middle line:84% But as we discussed, what is the problem with expected patent 01:47:41.040 --> 01:47:47.040 align:middle line:84% expirations is that it is looking at the empirical value 01:47:47.040 --> 01:47:48.640 align:middle line:90% rather than the goal. 01:47:48.640 --> 01:47:51.400 align:middle line:84% So it is adjusting towards what is already 01:47:51.400 --> 01:47:54.040 align:middle line:84% happening, which may not be aligned with your goal. 01:47:54.040 --> 01:47:57.620 align:middle line:84% So that's we saw that in Jason's model as well, 01:47:57.620 --> 01:48:00.740 align:middle line:84% accounting for that or putting that aside. 01:48:00.740 --> 01:48:06.960 align:middle line:84% Now for this one, we care about replacing the phase III success 01:48:06.960 --> 01:48:09.620 align:middle line:84% rate and the average phase III times. 01:48:09.620 --> 01:48:10.980 align:middle line:90% So this is a good formulation. 01:48:10.980 --> 01:48:13.840 align:middle line:84% It has expected patent expiration 01:48:13.840 --> 01:48:15.760 align:middle line:84% divided by success rate gives you 01:48:15.760 --> 01:48:20.640 align:middle line:84% the total inflow multiplied by average phase III time 01:48:20.640 --> 01:48:22.120 align:middle line:90% total stock. 01:48:22.120 --> 01:48:25.560 align:middle line:84% And then the rest are also following the same logic 01:48:25.560 --> 01:48:28.440 align:middle line:84% with the additional subtlety that now you 01:48:28.440 --> 01:48:31.560 align:middle line:84% have to multiply phase III and phase II success 01:48:31.560 --> 01:48:33.460 align:middle line:90% rates for the desired phase II. 01:48:33.460 --> 01:48:35.160 align:middle line:90% So this is important. 01:48:35.160 --> 01:48:38.360 align:middle line:84% In the version that Jason and a few others had-- 01:48:38.360 --> 01:48:40.720 align:middle line:90% I think Alban had it as well-- 01:48:40.720 --> 01:48:44.500 align:middle line:84% this cascade was happening inside the formulations, 01:48:44.500 --> 01:48:48.340 align:middle line:84% so each one was dividing by that success rate. 01:48:48.340 --> 01:48:51.760 align:middle line:84% And then the next one was dividing by that success rate. 01:48:51.760 --> 01:48:57.400 align:middle line:84% In this version, you are doing it explicitly in each step. 01:48:57.400 --> 01:49:01.200 align:middle line:84% Mathematically the same, no general preference 01:49:01.200 --> 01:49:02.300 align:middle line:90% for one or the other. 01:49:02.300 --> 01:49:03.560 align:middle line:90% Both are good. 01:49:03.560 --> 01:49:05.500 align:middle line:84% And so you're doing it well here. 01:49:05.500 --> 01:49:07.320 align:middle line:84% It's getting the right desired levels. 01:49:07.320 --> 01:49:10.160 align:middle line:90% 01:49:10.160 --> 01:49:11.760 align:middle line:84% And so when you get these desired 01:49:11.760 --> 01:49:14.420 align:middle line:84% levels, all of these stock adjustments down here, 01:49:14.420 --> 01:49:15.320 align:middle line:90% they work fine. 01:49:15.320 --> 01:49:19.480 align:middle line:84% They do what they need to do with the point 01:49:19.480 --> 01:49:22.340 align:middle line:84% that you brought up about the speed of adjustment. 01:49:22.340 --> 01:49:24.400 align:middle line:84% If you have a gap, you may actually 01:49:24.400 --> 01:49:27.000 align:middle line:84% inflate it to account for those failure 01:49:27.000 --> 01:49:29.920 align:middle line:90% rates that will happen as well. 01:49:29.920 --> 01:49:30.600 align:middle line:90% That's fair. 01:49:30.600 --> 01:49:32.300 align:middle line:90% That we could add here. 01:49:32.300 --> 01:49:33.140 align:middle line:90% Doesn't have it. 01:49:33.140 --> 01:49:35.240 align:middle line:90% But that's all right. 01:49:35.240 --> 01:49:37.760 align:middle line:84% You could incorporate that mental in the phase II 01:49:37.760 --> 01:49:40.440 align:middle line:84% adjustment times, but probably better to have it in the success 01:49:40.440 --> 01:49:41.920 align:middle line:90% rate. 01:49:41.920 --> 01:49:43.220 align:middle line:90% OK, so this is good. 01:49:43.220 --> 01:49:46.520 align:middle line:84% I think the stock adjustments are working very well here. 01:49:46.520 --> 01:49:50.560 align:middle line:84% The part that is missing is the correction for the success 01:49:50.560 --> 01:49:52.217 align:middle line:90% rate for the replacement. 01:49:52.217 --> 01:49:53.800 align:middle line:84% And then the other thing is the growth 01:49:53.800 --> 01:49:58.680 align:middle line:84% that I think every formulation so far has missed that. 01:49:58.680 --> 01:50:02.280 align:middle line:84% OK, let's now look at maybe one that does 01:50:02.280 --> 01:50:04.580 align:middle line:90% have the gross formulation. 01:50:04.580 --> 01:50:05.080 align:middle line:90% So-- 01:50:05.080 --> 01:50:07.680 align:middle line:90% 01:50:07.680 --> 01:50:09.860 align:middle line:84% AUDIENCE: I also have a good formulation in there. 01:50:09.860 --> 01:50:10.400 align:middle line:90% But-- 01:50:10.400 --> 01:50:12.483 align:middle line:84% HAZHIR RAHMANDAD: So what do you do for the gross? 01:50:12.483 --> 01:50:14.520 align:middle line:90% Tell us. 01:50:14.520 --> 01:50:19.280 align:middle line:84% AUDIENCE: I calculate the average revenue with the slope. 01:50:19.280 --> 01:50:20.520 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:50:20.520 --> 01:50:22.300 align:middle line:84% AUDIENCE: I added the desired growth rate. 01:50:22.300 --> 01:50:27.985 align:middle line:84% But the model doesn't behave the way we expected. 01:50:27.985 --> 01:50:29.360 align:middle line:84% HAZHIR RAHMANDAD: Yes, so you are 01:50:29.360 --> 01:50:31.520 align:middle line:84% calculating the average revenue from what 01:50:31.520 --> 01:50:33.000 align:middle line:90% is the current revenue. 01:50:33.000 --> 01:50:36.930 align:middle line:84% Then you are getting a target to get it to grow. 01:50:36.930 --> 01:50:39.850 align:middle line:84% And then, based on that, you get to the desired number 01:50:39.850 --> 01:50:41.090 align:middle line:90% of patented drugs. 01:50:41.090 --> 01:50:45.210 align:middle line:84% So that's very similar to, I think, Kathy's formulation 01:50:45.210 --> 01:50:48.550 align:middle line:84% that basically used the current revenue to set the target. 01:50:48.550 --> 01:50:50.770 align:middle line:84% And as we discussed there, that's 01:50:50.770 --> 01:50:54.150 align:middle line:90% conceptually correct and fine. 01:50:54.150 --> 01:50:57.410 align:middle line:84% It is closer to the real world than the alternative that makes 01:50:57.410 --> 01:50:59.970 align:middle line:90% the revenue target exogenous. 01:50:59.970 --> 01:51:02.610 align:middle line:84% It creates impetus for growth, so you 01:51:02.610 --> 01:51:04.510 align:middle line:90% will see growth in this model. 01:51:04.510 --> 01:51:07.970 align:middle line:84% But you wouldn't see matching of the desired 01:51:07.970 --> 01:51:12.090 align:middle line:84% and actual with these formulations. 01:51:12.090 --> 01:51:20.910 align:middle line:84% OK, so let's go to something that I built the other day. 01:51:20.910 --> 01:51:22.992 align:middle line:90% 01:51:22.992 --> 01:51:24.450 align:middle line:84% AUDIENCE: Can I ask you a question? 01:51:24.450 --> 01:51:25.530 align:middle line:90% HAZHIR RAHMANDAD: Sure. 01:51:25.530 --> 01:51:27.470 align:middle line:84% AUDIENCE: In terms of matching to the growth, 01:51:27.470 --> 01:51:31.610 align:middle line:84% even if you didn't have all of this top drug pipeline, 01:51:31.610 --> 01:51:35.090 align:middle line:90% it's just the stock cannot-- 01:51:35.090 --> 01:51:39.890 align:middle line:84% because it's always growing, does it even reach [INAUDIBLE]? 01:51:39.890 --> 01:51:41.870 align:middle line:84% HAZHIR RAHMANDAD: So that's the hard part. 01:51:41.870 --> 01:51:46.410 align:middle line:84% How can you set the initial-- the initiation rate so that it 01:51:46.410 --> 01:51:48.530 align:middle line:90% does match-- 01:51:48.530 --> 01:51:49.790 align:middle line:90% so that's the challenge. 01:51:49.790 --> 01:51:51.690 align:middle line:90% That's the whole point of the-- 01:51:51.690 --> 01:51:53.770 align:middle line:90% yeah, it is doable. 01:51:53.770 --> 01:51:55.870 align:middle line:84% If the question is, is it doable? 01:51:55.870 --> 01:51:57.630 align:middle line:90% Yes, the answer is yes. 01:51:57.630 --> 01:52:01.970 align:middle line:90% 01:52:01.970 --> 01:52:07.390 align:middle line:84% So this is what I put together yesterday. 01:52:07.390 --> 01:52:13.730 align:middle line:84% So here, you have basically the same basics very much. 01:52:13.730 --> 01:52:15.890 align:middle line:90% You're now all familiar with it. 01:52:15.890 --> 01:52:17.990 align:middle line:84% The desired revenue is exogenous. 01:52:17.990 --> 01:52:20.810 align:middle line:84% I'm right now driving it as a stock with some desired growth 01:52:20.810 --> 01:52:21.310 align:middle line:90% rate. 01:52:21.310 --> 01:52:24.250 align:middle line:84% You can drive it with an exogenous input 01:52:24.250 --> 01:52:29.230 align:middle line:84% like Alban's equation, which gives us desired drug. 01:52:29.230 --> 01:52:32.290 align:middle line:90% So all of that, very standard. 01:52:32.290 --> 01:52:37.130 align:middle line:84% Then we get to the desired adjustment 01:52:37.130 --> 01:52:41.670 align:middle line:84% for drugs in the market and desired adjustment for P3, P2, 01:52:41.670 --> 01:52:42.690 align:middle line:90% P1. 01:52:42.690 --> 01:52:47.130 align:middle line:84% And then you add them up as the total stock adjustment. 01:52:47.130 --> 01:52:53.130 align:middle line:84% You add that with the desired replacement for everything 01:52:53.130 --> 01:52:54.970 align:middle line:90% accounting for the growth. 01:52:54.970 --> 01:52:57.170 align:middle line:84% So we need to now go into the equations 01:52:57.170 --> 01:53:00.290 align:middle line:84% and understand how to account for growth. 01:53:00.290 --> 01:53:02.150 align:middle line:84% The rest is fairly straightforward. 01:53:02.150 --> 01:53:06.390 align:middle line:84% So we have the overall success rate here. 01:53:06.390 --> 01:53:09.030 align:middle line:90% Nothing to worry about. 01:53:09.030 --> 01:53:11.770 align:middle line:90% 01:53:11.770 --> 01:53:14.610 align:middle line:90% Then-- 01:53:14.610 --> 01:53:16.830 align:middle line:84% AUDIENCE: What are the desired phases, again? 01:53:16.830 --> 01:53:17.490 align:middle line:90% I'm sorry. 01:53:17.490 --> 01:53:19.407 align:middle line:84% HAZHIR RAHMANDAD: What are the desired phases? 01:53:19.407 --> 01:53:21.170 align:middle line:90% AUDIENCE: Yeah, is it just-- 01:53:21.170 --> 01:53:24.770 align:middle line:84% HAZHIR RAHMANDAD: We should go into the equations. 01:53:24.770 --> 01:53:28.890 align:middle line:84% So they are a little bit more complex but very similar 01:53:28.890 --> 01:53:30.620 align:middle line:90% to what you see-- 01:53:30.620 --> 01:53:33.260 align:middle line:90% you just saw. 01:53:33.260 --> 01:53:36.520 align:middle line:84% So let's first look at the replacement factor for growth. 01:53:36.520 --> 01:53:38.540 align:middle line:84% This is probably the more complex equation 01:53:38.540 --> 01:53:39.600 align:middle line:90% than the new equation. 01:53:39.600 --> 01:53:42.460 align:middle line:84% So this is trying to account for what 01:53:42.460 --> 01:53:46.980 align:middle line:84% you need to adjust to get the growth that is needed. 01:53:46.980 --> 01:53:52.560 align:middle line:84% And the formulation for it is, for each of the stocks, 01:53:52.560 --> 01:53:58.980 align:middle line:84% for each of the stages, you have 1 plus the duration multiplied 01:53:58.980 --> 01:54:02.260 align:middle line:84% by the desired growth rate or the perceived desired growth 01:54:02.260 --> 01:54:03.180 align:middle line:90% rate. 01:54:03.180 --> 01:54:08.980 align:middle line:84% So if my growth rate is 5% per year 01:54:08.980 --> 01:54:13.880 align:middle line:84% and that stage takes two years, that adds a 10%, 01:54:13.880 --> 01:54:20.140 align:middle line:84% 0.1, to 1 for expansion that comes from that stage. 01:54:20.140 --> 01:54:22.700 align:middle line:84% And then you multiply that for the expansion that 01:54:22.700 --> 01:54:25.900 align:middle line:84% comes from the next stage and the next stage 01:54:25.900 --> 01:54:30.420 align:middle line:84% and the final duration in the market stage. 01:54:30.420 --> 01:54:35.980 align:middle line:84% So those expansion factors are the drivers 01:54:35.980 --> 01:54:41.740 align:middle line:84% of what the total expansion needs 01:54:41.740 --> 01:54:51.180 align:middle line:84% to be to get the desired replacement so 01:54:51.180 --> 01:54:55.100 align:middle line:84% that 10 years from now we have enough coming in. 01:54:55.100 --> 01:54:57.860 align:middle line:84% Now, the question is where did I get these numbers from, 01:54:57.860 --> 01:55:00.300 align:middle line:90% these formulations from? 01:55:00.300 --> 01:55:05.300 align:middle line:84% So at the heart of that, it might be easier actually 01:55:05.300 --> 01:55:07.040 align:middle line:90% to look at one of these. 01:55:07.040 --> 01:55:10.340 align:middle line:90% 01:55:10.340 --> 01:55:12.640 align:middle line:84% Let me see which of these desired. 01:55:12.640 --> 01:55:14.640 align:middle line:90% So this one is easy. 01:55:14.640 --> 01:55:18.780 align:middle line:84% So sorry, the desired drugs is easy 01:55:18.780 --> 01:55:21.420 align:middle line:84% because it is the current value that you won't have. 01:55:21.420 --> 01:55:26.660 align:middle line:84% So desired P3 drugs is probably a good one to look at. 01:55:26.660 --> 01:55:33.900 align:middle line:84% So desired P3 drugs is desired drugs divided 01:55:33.900 --> 01:55:35.520 align:middle line:90% protected duration in market. 01:55:35.520 --> 01:55:38.900 align:middle line:84% So this is the total desired rate 01:55:38.900 --> 01:55:44.380 align:middle line:84% of exit of drugs from the market. 01:55:44.380 --> 01:55:47.320 align:middle line:84% We divide that by the P3 success rate. 01:55:47.320 --> 01:55:50.400 align:middle line:84% So this far, very similar to what you have already done. 01:55:50.400 --> 01:55:53.240 align:middle line:84% You're just expanding it to account for the success rate. 01:55:53.240 --> 01:55:56.020 align:middle line:84% You multiply that by the duration. 01:55:56.020 --> 01:55:58.340 align:middle line:84% Now we get to the last part, which 01:55:58.340 --> 01:56:03.460 align:middle line:84% is the expansion for the growth for-- 01:56:03.460 --> 01:56:13.860 align:middle line:84% when this is going in, it needs to account for the extra 01:56:13.860 --> 01:56:19.220 align:middle line:84% that it needs to give in so that during the period of markets 01:56:19.220 --> 01:56:20.420 align:middle line:90% being-- 01:56:20.420 --> 01:56:25.950 align:middle line:84% drugs being in the market, protected duration in market, 01:56:25.950 --> 01:56:32.390 align:middle line:84% you grow it enough to get the outflow rate that you want. 01:56:32.390 --> 01:56:37.970 align:middle line:84% This is where the formulation that Ross had comes in. 01:56:37.970 --> 01:56:42.430 align:middle line:90% So basically, the core idea is-- 01:56:42.430 --> 01:56:48.590 align:middle line:84% actually, maybe it is easier to do it in some. 01:56:48.590 --> 01:56:51.970 align:middle line:90% So we have the stock. 01:56:51.970 --> 01:56:55.190 align:middle line:90% 01:56:55.190 --> 01:56:58.610 align:middle line:90% Outflow, inflow. 01:56:58.610 --> 01:57:01.310 align:middle line:90% 01:57:01.310 --> 01:57:04.110 align:middle line:90% And the stock s. 01:57:04.110 --> 01:57:07.470 align:middle line:84% What we want is that, this stock, 01:57:07.470 --> 01:57:11.230 align:middle line:84% we want it to grow with a growth rate of g. 01:57:11.230 --> 01:57:23.590 align:middle line:84% So ds to dt is gs, which is I minus O. 01:57:23.590 --> 01:57:31.750 align:middle line:90% Now this has I minus-- whoops. 01:57:31.750 --> 01:57:41.030 align:middle line:90% 01:57:41.030 --> 01:57:44.670 align:middle line:90% So, yeah, OK. 01:57:44.670 --> 01:57:48.790 align:middle line:84% So we could write it in terms of s. 01:57:48.790 --> 01:57:56.430 align:middle line:90% So it would be s divided by tau. 01:57:56.430 --> 01:58:03.870 align:middle line:84% And then if we turn i into some multiple of O. So let's 01:58:03.870 --> 01:58:12.870 align:middle line:84% say it is some kO equals I. That is, if k equals 1, 01:58:12.870 --> 01:58:14.470 align:middle line:90% we are in equilibrium. 01:58:14.470 --> 01:58:26.990 align:middle line:84% A larger k then it becomes ks over tau minus s over tau 01:58:26.990 --> 01:58:30.750 align:middle line:90% equals gs. 01:58:30.750 --> 01:58:33.430 align:middle line:90% So s's is cancel out. 01:58:33.430 --> 01:58:45.590 align:middle line:84% So k-- so it could take 1 over tau out. 01:58:45.590 --> 01:58:49.950 align:middle line:90% k minus 1 equals g. 01:58:49.950 --> 01:58:59.550 align:middle line:84% Therefore, k equals g tau plus 1. 01:58:59.550 --> 01:59:04.750 align:middle line:84% So this is telling you what the inflow should be so 01:59:04.750 --> 01:59:07.430 align:middle line:84% that the stock can grow exponentially 01:59:07.430 --> 01:59:08.910 align:middle line:90% with the rate of g. 01:59:08.910 --> 01:59:12.270 align:middle line:84% So if your desired growth rate is g, 01:59:12.270 --> 01:59:17.210 align:middle line:84% the factor that goes into the inflow should be this factor. 01:59:17.210 --> 01:59:20.370 align:middle line:90% 01:59:20.370 --> 01:59:21.870 align:middle line:84% AUDIENCE: But this requires that you 01:59:21.870 --> 01:59:26.230 align:middle line:84% assume that you can write down the outflow as some multiple. 01:59:26.230 --> 01:59:30.270 align:middle line:84% Or you can write down the inflow as some multiple of outflow. 01:59:30.270 --> 01:59:33.190 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:59:33.190 --> 01:59:39.630 align:middle line:90% And if it is a variable-- 01:59:39.630 --> 01:59:43.790 align:middle line:84% if it is a function-- so if k is a function of time, 01:59:43.790 --> 01:59:46.807 align:middle line:90% it could be k of time or k of s. 01:59:46.807 --> 01:59:48.390 align:middle line:84% But this way, you see that it actually 01:59:48.390 --> 01:59:51.710 align:middle line:84% doesn't depend on time or s or anything. 01:59:51.710 --> 01:59:55.230 align:middle line:84% And therefore, it becomes a nice constant that you can use, 01:59:55.230 --> 01:59:59.550 align:middle line:84% and it will give you an exponential growth in the stock. 01:59:59.550 --> 02:00:01.930 align:middle line:84% Now, you didn't know that when you wrote the k. 02:00:01.930 --> 02:00:05.270 align:middle line:84% So this k could be a function of a lot of things. 02:00:05.270 --> 02:00:09.323 align:middle line:84% But the way it came out was that it is a simple thing. 02:00:09.323 --> 02:00:10.990 align:middle line:84% AUDIENCE: Because it's a linear system-- 02:00:10.990 --> 02:00:13.230 align:middle line:84% HAZHIR RAHMANDAD: Because it is linear-- 02:00:13.230 --> 02:00:18.080 align:middle line:84% because of the first-order differential equation solution 02:00:18.080 --> 02:00:24.360 align:middle line:84% that says if stock is growing exponentially, 02:00:24.360 --> 02:00:26.680 align:middle line:84% the net flow is also growing exponentially 02:00:26.680 --> 02:00:27.780 align:middle line:90% with the same rate. 02:00:27.780 --> 02:00:30.540 align:middle line:84% So that's really at the heart of why this formulation, 02:00:30.540 --> 02:00:32.580 align:middle line:90% this factor works out. 02:00:32.580 --> 02:00:35.320 align:middle line:90% 02:00:35.320 --> 02:00:37.480 align:middle line:84% AUDIENCE: Does this also cover if the growth 02:00:37.480 --> 02:00:38.660 align:middle line:90% rate is exponential? 02:00:38.660 --> 02:00:40.840 align:middle line:90% If it is, then-- 02:00:40.840 --> 02:00:42.560 align:middle line:84% HAZHIR RAHMANDAD: No, then the g will 02:00:42.560 --> 02:00:46.060 align:middle line:84% be changing over time because, as you grow, 02:00:46.060 --> 02:00:48.760 align:middle line:84% the fractional growth rate goes down. 02:00:48.760 --> 02:00:54.940 align:middle line:84% So if you make the g time variant and account for that, 02:00:54.940 --> 02:00:56.300 align:middle line:90% then it probably works. 02:00:56.300 --> 02:01:00.560 align:middle line:84% I haven't tested it explicitly, but I think it probably works. 02:01:00.560 --> 02:01:06.920 align:middle line:84% But then you have a moving g that accounts for it. 02:01:06.920 --> 02:01:09.440 align:middle line:90% OK, so this is actually-- 02:01:09.440 --> 02:01:14.560 align:middle line:84% gives you a very simple solution to the problem of OK, 02:01:14.560 --> 02:01:18.680 align:middle line:84% what should be the inflow expansion factor 02:01:18.680 --> 02:01:21.560 align:middle line:84% to make the stock grow exponentially? 02:01:21.560 --> 02:01:25.200 align:middle line:84% Now I have created this inflow expansion factor. 02:01:25.200 --> 02:01:28.920 align:middle line:84% We can go back to the formulation. 02:01:28.920 --> 02:01:33.360 align:middle line:84% So this is the inflow expansion factor for-- 02:01:33.360 --> 02:01:37.640 align:middle line:84% drugs in phase III is coming from the-- so this 02:01:37.640 --> 02:01:42.240 align:middle line:84% is the P2 success versus P3 success. 02:01:42.240 --> 02:01:44.000 align:middle line:90% Sorry. 02:01:44.000 --> 02:01:45.960 align:middle line:90% Yes. 02:01:45.960 --> 02:01:58.040 align:middle line:84% OK, so now, going back to this desired P3, so desired P3. 02:01:58.040 --> 02:02:06.200 align:middle line:84% Now you can see, it is based on the desired inflow-- 02:02:06.200 --> 02:02:13.840 align:middle line:84% desired outflow being expanded to account for the next step's 02:02:13.840 --> 02:02:15.000 align:middle line:90% growth rate. 02:02:15.000 --> 02:02:20.680 align:middle line:84% That is, this term is saying, in the next step, 02:02:20.680 --> 02:02:23.640 align:middle line:84% you need to expand things by this much. 02:02:23.640 --> 02:02:26.880 align:middle line:84% Therefore, the outflow of phase III 02:02:26.880 --> 02:02:29.640 align:middle line:84% should have that expansion built into it, which is 02:02:29.640 --> 02:02:31.760 align:middle line:90% the inflow of the next phase. 02:02:31.760 --> 02:02:33.640 align:middle line:90% And then you get that. 02:02:33.640 --> 02:02:35.020 align:middle line:90% You go backwards. 02:02:35.020 --> 02:02:39.680 align:middle line:90% You go to the desired phase II. 02:02:39.680 --> 02:02:45.440 align:middle line:84% It starts with desired P3 drugs which already have this factor 02:02:45.440 --> 02:02:50.480 align:middle line:84% and then multiplies it by this factor for the phase IIIs 02:02:50.480 --> 02:02:51.720 align:middle line:90% duration. 02:02:51.720 --> 02:02:55.640 align:middle line:84% And then the next one does the same expansion 02:02:55.640 --> 02:02:59.400 align:middle line:90% for phase II and phase I. 02:02:59.400 --> 02:03:01.520 align:middle line:90% So that's where the-- 02:03:01.520 --> 02:03:02.520 align:middle line:90% Alexander. 02:03:02.520 --> 02:03:05.380 align:middle line:84% AUDIENCE: I was confused why you divide it by P3 duration, 02:03:05.380 --> 02:03:07.760 align:middle line:84% but now I see that that's the equilibrium. 02:03:07.760 --> 02:03:09.820 align:middle line:84% HAZHIR RAHMANDAD: Yes, that's to get to there. 02:03:09.820 --> 02:03:12.000 align:middle line:84% AUDIENCE: Why do you need to multiply by the factor 02:03:12.000 --> 02:03:13.643 align:middle line:84% again here if you've already done it? 02:03:13.643 --> 02:03:15.310 align:middle line:84% HAZHIR RAHMANDAD: This is for the next-- 02:03:15.310 --> 02:03:17.390 align:middle line:90% this is for P3 duration. 02:03:17.390 --> 02:03:20.090 align:middle line:84% So the previous one was accounting, 02:03:20.090 --> 02:03:21.950 align:middle line:90% so let's go back to the P3. 02:03:21.950 --> 02:03:27.410 align:middle line:84% So the P3 desired stock is looking at the P3 success rate. 02:03:27.410 --> 02:03:30.770 align:middle line:84% But a P3 success rate that allows drugs in 02:03:30.770 --> 02:03:34.750 align:middle line:84% market to grow with the desired factor, 02:03:34.750 --> 02:03:39.130 align:middle line:84% that is, to grow exponentially with the desired growth rate. 02:03:39.130 --> 02:03:42.450 align:middle line:84% So for drugs in market to grow exponentially, 02:03:42.450 --> 02:03:48.770 align:middle line:84% you need 1 plus this protected duration in market 02:03:48.770 --> 02:03:52.970 align:middle line:90% multiplied by the growth rate. 02:03:52.970 --> 02:03:57.690 align:middle line:84% So rather than patent expiry, it should be really 02:03:57.690 --> 02:04:04.330 align:middle line:84% patent expiry expanded to account for that factor. 02:04:04.330 --> 02:04:06.810 align:middle line:84% AUDIENCE: I didn't understand at all. 02:04:06.810 --> 02:04:08.570 align:middle line:90% I'm just confused why you're-- 02:04:08.570 --> 02:04:10.410 align:middle line:90% I was confused why-- 02:04:10.410 --> 02:04:13.490 align:middle line:84% because you necessarily need drugs in phase 02:04:13.490 --> 02:04:15.690 align:middle line:90% III to be growing [INAUDIBLE]. 02:04:15.690 --> 02:04:17.330 align:middle line:90% HAZHIR RAHMANDAD: Yes. 02:04:17.330 --> 02:04:21.970 align:middle line:84% So once you want something to grow exponentially 02:04:21.970 --> 02:04:24.530 align:middle line:84% in this system, everything needs to grow exponentially 02:04:24.530 --> 02:04:25.630 align:middle line:90% in this system. 02:04:25.630 --> 02:04:28.810 align:middle line:84% Basically, because the net flow-- all of these net flows 02:04:28.810 --> 02:04:31.890 align:middle line:84% are growing exponentially with the same rate, 02:04:31.890 --> 02:04:36.050 align:middle line:84% same rate of growth for the stocks 02:04:36.050 --> 02:04:39.210 align:middle line:84% to be able to grow exponentially. 02:04:39.210 --> 02:04:40.850 align:middle line:84% AUDIENCE: And why is that not accounted 02:04:40.850 --> 02:04:45.430 align:middle line:84% for when you had that growth factor in the desired P3 drugs? 02:04:45.430 --> 02:04:49.410 align:middle line:84% HAZHIR RAHMANDAD: So in the desired P3 drugs in here, 02:04:49.410 --> 02:04:54.930 align:middle line:84% I only accounted for what this P3 success should be 02:04:54.930 --> 02:04:59.530 align:middle line:90% compared to the patent expiry. 02:04:59.530 --> 02:05:01.930 align:middle line:84% Because this needs to be bigger than patent 02:05:01.930 --> 02:05:04.410 align:middle line:90% expiry for this guy to grow. 02:05:04.410 --> 02:05:09.250 align:middle line:84% And then I calculated based on that P3 success that results, 02:05:09.250 --> 02:05:11.690 align:middle line:84% what should be the stock of drugs in P3? 02:05:11.690 --> 02:05:14.050 align:middle line:84% So that part was what you already had seen. 02:05:14.050 --> 02:05:16.790 align:middle line:84% In a lot of other formulations that you had, 02:05:16.790 --> 02:05:21.570 align:middle line:84% you had that calculation that you get the outflow P3 success, 02:05:21.570 --> 02:05:23.430 align:middle line:90% but the desired value of it. 02:05:23.430 --> 02:05:25.330 align:middle line:84% And I'm using the desired values based 02:05:25.330 --> 02:05:27.090 align:middle line:84% on the desired drugs in market, not 02:05:27.090 --> 02:05:31.850 align:middle line:84% the actual so that accounts for the other issue that we saw. 02:05:31.850 --> 02:05:37.610 align:middle line:84% Similarly, for-- but then, when I get into desired P2, 02:05:37.610 --> 02:05:40.890 align:middle line:84% I need to get it based on P2 success 02:05:40.890 --> 02:05:47.850 align:middle line:84% and P2 success should account for the duration of phase III. 02:05:47.850 --> 02:05:52.610 align:middle line:84% So it now has the 1 plus phase III duration multiplied 02:05:52.610 --> 02:05:59.650 align:middle line:84% by the growth rate added to it so that the P2 success is larger 02:05:59.650 --> 02:06:00.910 align:middle line:90% enough, large-- 02:06:00.910 --> 02:06:04.650 align:middle line:84% is bigger than P3 success so that the drugs in P3 02:06:04.650 --> 02:06:07.540 align:middle line:90% can grow exponentially. 02:06:07.540 --> 02:06:10.000 align:middle line:84% AUDIENCE: Yeah, I guess I'm just confused. 02:06:10.000 --> 02:06:12.360 align:middle line:90% So right, this is all-- 02:06:12.360 --> 02:06:15.220 align:middle line:84% I guess I'm just confused as to why-- 02:06:15.220 --> 02:06:18.720 align:middle line:84% OK, so I get that you want the stocks to grow at a rate of g, 02:06:18.720 --> 02:06:19.720 align:middle line:90% the intermediate stocks. 02:06:19.720 --> 02:06:21.000 align:middle line:90% But I'm just confused. 02:06:21.000 --> 02:06:24.700 align:middle line:90% 02:06:24.700 --> 02:06:29.020 align:middle line:84% And that's not a common for when you calculate desired P3 drugs? 02:06:29.020 --> 02:06:30.280 align:middle line:90% I get how you calculated it. 02:06:30.280 --> 02:06:32.040 align:middle line:90% But if-- 02:06:32.040 --> 02:06:34.980 align:middle line:84% HAZHIR RAHMANDAD: So when I'm calculating desired P3 stocks, 02:06:34.980 --> 02:06:38.900 align:middle line:84% I didn't look at the P3 duration at all, 02:06:38.900 --> 02:06:41.220 align:middle line:90% that is, the adjustment-- 02:06:41.220 --> 02:06:44.660 align:middle line:84% the difference between P3 success and P2 success. 02:06:44.660 --> 02:06:49.200 align:middle line:84% So P3 success is going to be smaller than P2 success 02:06:49.200 --> 02:06:53.020 align:middle line:84% if we want drugs in P3, in phase III, to grow. 02:06:53.020 --> 02:06:57.260 align:middle line:84% That was not part of the calculation of the desired P3 02:06:57.260 --> 02:06:58.620 align:middle line:90% drugs. 02:06:58.620 --> 02:07:00.440 align:middle line:84% AUDIENCE: So then-- just out of curiosity, 02:07:00.440 --> 02:07:01.898 align:middle line:84% for the sake of understanding, what 02:07:01.898 --> 02:07:05.420 align:middle line:84% happens if you don't account for it in the desired phase II? 02:07:05.420 --> 02:07:07.300 align:middle line:84% HAZHIR RAHMANDAD: So basically, we 02:07:07.300 --> 02:07:11.620 align:middle line:84% underestimate the drugs in the pipeline in the phase II 02:07:11.620 --> 02:07:13.380 align:middle line:90% that are desired. 02:07:13.380 --> 02:07:16.620 align:middle line:84% In this model, it means the initialization will not 02:07:16.620 --> 02:07:18.780 align:middle line:90% be in equilibrium. 02:07:18.780 --> 02:07:24.420 align:middle line:84% And it also means if you have any out-of-equilibrium dynamics, 02:07:24.420 --> 02:07:26.080 align:middle line:90% it will not work. 02:07:26.080 --> 02:07:27.820 align:middle line:90% It wouldn't close the gap. 02:07:27.820 --> 02:07:31.780 align:middle line:84% And in fact, it will create a steady-state problem 02:07:31.780 --> 02:07:36.620 align:middle line:84% if you do it that way because you're always 02:07:36.620 --> 02:07:39.300 align:middle line:84% lacking lagging in how many drugs 02:07:39.300 --> 02:07:44.820 align:middle line:84% you try to have in P2 stock or in P3 stock. 02:07:44.820 --> 02:07:47.900 align:middle line:84% So it will lead to a steady-state error in the growth 02:07:47.900 --> 02:07:49.460 align:middle line:90% rate. 02:07:49.460 --> 02:07:56.100 align:middle line:84% So now you get these steps, how they are coming together. 02:07:56.100 --> 02:08:00.620 align:middle line:84% I actually have something that is not the best formulation 02:08:00.620 --> 02:08:01.120 align:middle line:90% here. 02:08:01.120 --> 02:08:06.900 align:middle line:84% And that is I'm using the patent expiry to drive the drug 02:08:06.900 --> 02:08:10.620 align:middle line:90% replacement with growth. 02:08:10.620 --> 02:08:12.740 align:middle line:84% I could use the same thing that I used actually 02:08:12.740 --> 02:08:19.100 align:middle line:84% in the phase II drugs, which is the desired drugs 02:08:19.100 --> 02:08:24.780 align:middle line:84% p divided by protected duration in market. 02:08:24.780 --> 02:08:26.960 align:middle line:84% The difference in equilibrium is nothing 02:08:26.960 --> 02:08:29.900 align:middle line:84% because, in equilibrium, we're starting from the right value 02:08:29.900 --> 02:08:31.700 align:middle line:90% for the desired drugs p. 02:08:31.700 --> 02:08:34.540 align:middle line:84% But if we start out of equilibrium, 02:08:34.540 --> 02:08:37.940 align:middle line:84% then this patent expiry at the beginning gives the wrong-- 02:08:37.940 --> 02:08:42.140 align:middle line:84% or kind of under- or overestimated replacement rate. 02:08:42.140 --> 02:08:45.020 align:middle line:84% So a better formulation here would 02:08:45.020 --> 02:08:49.480 align:middle line:90% be to use what we had there. 02:08:49.480 --> 02:08:56.420 align:middle line:90% 02:08:56.420 --> 02:08:59.220 align:middle line:90% Yes. 02:08:59.220 --> 02:09:00.340 align:middle line:90% AUDIENCE: Makes sense. 02:09:00.340 --> 02:09:05.528 align:middle line:84% HAZHIR RAHMANDAD: So is the logic fairly clear now? 02:09:05.528 --> 02:09:07.070 align:middle line:84% AUDIENCE: I know I was getting into-- 02:09:07.070 --> 02:09:09.023 align:middle line:84% HAZHIR RAHMANDAD: No, no, it's good. 02:09:09.023 --> 02:09:11.190 align:middle line:84% AUDIENCE: So when you're calculating the replacement 02:09:11.190 --> 02:09:16.270 align:middle line:84% factor for the patent expiry, why is it not just 1 02:09:16.270 --> 02:09:19.330 align:middle line:84% plus g times drug development cycle. 02:09:19.330 --> 02:09:21.570 align:middle line:84% Why are you multiplying all the factors all together? 02:09:21.570 --> 02:09:24.030 align:middle line:84% HAZHIR RAHMANDAD: Very good question. 02:09:24.030 --> 02:09:28.710 align:middle line:90% Basically, if you write the-- 02:09:28.710 --> 02:09:32.670 align:middle line:84% if you try to do it that way, you just 02:09:32.670 --> 02:09:38.130 align:middle line:84% get the wrong answer because this is not a first-order delay. 02:09:38.130 --> 02:09:39.790 align:middle line:84% So that would assume a first-order 02:09:39.790 --> 02:09:44.630 align:middle line:84% delay, From a start to the very end 02:09:44.630 --> 02:09:51.070 align:middle line:84% whereas this is a fourth-order delay. 02:09:51.070 --> 02:09:53.750 align:middle line:84% And therefore, the multiplication factor 02:09:53.750 --> 02:09:59.470 align:middle line:84% needs to break down to factors coming from each of those four 02:09:59.470 --> 02:10:01.853 align:middle line:90% steps coming together. 02:10:01.853 --> 02:10:03.770 align:middle line:84% AUDIENCE: Which factors are you talking about? 02:10:03.770 --> 02:10:05.970 align:middle line:84% HAZHIR RAHMANDAD: So these are the factors you saw. 02:10:05.970 --> 02:10:09.330 align:middle line:84% For example, in the desired drug P3, 02:10:09.330 --> 02:10:13.190 align:middle line:84% you had 1 plus perceived growth rate or desired growth 02:10:13.190 --> 02:10:15.690 align:middle line:84% rate multiplied by projected duration in market. 02:10:15.690 --> 02:10:17.530 align:middle line:84% That's the projected duration in market. 02:10:17.530 --> 02:10:21.170 align:middle line:84% Then you have the P3 factor, P2 factor, and P1 factor. 02:10:21.170 --> 02:10:23.590 align:middle line:84% We multiplied all those four with each other 02:10:23.590 --> 02:10:25.970 align:middle line:84% into this replacement factor for growth. 02:10:25.970 --> 02:10:31.030 align:middle line:84% So this weird-- this complex-looking formulation 02:10:31.030 --> 02:10:34.910 align:middle line:84% is just multiplication of those four factors. 02:10:34.910 --> 02:10:37.090 align:middle line:84% It was overwhelming when we saw it first. 02:10:37.090 --> 02:10:40.470 align:middle line:84% But when you go through the steps, you see that each of them 02:10:40.470 --> 02:10:45.110 align:middle line:84% is fairly straightforward why you need that expansion factor. 02:10:45.110 --> 02:10:48.870 align:middle line:84% And so the way it works is basically it is saying, 02:10:48.870 --> 02:10:55.790 align:middle line:84% this P3 success needs to be the first or the last component 02:10:55.790 --> 02:10:58.730 align:middle line:90% bigger than the patent expiry. 02:10:58.730 --> 02:11:03.750 align:middle line:84% P2 success to P3 success needs the next multiplier. 02:11:03.750 --> 02:11:05.630 align:middle line:90% P1 success, P2-- 02:11:05.630 --> 02:11:08.030 align:middle line:84% P2 success has the next component. 02:11:08.030 --> 02:11:11.370 align:middle line:84% And then P1 is start, so P1 success has the last one. 02:11:11.370 --> 02:11:13.790 align:middle line:84% So that's how these four come together 02:11:13.790 --> 02:11:17.190 align:middle line:84% to tell you how much you need to start at the beginning to get 02:11:17.190 --> 02:11:20.230 align:middle line:90% the right level at the end. 02:11:20.230 --> 02:11:24.110 align:middle line:84% OK, so now you can simulate this model. 02:11:24.110 --> 02:11:29.710 align:middle line:84% And hopefully, I didn't break something. 02:11:29.710 --> 02:11:31.190 align:middle line:90% AUDIENCE: [INAUDIBLE]? 02:11:31.190 --> 02:11:33.570 align:middle line:84% HAZHIR RAHMANDAD: So good question. 02:11:33.570 --> 02:11:35.030 align:middle line:84% So we have these stock adjustments 02:11:35.030 --> 02:11:36.670 align:middle line:90% that are very stochastic. 02:11:36.670 --> 02:11:39.190 align:middle line:84% And that is actually a good reassuring thing for me 02:11:39.190 --> 02:11:41.870 align:middle line:84% when I saw it because I know this means 02:11:41.870 --> 02:11:43.710 align:middle line:90% the numbers are very small. 02:11:43.710 --> 02:11:46.290 align:middle line:84% So this is 10 to the power of minus 13. 02:11:46.290 --> 02:11:49.870 align:middle line:84% So it is basically saying, stock adjustment is 0. 02:11:49.870 --> 02:11:51.950 align:middle line:90% It's just numerical. 02:11:51.950 --> 02:11:55.110 align:middle line:84% So that means, great, I have started from equilibrium 02:11:55.110 --> 02:11:57.960 align:middle line:84% without any need for adjusting anything. 02:11:57.960 --> 02:12:04.080 align:middle line:84% And in fact, all of the stock adjustments are basically 0. 02:12:04.080 --> 02:12:07.880 align:middle line:84% And now you can see that the drugs in market 02:12:07.880 --> 02:12:14.620 align:middle line:84% versus those in different phases are all growing exponentially. 02:12:14.620 --> 02:12:17.980 align:middle line:84% But they are growing with the same rate. 02:12:17.980 --> 02:12:21.152 align:middle line:84% But because they are at different points, 02:12:21.152 --> 02:12:22.860 align:middle line:84% they look very different from each other. 02:12:22.860 --> 02:12:25.580 align:middle line:84% In fact, if you expand the growth rate 02:12:25.580 --> 02:12:29.960 align:middle line:84% and you can make it even much larger, the system will be-- 02:12:29.960 --> 02:12:34.440 align:middle line:84% this is 10% per month, which is a huge growth rate. 02:12:34.440 --> 02:12:37.060 align:middle line:84% So they would look really different from each other. 02:12:37.060 --> 02:12:41.440 align:middle line:84% So drugs in phase III and drugs in market 02:12:41.440 --> 02:12:44.640 align:middle line:84% are now much smaller than the numbers 02:12:44.640 --> 02:12:47.980 align:middle line:84% you are seeing for phase I because of the delay. 02:12:47.980 --> 02:12:50.760 align:middle line:90% So a phase I-- 02:12:50.760 --> 02:12:54.400 align:middle line:90% so to get to these-- 02:12:54.400 --> 02:13:00.080 align:middle line:84% so here, we have drugs in the market that go up to 200,000-ish 02:13:00.080 --> 02:13:00.880 align:middle line:90% by the end. 02:13:00.880 --> 02:13:07.340 align:middle line:84% To be able to get to 200,000-ish by the end, you need phase I-- 02:13:07.340 --> 02:13:10.760 align:middle line:90% 02:13:10.760 --> 02:13:12.800 align:middle line:84% or maybe looking at the flows are 02:13:12.800 --> 02:13:16.440 align:middle line:84% better because exploration because the time in the market-- 02:13:16.440 --> 02:13:18.060 align:middle line:84% I mean, doesn't make a big difference. 02:13:18.060 --> 02:13:20.880 align:middle line:84% So this one is in the hundred million 02:13:20.880 --> 02:13:24.260 align:middle line:84% range, partly because of the success rate. 02:13:24.260 --> 02:13:25.840 align:middle line:84% But the bigger impact is actually, 02:13:25.840 --> 02:13:28.440 align:middle line:84% because of this fast growth rate, 02:13:28.440 --> 02:13:33.840 align:middle line:84% it is saying if you want to grow 10% a month 20 months from now, 02:13:33.840 --> 02:13:37.620 align:middle line:84% you actually need to start 10 times more or something-- 02:13:37.620 --> 02:13:41.320 align:middle line:84% I mean, you do the rule of 70, you 02:13:41.320 --> 02:13:45.940 align:middle line:84% can get a quick approximation of how much more you need to start. 02:13:45.940 --> 02:13:49.240 align:middle line:90% But that's the idea. 02:13:49.240 --> 02:13:51.520 align:middle line:84% AUDIENCE: So general process question. 02:13:51.520 --> 02:13:56.700 align:middle line:84% How in the world should we have come up with this? 02:13:56.700 --> 02:13:58.602 align:middle line:84% I'm not saying that the question was like-- 02:13:58.602 --> 02:14:00.560 align:middle line:84% I could've done this for a year, and I probably 02:14:00.560 --> 02:14:01.852 align:middle line:90% wouldn't have done this, like-- 02:14:01.852 --> 02:14:04.920 align:middle line:84% HAZHIR RAHMANDAD: Well, that's the point of this class. 02:14:04.920 --> 02:14:10.200 align:middle line:84% Next week, you can do it in one week. 02:14:10.200 --> 02:14:12.480 align:middle line:84% AUDIENCE: How do you approach problems like this? 02:14:12.480 --> 02:14:17.040 align:middle line:84% HAZHIR RAHMANDAD: OK, so I'm designing things that definitely 02:14:17.040 --> 02:14:18.840 align:middle line:90% have new components for you. 02:14:18.840 --> 02:14:22.100 align:middle line:84% So almost no week, you come here and you say, 02:14:22.100 --> 02:14:25.860 align:middle line:84% OK, this was trivial, but it is not also something that you say, 02:14:25.860 --> 02:14:27.940 align:middle line:84% I have no idea even how to start. 02:14:27.940 --> 02:14:33.720 align:middle line:84% So the goal for me is to get you to think about things that you 02:14:33.720 --> 02:14:36.673 align:middle line:84% haven't thought about when you have been modeling in the past. 02:14:36.673 --> 02:14:38.840 align:middle line:84% AUDIENCE: Well, I guess, I'm just asking in general, 02:14:38.840 --> 02:14:39.575 align:middle line:90% when you're-- 02:14:39.575 --> 02:14:41.200 align:middle line:84% and maybe this is a very broad question 02:14:41.200 --> 02:14:43.450 align:middle line:84% that this class is supposed to answer, but in general, 02:14:43.450 --> 02:14:46.200 align:middle line:84% when you're approaching these sorts of difficult modeling 02:14:46.200 --> 02:14:50.520 align:middle line:84% questions, how do you approach them? 02:14:50.520 --> 02:14:53.188 align:middle line:84% Again, maybe this is so big it's not meaningful. 02:14:53.188 --> 02:14:54.230 align:middle line:90% But what's your problem-- 02:14:54.230 --> 02:14:57.130 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so actually, 02:14:57.130 --> 02:14:59.950 align:middle line:84% a lot of these-- this one, I had never solved it before. 02:14:59.950 --> 02:15:02.510 align:middle line:84% So when I yesterday started, I said, 02:15:02.510 --> 02:15:04.130 align:middle line:84% OK, let me actually think about it so 02:15:04.130 --> 02:15:06.050 align:middle line:84% that, when I come to the class, I'm 02:15:06.050 --> 02:15:09.590 align:middle line:84% not going to be looking at it and say, oh, shit, 02:15:09.590 --> 02:15:12.170 align:middle line:84% I haven't thought about this part of it. 02:15:12.170 --> 02:15:15.430 align:middle line:90% So that was my starting point. 02:15:15.430 --> 02:15:18.370 align:middle line:84% And when I went into it, I said, OK, this growth thing 02:15:18.370 --> 02:15:19.610 align:middle line:90% is not trivial. 02:15:19.610 --> 02:15:23.190 align:middle line:84% I have asked you to do something that I have not done myself. 02:15:23.190 --> 02:15:25.150 align:middle line:84% So let me actually write it down. 02:15:25.150 --> 02:15:28.970 align:middle line:84% And I had to actually create that, so the analytical thing 02:15:28.970 --> 02:15:32.930 align:middle line:84% that I showed you, to get to the point of-- 02:15:32.930 --> 02:15:36.230 align:middle line:84% and I started-- so let me tell you my process. 02:15:36.230 --> 02:15:38.530 align:middle line:84% So I started and said, OK, this is easy. 02:15:38.530 --> 02:15:42.210 align:middle line:90% You start with some inflow. 02:15:42.210 --> 02:15:45.450 align:middle line:84% Start, you multiply that with the time constant, 02:15:45.450 --> 02:15:48.650 align:middle line:84% and you get to the desired value for each stock. 02:15:48.650 --> 02:15:50.530 align:middle line:84% And then I was going towards the end, 02:15:50.530 --> 02:15:53.210 align:middle line:84% and I said, oh, I don't have the inflow. 02:15:53.210 --> 02:15:55.630 align:middle line:84% I'll get the simultaneous equation error. 02:15:55.630 --> 02:15:59.130 align:middle line:84% So I have to drive the equilibrium from backwards. 02:15:59.130 --> 02:16:01.710 align:middle line:84% So I drove the equilibrium from backwards. 02:16:01.710 --> 02:16:05.090 align:middle line:84% And I said let me stop, not worry about growth. 02:16:05.090 --> 02:16:08.090 align:middle line:84% I first solved the problem without growth. 02:16:08.090 --> 02:16:12.370 align:middle line:84% Then I said, OK, now I need to think very clearly about growth. 02:16:12.370 --> 02:16:16.310 align:middle line:84% Let me solve the growth problem without having multiple phases. 02:16:16.310 --> 02:16:20.690 align:middle line:84% Let me just solve the growth problem for the market condition 02:16:20.690 --> 02:16:23.050 align:middle line:84% where things go directly into the market. 02:16:23.050 --> 02:16:26.830 align:middle line:84% So I wrote down that equation, solved it, 02:16:26.830 --> 02:16:30.290 align:middle line:84% and said, OK, now I have a growth factor that comes in. 02:16:30.290 --> 02:16:31.990 align:middle line:90% Then the rest falls in place. 02:16:31.990 --> 02:16:34.850 align:middle line:84% It's kind of-- was relatively straightforward. 02:16:34.850 --> 02:16:37.230 align:middle line:84% And of course, I was doing testing all the time. 02:16:37.230 --> 02:16:41.870 align:middle line:84% So without growth, I needed to be in equilibrium. 02:16:41.870 --> 02:16:46.209 align:middle line:84% And things adjust fast, and then it grows. 02:16:46.209 --> 02:16:49.990 align:middle line:84% So anyway, that's the mental model. 02:16:49.990 --> 02:16:52.129 align:middle line:90% Now, this is doing OK. 02:16:52.129 --> 02:16:55.590 align:middle line:84% We don't know whether it will oscillate or do weird things, 02:16:55.590 --> 02:16:57.809 align:middle line:90% so we could test those as well. 02:16:57.809 --> 02:17:01.969 align:middle line:84% So for example, if I change the desired 02:17:01.969 --> 02:17:07.850 align:middle line:84% revenue to do something other than exponential growth, so-- 02:17:07.850 --> 02:17:09.184 align:middle line:90% AUDIENCE: Try the line. 02:17:09.184 --> 02:17:10.309 align:middle line:90% HAZHIR RAHMANDAD: Try what? 02:17:10.309 --> 02:17:11.170 align:middle line:90% AUDIENCE: The ramp. 02:17:11.170 --> 02:17:12.870 align:middle line:84% HAZHIR RAHMANDAD: Yeah, we could even do the ramp. 02:17:12.870 --> 02:17:15.129 align:middle line:84% But let's do the step change because it's easier 02:17:15.129 --> 02:17:17.830 align:middle line:90% to get started with. 02:17:17.830 --> 02:17:20.650 align:middle line:90% So, I don't know, 250. 02:17:20.650 --> 02:17:25.850 align:middle line:84% So right now, this is getting things out of equilibrium 02:17:25.850 --> 02:17:29.770 align:middle line:84% because my desired growth rate is 02:17:29.770 --> 02:17:34.590 align:middle line:84% 10% whereas the actual desired growth rate is 0. 02:17:34.590 --> 02:17:36.110 align:middle line:84% So I need to fix this one as well. 02:17:36.110 --> 02:17:38.770 align:middle line:84% So that just needs a little bit of fixing 02:17:38.770 --> 02:17:42.090 align:middle line:84% so that they are consistent internally with each other. 02:17:42.090 --> 02:17:44.930 align:middle line:84% Otherwise, the system learns the actual growth 02:17:44.930 --> 02:17:47.799 align:middle line:84% rate and the perceived desire growth goes down, 02:17:47.799 --> 02:17:50.260 align:middle line:84% but it takes so long that it creates 02:17:50.260 --> 02:17:52.040 align:middle line:90% a lot of hectic dynamics. 02:17:52.040 --> 02:17:56.540 align:middle line:84% OK, so now we have the desired growth rate. 02:17:56.540 --> 02:18:00.360 align:middle line:84% You see that the drugs in the market take a while. 02:18:00.360 --> 02:18:03.100 align:middle line:84% In fact, in 100 months, they don't get there 02:18:03.100 --> 02:18:07.780 align:middle line:84% because the drug development process is that long. 02:18:07.780 --> 02:18:12.440 align:middle line:84% But they are moving in the right level. 02:18:12.440 --> 02:18:16.120 align:middle line:84% That is, if you look at the revenue versus desired revenue-- 02:18:16.120 --> 02:18:17.520 align:middle line:90% so where is the revenues? 02:18:17.520 --> 02:18:20.620 align:middle line:90% 02:18:20.620 --> 02:18:25.879 align:middle line:84% They are-- no, they are not moving in the right-- 02:18:25.879 --> 02:18:28.540 align:middle line:90% 02:18:28.540 --> 02:18:33.580 align:middle line:84% ah, interesting because I have created a perceived growth 02:18:33.580 --> 02:18:36.620 align:middle line:90% rate that is nonzero. 02:18:36.620 --> 02:18:37.379 align:middle line:90% You see? 02:18:37.379 --> 02:18:39.700 align:middle line:84% So the perceived growth rate, the signal 02:18:39.700 --> 02:18:42.540 align:middle line:84% from that step function to the system 02:18:42.540 --> 02:18:46.020 align:middle line:84% is that, wow, there is huge growth rate, 02:18:46.020 --> 02:18:48.100 align:middle line:84% and now it is adjusting everything 02:18:48.100 --> 02:18:50.240 align:middle line:90% towards that huge growth rate. 02:18:50.240 --> 02:18:55.459 align:middle line:84% So actually, I have to also fix this guy if we want to see-- 02:18:55.459 --> 02:18:57.580 align:middle line:84% AUDIENCE: What is the role of the perceived growth 02:18:57.580 --> 02:18:59.320 align:middle line:90% rate even in the growth sector? 02:18:59.320 --> 02:19:01.420 align:middle line:84% Why don't we just-- because this is-- 02:19:01.420 --> 02:19:03.295 align:middle line:84% HAZHIR RAHMANDAD: It doesn't have a big role. 02:19:03.295 --> 02:19:06.320 align:middle line:84% I could easily just use the desired growth rate to drive it. 02:19:06.320 --> 02:19:10.120 align:middle line:84% It is just taking a little bit of an adjustment 02:19:10.120 --> 02:19:13.879 align:middle line:84% so that growth rate is perceived rather than the real. 02:19:13.879 --> 02:19:17.860 align:middle line:84% It's very easy to drop that and perhaps better in this case. 02:19:17.860 --> 02:19:18.700 align:middle line:90% Good point. 02:19:18.700 --> 02:19:23.360 align:middle line:84% But that was a good test case for it doesn't work. 02:19:23.360 --> 02:19:27.580 align:middle line:84% So in this case, if I make it a constant with a slider 02:19:27.580 --> 02:19:32.820 align:middle line:84% and have its base value at 0, then things 02:19:32.820 --> 02:19:38.959 align:middle line:84% should work better for desired versus actual revenue. 02:19:38.959 --> 02:19:42.379 align:middle line:90% 02:19:42.379 --> 02:19:48.299 align:middle line:84% Yeah, but it is going now very slowly because it is not getting 02:19:48.299 --> 02:19:49.520 align:middle line:90% the signal of the growth. 02:19:49.520 --> 02:19:52.820 align:middle line:84% It is just very slowly adjusting towards it. 02:19:52.820 --> 02:19:55.060 align:middle line:84% And this is 100 months, so I should probably 02:19:55.060 --> 02:20:00.580 align:middle line:84% simulate it for longer to see meaningful impacts. 02:20:00.580 --> 02:20:03.660 align:middle line:90% Let me reset these-- 02:20:03.660 --> 02:20:04.160 align:middle line:90% no. 02:20:04.160 --> 02:20:10.980 align:middle line:90% 02:20:10.980 --> 02:20:18.780 align:middle line:84% So now let's do something that changes the growth rate from 0 02:20:18.780 --> 02:20:19.320 align:middle line:90% to-- 02:20:19.320 --> 02:20:23.340 align:middle line:90% 02:20:23.340 --> 02:20:28.040 align:middle line:90% so maybe it starts at 3%. 02:20:28.040 --> 02:20:30.820 align:middle line:90% 02:20:30.820 --> 02:20:32.780 align:middle line:90% Did I do this step? 02:20:32.780 --> 02:20:34.240 align:middle line:90% No, I didn't. 02:20:34.240 --> 02:20:37.660 align:middle line:90% 02:20:37.660 --> 02:20:39.780 align:middle line:84% So I want the growth rate to be positive 02:20:39.780 --> 02:20:42.650 align:middle line:84% and then becomes smaller, not as big. 02:20:42.650 --> 02:20:44.490 align:middle line:84% So it goes through a step change. 02:20:44.490 --> 02:20:49.910 align:middle line:84% It starts from, let's say, 2% per month 02:20:49.910 --> 02:21:02.150 align:middle line:84% to 1% per month at time 50 or something like that. 02:21:02.150 --> 02:21:07.530 align:middle line:84% So the desired growth rate is now changing in a step function. 02:21:07.530 --> 02:21:11.070 align:middle line:90% 02:21:11.070 --> 02:21:14.630 align:middle line:84% What you can see is that the P1 start rate 02:21:14.630 --> 02:21:16.450 align:middle line:90% goes down but doesn't go to 0. 02:21:16.450 --> 02:21:21.230 align:middle line:84% So the max zero constraint doesn't kick in. 02:21:21.230 --> 02:21:26.190 align:middle line:84% And then drugs in the market-- or we 02:21:26.190 --> 02:21:28.430 align:middle line:84% can take a look at the revenue, see how well 02:21:28.430 --> 02:21:31.630 align:middle line:90% the revenue works in this case. 02:21:31.630 --> 02:21:34.270 align:middle line:84% And again, remember that the perceived desire. 02:21:34.270 --> 02:21:38.230 align:middle line:84% So if we make this perception time faster-- 02:21:38.230 --> 02:21:41.290 align:middle line:84% we could even make it very fast-- 02:21:41.290 --> 02:21:45.030 align:middle line:84% then the adjustment becomes faster so you don't have 02:21:45.030 --> 02:21:50.430 align:middle line:84% the long adjustment period because you don't measure the-- 02:21:50.430 --> 02:21:52.045 align:middle line:90% AUDIENCE: You're hitting the-- 02:21:52.045 --> 02:21:54.170 align:middle line:84% HAZHIR RAHMANDAD: Yes, and now I'm hitting the max, 02:21:54.170 --> 02:21:58.170 align:middle line:84% so that will create some steady state-- not a steady state, 02:21:58.170 --> 02:22:03.630 align:middle line:84% but it will create some additional. 02:22:03.630 --> 02:22:04.910 align:middle line:90% Yes. 02:22:04.910 --> 02:22:06.790 align:middle line:90% What's that? 02:22:06.790 --> 02:22:13.590 align:middle line:84% Oh, so, here, in the P1 start, now I just 02:22:13.590 --> 02:22:15.510 align:middle line:84% can't get rid of these drugs because we 02:22:15.510 --> 02:22:16.570 align:middle line:90% don't have cancellation. 02:22:16.570 --> 02:22:20.730 align:middle line:84% If we add cancellation, we don't need to worry about this. 02:22:20.730 --> 02:22:26.310 align:middle line:84% So perhaps we could change this guy 02:22:26.310 --> 02:22:30.150 align:middle line:84% to go to 0 point I don't know 13. 02:22:30.150 --> 02:22:35.270 align:middle line:84% Yeah, so now it wouldn't hit 0 I think. 02:22:35.270 --> 02:22:38.630 align:middle line:90% Yeah, it just goes to 0. 02:22:38.630 --> 02:22:40.870 align:middle line:84% So now let's see what's happening with the desired 02:22:40.870 --> 02:22:42.270 align:middle line:90% revenue. 02:22:42.270 --> 02:22:45.390 align:middle line:84% So I'm now doing tests that I haven't done myself. 02:22:45.390 --> 02:22:52.190 align:middle line:84% So there is still some steady-state difference. 02:22:52.190 --> 02:22:57.730 align:middle line:84% And I think if we simulate it for longer, that should go away. 02:22:57.730 --> 02:23:01.470 align:middle line:84% But let's see if I have x final time. 02:23:01.470 --> 02:23:04.970 align:middle line:84% Always put the final time on your model screen. 02:23:04.970 --> 02:23:18.630 align:middle line:90% 02:23:18.630 --> 02:23:19.930 align:middle line:90% So let's see. 02:23:19.930 --> 02:23:40.040 align:middle line:90% 02:23:40.040 --> 02:23:44.160 align:middle line:84% Because we have 2% and then 13 or something like that. 02:23:44.160 --> 02:23:45.800 align:middle line:90% Yeah. 02:23:45.800 --> 02:23:50.600 align:middle line:84% And then or maybe 15, I'm not sure. 02:23:50.600 --> 02:23:52.820 align:middle line:90% And then we said, this guy. 02:23:52.820 --> 02:23:57.960 align:middle line:84% Let's make it very small so that we quickly adjust. 02:23:57.960 --> 02:24:01.520 align:middle line:84% Yeah, this is kind of doing fine. 02:24:01.520 --> 02:24:05.840 align:middle line:84% And then we can go to 500 or something. 02:24:05.840 --> 02:24:13.160 align:middle line:90% So we see the full range. 02:24:13.160 --> 02:24:14.112 align:middle line:90% What happened? 02:24:14.112 --> 02:24:16.320 align:middle line:84% AUDIENCE: Did you mean to make [INAUDIBLE] to go down 02:24:16.320 --> 02:24:17.220 align:middle line:90% or to go up? 02:24:17.220 --> 02:24:18.720 align:middle line:90% HAZHIR RAHMANDAD: Huh? 02:24:18.720 --> 02:24:20.980 align:middle line:84% I wanted the desired growth rate-- well, 02:24:20.980 --> 02:24:24.200 align:middle line:90% I didn't mind going down. 02:24:24.200 --> 02:24:26.720 align:middle line:84% But somehow something weird happened here 02:24:26.720 --> 02:24:28.800 align:middle line:90% that I don't know what it is. 02:24:28.800 --> 02:24:30.460 align:middle line:90% No, nothing weird is happening. 02:24:30.460 --> 02:24:32.600 align:middle line:90% It's doing what it is doing. 02:24:32.600 --> 02:24:34.720 align:middle line:90% So desired revenue and revenue. 02:24:34.720 --> 02:24:36.140 align:middle line:90% Let's see if it can catch up. 02:24:36.140 --> 02:24:38.440 align:middle line:84% Yeah, you can see that it does catch up. 02:24:38.440 --> 02:24:42.140 align:middle line:84% Now, here I'm doing the change at time 10. 02:24:42.140 --> 02:24:47.360 align:middle line:84% That's too early, so let's do it at time 100 02:24:47.360 --> 02:24:53.160 align:middle line:84% so that you have a longer period of the faster growth. 02:24:53.160 --> 02:24:56.760 align:middle line:84% You still get the behaviors to match. 02:24:56.760 --> 02:25:04.000 align:middle line:84% In fact, even if you went into a no-growth process, which we can 02:25:04.000 --> 02:25:04.920 align:middle line:90% test. 02:25:04.920 --> 02:25:10.040 align:middle line:90% So we go to minus 0.01. 02:25:10.040 --> 02:25:15.600 align:middle line:84% For a while, it wouldn't do well because of the-- 02:25:15.600 --> 02:25:24.220 align:middle line:84% because of-- yeah, that's a long while that it doesn't do well. 02:25:24.220 --> 02:25:26.600 align:middle line:90% AUDIENCE: Why is it? 02:25:26.600 --> 02:25:28.240 align:middle line:84% HAZHIR RAHMANDAD: So the reason is 02:25:28.240 --> 02:25:31.280 align:middle line:84% that now you have a lot of revenue, 02:25:31.280 --> 02:25:33.100 align:middle line:84% and you can't get rid of this pipeline. 02:25:33.100 --> 02:25:34.042 align:middle line:90% And it takes-- 02:25:34.042 --> 02:25:35.500 align:middle line:84% AUDIENCE: --time for it to process. 02:25:35.500 --> 02:25:36.880 align:middle line:84% HAZHIR RAHMANDAD: Yes, basically, 02:25:36.880 --> 02:25:40.640 align:middle line:84% a long time to get rid of all the things that you had-- 02:25:40.640 --> 02:25:44.160 align:middle line:84% you already was expecting these huge growth rates you 02:25:44.160 --> 02:25:46.100 align:middle line:90% were pumping into the pipeline. 02:25:46.100 --> 02:25:48.640 align:middle line:84% And now, without cancellation, so this 02:25:48.640 --> 02:25:51.000 align:middle line:84% shows basically the importance of cancellation 02:25:51.000 --> 02:25:53.480 align:middle line:84% in the conditions when things are going down. 02:25:53.480 --> 02:25:56.640 align:middle line:84% AUDIENCE: So the time between those two peaks 02:25:56.640 --> 02:26:01.920 align:middle line:84% should be about the total time, the total duration from start. 02:26:01.920 --> 02:26:04.780 align:middle line:90% 02:26:04.780 --> 02:26:07.400 align:middle line:84% HAZHIR RAHMANDAD: Not to start to finish-- eh, it's harder 02:26:07.400 --> 02:26:18.360 align:middle line:84% to say because, as soon as you see that the perceived 02:26:18.360 --> 02:26:20.320 align:middle line:84% desired growth is going down and that 02:26:20.320 --> 02:26:26.280 align:middle line:84% is happening relatively quickly, now, you will stop investing. 02:26:26.280 --> 02:26:28.860 align:middle line:90% But stopping investing means 0. 02:26:28.860 --> 02:26:29.800 align:middle line:90% So now it is 0. 02:26:29.800 --> 02:26:32.580 align:middle line:84% You see, all the way to the end, it has remained 0. 02:26:32.580 --> 02:26:35.760 align:middle line:84% It just can't do anything more than this. 02:26:35.760 --> 02:26:46.640 align:middle line:84% And with that 0 rate, it still cannot match the desired stock. 02:26:46.640 --> 02:26:51.300 align:middle line:84% So when that peaks, so that is your revenue. 02:26:51.300 --> 02:26:53.320 align:middle line:84% It is when your drugs in the market peaks. 02:26:53.320 --> 02:26:57.120 align:middle line:84% And the drugs in the market peak when the inflow 02:26:57.120 --> 02:26:59.760 align:middle line:90% starts to go below outflow. 02:26:59.760 --> 02:27:02.520 align:middle line:84% That depends on the length of these three first step 02:27:02.520 --> 02:27:04.380 align:middle line:90% delays, not the last one. 02:27:04.380 --> 02:27:07.120 align:middle line:90% 02:27:07.120 --> 02:27:10.600 align:middle line:84% So it is more about the length of those delays rather than 02:27:10.600 --> 02:27:12.112 align:middle line:90% the last step. 02:27:12.112 --> 02:27:14.320 align:middle line:84% AUDIENCE: [INAUDIBLE] problem with the third question 02:27:14.320 --> 02:27:17.760 align:middle line:84% is I almost feel like perceived desired growth 02:27:17.760 --> 02:27:20.560 align:middle line:84% rate in the real world should be not 02:27:20.560 --> 02:27:23.700 align:middle line:84% a function of a exogenous desired growth rate, 02:27:23.700 --> 02:27:26.720 align:middle line:84% but a function of exogenous desired revenue. 02:27:26.720 --> 02:27:29.870 align:middle line:84% HAZHIR RAHMANDAD: Yes, it should be based on desired revenue. 02:27:29.870 --> 02:27:34.550 align:middle line:84% So we could get it from the desired revenue directly. 02:27:34.550 --> 02:27:37.810 align:middle line:90% 02:27:37.810 --> 02:27:40.730 align:middle line:90% Yeah, absolutely. 02:27:40.730 --> 02:27:44.690 align:middle line:84% We could get it just directly from the desired revenue. 02:27:44.690 --> 02:27:46.510 align:middle line:90% I don't remember whether I-- 02:27:46.510 --> 02:27:53.690 align:middle line:90% 02:27:53.690 --> 02:27:57.030 align:middle line:84% actually, I might actually have it. 02:27:57.030 --> 02:27:59.650 align:middle line:90% 02:27:59.650 --> 02:28:01.610 align:middle line:84% Actually, the perceived-- yeah, it's 02:28:01.610 --> 02:28:02.910 align:middle line:90% the same numbers that we have. 02:28:02.910 --> 02:28:05.670 align:middle line:84% So it is converging to the right numbers. 02:28:05.670 --> 02:28:10.610 align:middle line:84% But you could get it from the trend of the desired revenue. 02:28:10.610 --> 02:28:14.130 align:middle line:84% So anyway, I'll share this model. 02:28:14.130 --> 02:28:26.450 align:middle line:84% For next week, we have our old friend Mr. Ponzi joining us. 02:28:26.450 --> 02:28:30.030 align:middle line:84% So some of you are familiar with the Ponzi model. 02:28:30.030 --> 02:28:31.250 align:middle line:90% Some of you are not. 02:28:31.250 --> 02:28:35.410 align:middle line:84% So Ponzi is this guy, Charles Ponzi. 02:28:35.410 --> 02:28:37.770 align:middle line:84% In the early 20th century in Boston, 02:28:37.770 --> 02:28:41.250 align:middle line:84% he made a claim that I can give you great returns 02:28:41.250 --> 02:28:45.490 align:middle line:84% on your investments because I found this loophole in some 02:28:45.490 --> 02:28:49.690 align:middle line:84% bullshit story, basically, that you can buy these stamps here 02:28:49.690 --> 02:28:53.770 align:middle line:84% and sell them in Spain for 10 times the price or something 02:28:53.770 --> 02:28:54.350 align:middle line:90% like that. 02:28:54.350 --> 02:29:00.850 align:middle line:84% And I'll give you a 50% return on your investment over a 45-day 02:29:00.850 --> 02:29:02.370 align:middle line:90% period. 02:29:02.370 --> 02:29:04.910 align:middle line:84% And people, of course, were skeptical at the beginning, 02:29:04.910 --> 02:29:08.770 align:middle line:84% but he started paying those who came back after 45 days 02:29:08.770 --> 02:29:10.870 align:middle line:90% the promised return. 02:29:10.870 --> 02:29:12.670 align:middle line:90% So more and more people joined. 02:29:12.670 --> 02:29:15.010 align:middle line:84% In a few months, almost half of the Boston 02:29:15.010 --> 02:29:17.740 align:middle line:90% was investing with Mr. Ponzi. 02:29:17.740 --> 02:29:21.490 align:middle line:84% It grew exponentially, and then it crashed. 02:29:21.490 --> 02:29:24.690 align:middle line:84% And what he was doing was basically getting money 02:29:24.690 --> 02:29:27.170 align:middle line:84% from this group that are investing and paying 02:29:27.170 --> 02:29:30.290 align:middle line:84% to the group that are coming back to get their investments. 02:29:30.290 --> 02:29:34.330 align:middle line:90% That was the mechanism. 02:29:34.330 --> 02:29:40.610 align:middle line:84% So the task is to build a model of the story of Ponzi. 02:29:40.610 --> 02:29:45.330 align:middle line:84% In some ways, it is easier than some of the previous tasks 02:29:45.330 --> 02:29:49.330 align:middle line:84% because it is not a very complex story, but it-- 02:29:49.330 --> 02:29:54.570 align:middle line:84% and it doesn't have very strange or technically complex 02:29:54.570 --> 02:29:58.690 align:middle line:84% formulations, but it does require you to actually bring 02:29:58.690 --> 02:30:00.110 align:middle line:90% different pieces together. 02:30:00.110 --> 02:30:02.610 align:middle line:90% So you need a financial sector. 02:30:02.610 --> 02:30:07.250 align:middle line:84% You need to account for actual money versus what 02:30:07.250 --> 02:30:08.350 align:middle line:90% he has promised. 02:30:08.350 --> 02:30:09.970 align:middle line:90% These two are not the same. 02:30:09.970 --> 02:30:12.210 align:middle line:84% And that's very important because you run out 02:30:12.210 --> 02:30:13.030 align:middle line:90% of actual money. 02:30:13.030 --> 02:30:17.450 align:middle line:84% That's when basically you go bankrupt and people-- 02:30:17.450 --> 02:30:22.110 align:middle line:84% whereas what you have promised is what you are paying based on. 02:30:22.110 --> 02:30:23.920 align:middle line:90% So that's important. 02:30:23.920 --> 02:30:28.820 align:middle line:84% You need to somehow account for trust in the system one 02:30:28.820 --> 02:30:29.480 align:middle line:90% way or another. 02:30:29.480 --> 02:30:30.560 align:middle line:90% Now you should decide. 02:30:30.560 --> 02:30:32.660 align:middle line:84% So there is a lot more flexibility 02:30:32.660 --> 02:30:35.820 align:middle line:90% in how you model Ponzi's story. 02:30:35.820 --> 02:30:39.500 align:middle line:84% So the problem statement that is in the folder 02:30:39.500 --> 02:30:43.060 align:middle line:84% has the basic story of Ponzi in one paragraph. 02:30:43.060 --> 02:30:44.720 align:middle line:90% There is link to Wikipedia page. 02:30:44.720 --> 02:30:45.280 align:middle line:90% Read that. 02:30:45.280 --> 02:30:47.113 align:middle line:84% That gives you a little bit more background. 02:30:47.113 --> 02:30:49.700 align:middle line:84% That's five minutes of reading so that you 02:30:49.700 --> 02:30:52.320 align:middle line:90% are grounded in the core story. 02:30:52.320 --> 02:30:56.020 align:middle line:84% But don't forget the desire to build something that 02:30:56.020 --> 02:30:59.020 align:middle line:90% is a little bit more generic. 02:30:59.020 --> 02:31:02.220 align:middle line:84% That is, you can think about Social Security 02:31:02.220 --> 02:31:04.540 align:middle line:84% to be a Ponzi scheme in the sense 02:31:04.540 --> 02:31:10.940 align:middle line:84% that each generation is paying the previous generation's 02:31:10.940 --> 02:31:13.860 align:middle line:84% retirement, Social Security benefits. 02:31:13.860 --> 02:31:16.840 align:middle line:84% As long as there is enough inflow to replace that, 02:31:16.840 --> 02:31:19.580 align:middle line:90% things work out fine. 02:31:19.580 --> 02:31:23.420 align:middle line:84% So Ponzi schemes are not generally neither illegal 02:31:23.420 --> 02:31:26.180 align:middle line:84% fully as long as you are clear what you are doing. 02:31:26.180 --> 02:31:28.300 align:middle line:84% So if he told people that I'm getting money 02:31:28.300 --> 02:31:30.800 align:middle line:84% from one to pay to the other, it would've been legal, 02:31:30.800 --> 02:31:36.300 align:middle line:84% but then he wouldn't have any money-- any investors. 02:31:36.300 --> 02:31:41.420 align:middle line:84% And you can change them in a way that it kind of works. 02:31:41.420 --> 02:31:46.100 align:middle line:84% Madoff, the other big Ponzi schemer of the 21st century 02:31:46.100 --> 02:31:49.420 align:middle line:84% and late 20th century, he's as famous. 02:31:49.420 --> 02:31:53.300 align:middle line:84% He passed away in prison just a couple of years ago, 02:31:53.300 --> 02:31:59.020 align:middle line:84% but he actually scammed a lot more, many billions of dollars. 02:31:59.020 --> 02:32:02.160 align:middle line:84% And there are many other Ponzi-type stories around us. 02:32:02.160 --> 02:32:08.500 align:middle line:84% And there is the whole history of dozens of interesting cases. 02:32:08.500 --> 02:32:14.340 align:middle line:84% OK, so that's the plan for the coming session. 02:32:14.340 --> 02:32:17.060 align:middle line:84% Hopefully, it would be a fun model. 02:32:17.060 --> 02:32:21.800 align:middle line:84% Make sure you have a model that follows all the basics, 02:32:21.800 --> 02:32:29.660 align:middle line:84% but also creates the growth and collapse history of Mr. Ponzi's 02:32:29.660 --> 02:32:35.420 align:middle line:84% scam with reasonable empirical ranges for parameters and so on, 02:32:35.420 --> 02:32:41.340 align:middle line:84% without getting bogged down into parameterization. 02:32:41.340 --> 02:32:41.840 align:middle line:90% Yes. 02:32:41.840 --> 02:32:43.798 align:middle line:84% AUDIENCE: You're assuming that there's actually 02:32:43.798 --> 02:32:45.000 align:middle line:90% no investment happening. 02:32:45.000 --> 02:32:48.420 align:middle line:84% [INAUDIBLE] no growth [INAUDIBLE]. 02:32:48.420 --> 02:32:50.440 align:middle line:84% HAZHIR RAHMANDAD: See what you want to do. 02:32:50.440 --> 02:32:53.300 align:middle line:84% You can have a real investment happening 02:32:53.300 --> 02:32:59.060 align:middle line:84% with a real rate of return that Mr. Ponzi's privy to but others 02:32:59.060 --> 02:33:00.500 align:middle line:90% are not seeing. 02:33:00.500 --> 02:33:03.520 align:middle line:90% And that's what Madoff did. 02:33:03.520 --> 02:33:06.340 align:middle line:84% He did invest, but he promised more than 02:33:06.340 --> 02:33:08.660 align:middle line:90% what he was actually delivering. 02:33:08.660 --> 02:33:10.140 align:middle line:84% So for a generic model-- or Social 02:33:10.140 --> 02:33:12.340 align:middle line:90% Security does invest the money. 02:33:12.340 --> 02:33:14.260 align:middle line:90% There is a return. 02:33:14.260 --> 02:33:18.010 align:middle line:84% So a generic model that is more generalizable would have that. 02:33:18.010 --> 02:33:19.510 align:middle line:84% But if you're short of time, that 02:33:19.510 --> 02:33:21.510 align:middle line:90% wouldn't be my first priority. 02:33:21.510 --> 02:33:26.470 align:middle line:84% So you can decide what you want to prioritize on that. 02:33:26.470 --> 02:33:29.850 align:middle line:84% I think we're out of time, so let's be done with it. 02:33:29.850 --> 02:33:31.350 align:middle line:84% For those interested, I'm just going 02:33:31.350 --> 02:33:35.370 align:middle line:84% to show you one last thing, and you can take off if you want. 02:33:35.370 --> 02:33:39.470 align:middle line:84% But with the current AI stuff, there 02:33:39.470 --> 02:33:42.870 align:middle line:84% are good things you can do with model documentation 02:33:42.870 --> 02:33:44.330 align:middle line:90% and parameterization. 02:33:44.330 --> 02:33:48.776 align:middle line:84% So with the pharma model, just to let you know, 02:33:48.776 --> 02:33:51.575 align:middle line:84% I turned it into text in Vensim-- 02:33:51.575 --> 02:33:52.450 align:middle line:90% I didn't do anything. 02:33:52.450 --> 02:33:54.070 align:middle line:90% It's just you do this in Vensim. 02:33:54.070 --> 02:33:57.330 align:middle line:84% So you can get this text of the model. 02:33:57.330 --> 02:34:02.710 align:middle line:84% I sent it to Cloud AI and told it please document my model. 02:34:02.710 --> 02:34:05.370 align:middle line:84% Basically, it provided comments for every equation. 02:34:05.370 --> 02:34:07.870 align:middle line:84% So the comments you will see in this pharma model 02:34:07.870 --> 02:34:09.690 align:middle line:90% are not by my hand. 02:34:09.690 --> 02:34:14.630 align:middle line:84% They are all cloud commenting, the model, 02:34:14.630 --> 02:34:15.890 align:middle line:90% and it does a decent job. 02:34:15.890 --> 02:34:18.630 align:middle line:84% That is, it understands what the equation is doing. 02:34:18.630 --> 02:34:21.850 align:middle line:84% It provides meaningful explanation. 02:34:21.850 --> 02:34:24.030 align:middle line:90% Now, that is pretty impressive. 02:34:24.030 --> 02:34:29.090 align:middle line:84% What is magical is that I told it, in another prompt 02:34:29.090 --> 02:34:32.310 align:middle line:84% and discussion, OK, this is a model of pharma industry. 02:34:32.310 --> 02:34:35.350 align:middle line:84% Please go and find the parameters 02:34:35.350 --> 02:34:40.910 align:middle line:84% from the literature and ranges for those parameters. 02:34:40.910 --> 02:34:45.510 align:middle line:84% Put them into a table with citations, 02:34:45.510 --> 02:34:48.190 align:middle line:84% and then insert them into the model. 02:34:48.190 --> 02:34:49.790 align:middle line:90% And it did that as well. 02:34:49.790 --> 02:34:51.550 align:middle line:84% So now you can look at this model, 02:34:51.550 --> 02:34:55.750 align:middle line:84% and you will see that, every equation, every parameter 02:34:55.750 --> 02:34:59.870 align:middle line:84% has a detailed explanation with a bunch of citations. 02:34:59.870 --> 02:35:02.030 align:middle line:90% And I checked a few of them. 02:35:02.030 --> 02:35:04.190 align:middle line:84% They are not all fully correct, but they are 02:35:04.190 --> 02:35:06.530 align:middle line:90% all in the reasonable ranges. 02:35:06.530 --> 02:35:12.030 align:middle line:84% That is, so these are the citations in this-- 02:35:12.030 --> 02:35:13.750 align:middle line:90% you will see. 02:35:13.750 --> 02:35:16.850 align:middle line:84% It has taken numbers from the paper, 02:35:16.850 --> 02:35:20.130 align:middle line:84% but sometimes not the best number, sometimes a number 02:35:20.130 --> 02:35:22.750 align:middle line:84% that is-- for example, there are lots 02:35:22.750 --> 02:35:26.790 align:middle line:84% of these papers that look at drug success rates that 02:35:26.790 --> 02:35:29.170 align:middle line:84% are looking at different categories. 02:35:29.170 --> 02:35:31.670 align:middle line:84% So it has not always found the right category. 02:35:31.670 --> 02:35:33.170 align:middle line:84% Rather than the biggest category, 02:35:33.170 --> 02:35:35.890 align:middle line:84% sometimes it has anchored to a subset of drugs, 02:35:35.890 --> 02:35:38.030 align:middle line:90% things like that, which-- 02:35:38.030 --> 02:35:41.290 align:middle line:84% so always go and check the ultimate source. 02:35:41.290 --> 02:35:43.390 align:middle line:84% But this thing would've been something 02:35:43.390 --> 02:35:46.630 align:middle line:84% I would never do it for a class like this, but now it takes me 02:35:46.630 --> 02:35:49.030 align:middle line:90% 10 minutes to do it, so why not? 02:35:49.030 --> 02:35:51.147 align:middle line:90% So OK, go have fun. 02:35:51.147 --> 02:35:52.730 align:middle line:84% AUDIENCE: You're saying, in two years, 02:35:52.730 --> 02:35:55.418 align:middle line:84% we won't even have to learn how to build these models. 02:35:55.418 --> 02:35:56.710 align:middle line:90% HAZHIR RAHMANDAD: I don't know. 02:35:56.710 --> 02:35:59.270 align:middle line:90% So I think there is always-- 02:35:59.270 --> 02:36:02.830 align:middle line:84% not always, up to some point that these AIs 02:36:02.830 --> 02:36:05.310 align:middle line:90% can do all of the modeling. 02:36:05.310 --> 02:36:08.030 align:middle line:84% You can become much more productive 02:36:08.030 --> 02:36:12.040 align:middle line:90% with getting help from AI. 02:36:12.040 --> 02:36:16.600 align:middle line:84% There is a point, who knows when in the future, where you can't 02:36:16.600 --> 02:36:21.120 align:middle line:84% actually add much value beyond telling AI what model you want 02:36:21.120 --> 02:36:23.460 align:middle line:84% and how to calibrate it and so on. 02:36:23.460 --> 02:36:24.460 align:middle line:90% We are not still there. 02:36:24.460 --> 02:36:28.700 align:middle line:84% I don't expect it to be in the next four, five years, 02:36:28.700 --> 02:36:30.580 align:middle line:84% but because things are growing so fast, 02:36:30.580 --> 02:36:36.720 align:middle line:84% I have no idea whether that thing is coming soon or not. 02:36:36.720 --> 02:36:42.220 align:middle line:84% In a way, modeling is one of the most complex human things 02:36:42.220 --> 02:36:44.880 align:middle line:84% because you have to make so many assumptions about what 02:36:44.880 --> 02:36:46.980 align:middle line:84% is important, what is not important. 02:36:46.980 --> 02:36:51.200 align:middle line:84% That's what our brains are still fairly good at 02:36:51.200 --> 02:36:53.880 align:middle line:90% compared to many of the AIs. 02:36:53.880 --> 02:36:58.255 align:middle line:84% So the point that this task becomes completely automatable, 02:36:58.255 --> 02:36:59.880 align:middle line:84% I don't know what competitive advantage 02:36:59.880 --> 02:37:03.200 align:middle line:84% we have on the cognitive task, but that's 02:37:03.200 --> 02:37:08.390 align:middle line:84% a conversation for a beer rather than end of the class. 02:37:08.390 --> 02:37:11.000 align:middle line:90%