MIT OpenCourseWareSession 5: Managing Drug Development Pipeline
MIT OpenCourseWare
Model limits 0:00
The predator-prey model is tied to oscillation, but the classical form misses saturation. A predator is not eating a fraction of prey in a period, and once saturation is added the model is much less likely to oscillate. Real swings may come from movement across regions instead, and the harder nonlinear forms also make equilibrium analysis more difficult.
Drug pipeline setup 6:05
The drug pipeline model has three phases, failure to nowhere, and patent expiry, with generics cutting revenue fast. The desired revenue sets the desired drugs in market, and the gap from actual drives adjustment. The main challenge is the replacement rate: if growth is wanted and pipeline success is low, you must start many more drugs than the expiring ones alone.
Cascade adjustment 21:31
A cascade method can be used to put the pipeline in balance. You start with the desired final stock, work back to the inflow needed for that stock, then work back again to phase 3 and earlier phases. The main question is whether to fold the market adjustment into the phase-to-phase targets or keep it as a separate stock adjustment. The speaker also notes that patent timing matters, and growth is harder to handle cleanly.
Phase structure choices 26:32
Hassam’s model is praised for being compact, with separate stocks for drugs that pass each phase. The broader point is that drugs need not always move on, even after success, because they can wait or be dropped. The phase equations are fine, but the model drifts away from the original stock-adjustment problem. Kathy’s version is simpler, though the initial values are not analytically balanced, and the revenue-growth target is easier to manage if it stays exogenous.
Growth needs replacement 40:31
The discussion turns on why a stock-adjustment model works for equilibrium but not for growth. If drugs in the market are doubling, the system must replace what will exit years ahead, not just what exits today. A drug leaving phase I or the market now stands in for a larger flow later, so the expected loss rate has to grow with the pipeline.
Separate phases and flow 49:00
The same point comes up in the supply line. The desired total cannot be built by one rough aggregate, because you first need the desired level for phase I, phase II, and phase III, then add them. The model also needs real flow between phases, with drugs drained forward from earlier stages, not just a change in success or obsoletion rates.
Success rate and timing 1:00:30
The adjustment order is tied to desired annual revenue, patent expiry, and the drugs already in market. The success rate is used as a divider so the model asks for enough starts to cover failures. That makes the adjustment faster, but it does not change the target level itself.
Pipeline feedback issues 1:08:30
The missing pipeline adjustment is the main weakness here, and it can create oscillations. The group also separates two ways of thinking about the same flow: replacement for patent expiry and extra correction for phase-to-phase movement. The better form keeps each phase's desired level isolated, then sends those adjustments into the start rate.
Failure rates and flow 1:20:30
Hazhir explains that success rates are already built into the model, but they must be used in the right place. He says the desired move to the next phase should be set from the goal level, then divided by the phase success rate so failures are accounted for. If you use the current stock instead, you under-replace and can create oscillations.
Drug pipeline adjustments 1:28:30
He then looks at a version that treats all drugs in development as one stock. That setup reaches a steady state but not the desired level, because stock adjustments need to be done by stage and combined later. He also notes that cancellations matter in principle, though they are left out here for simplicity.
Replacement needs growth 1:40:32
Hazhir says the pipeline logic is close, but one key piece is missing. If only 10% of phase III drugs succeed, you must start about 100 to replace 10 that expire. The same idea applies to phase II and phase I. He says the desired stock levels and stock adjustments are mostly right, but replacement must also account for success rates, not just patent expiry.
Growth factor for inflow 1:52:32
He then shows how to build growth into the inflow itself. If a stock grows at rate g and its outflow has delay τ, the inflow must be multiplied by 1 plus gτ. That factor is carried back through phase III, phase II, and phase I, so each stage expands enough to support future growth. The result is a simple constant factor for exponential growth.
Growth needs matching stocks 2:04:04
To make the pipeline grow exponentially, every stock has to grow at the same rate. The desired phase III stock is set from patent expiry and then used to infer the phase III success flow. Phase II has to be adjusted again, because it must be large enough to support phase III growth over the full phase III duration. If you leave that out, the model starts below equilibrium and develops a steady-state error.
Four factors in replacement 2:09:00
The replacement factor is not just one plus growth times development cycle, because this is not a first-order delay. It is a fourth-order delay, so the expansion has to combine four pieces: projected market duration, phase III, phase II, and phase I. Put together, they tell you how much you need at the start to reach the right level at the end.
Ponzi model and AI help 2:28:30
Next week’s model is Ponzi’s scam. He promised 50 percent returns in 45 days, paid early investors with new money, and then collapsed. The model should include actual money, promised payouts, and some measure of trust. You can also make it more general, like Social Security or Madoff, where real investing exists but promised returns are too high. He then shows AI can document equations and find parameter ranges from the literature, though you still need to check the sources.
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