Javier Romanelli

the average patient doesn't exist

Sit with a drug that helps only three in ten of the people who take it, and notice how fast the instinct is to call it weak and move on. That framing hides a more interesting possibility. For those three it may be life changing while for the other seven it does nothing, so the thirty percent is an average smeared across two groups we failed to tell apart.

\[ \begin{aligned} \bar{x} &= p\,\Delta_{\text{resp}} + (1-p)\,\Delta_{\text{non}} \\ &= 0.3\,(50) + 0.7\,(0) \\ &= 15 \end{aligned} \]

x-bar is the average effect the trial reports, p the fraction of people who respond, delta-resp the effect in responders, and delta-non the effect in everyone else. it's just a weighted average. if 30 percent of people gain 50 and the rest gain nothing, the trial reports 15, a number no real patient experiences. find the trait that marks the 30 percent and the same drug reads as a major win.

So the goal is to find what makes the 30 percent different from everyone else, ideally before you spend a billion dollars treating them all the same. A lot of drugs that look mediocre are really two drugs hiding inside one trial -- and nobody has split them yet.