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I develop a model of a randomized experiment with a binary intervention and abinary outcome. Potential outcomes in the intervention and control groups giverise to four types of participants. Fixing ideas such that the outcome ismortality, some participants would live regardless, others would be saved,others would be killed, and others would die regardless. These potentialoutcome types are not observable. However, I use the model to developestimators of the number of participants of each type. The model relies on therandomization within the experiment and on deductive reasoning. I apply themodel to an important clinical trial, the PROWESS trial, and I perform a MonteCarlo simulation calibrated to estimates from the trial. The reduced form fromthe trial shows a reduction in mortality, which provided a rationale for FDAapproval. However, I find that the intervention killed two participants forevery three it saved.

A Model of a Randomized Experiment with an Application to the PROWESS Clinical Trial