A model of a randomized experiment with an application to the PROWESS clinical trial

I develop a model of a randomized experiment with a binary intervention and a binary outcome. Potential outcomes in the intervention and control groups give rise to four types of participants. Fixing ideas such that the outcome is mortality, some participants would live regardless, others would be saved, others would be killed, and others would die regardless. These potential outcome types are not observable. However, I use the model to develop estimators of the number of participants of each type. The model relies on the randomization within the experiment and on deductive reasoning. I apply the model to an important clinical trial, the PROWESS trial, and I perform a Monte Carlo simulation calibrated to estimates from the trial. The reduced form from the trial shows a reduction in mortality, which provided a rationale for FDA approval. However, I find that the intervention killed two participants for every three it saved.