Counting Defiers: Examples from Health Care

Abstract: I propose a finite sample inference procedure that uses a likelihood function derived from the randomization process within an experiment to conduct inference on various quantities that capture heterogeneous intervention effects. One such quantity is the number of defiers---individuals whose treatment runs counter to the intervention. Results from the literature make informative inference on this quantity seem impossible, but they rely on different assumptions and data. I only require data on the cross-tabulations of a binary intervention and a binary treatment. Replacing the treatment variable with a more general outcome variable, I can perform inference on important quantities analogous to the number of defiers. I apply the procedure to test safety and efficacy in hypothetical drug trials for which the point estimate of the average intervention effect implies that at least 40 out of 100 individuals would be saved. In one trial, I infer with 95% confidence that at least 3 individuals would be killed, which could stop the drug from being approved.