General Finite Sample Inference for Experiments with Examples from Health Care
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I exploit knowledge of the randomization process within an experiment to conduct finite sample inference on quantities that capture heterogeneous intervention effects. The only data that I use are the cross-tabulations of a discrete randomized intervention and a discrete outcome. The inference procedure is general in the sense that it can test hypotheses and construct confidence intervals on various quantities. My main contribution is that I can conduct informative inference on quantities for which previous methods are uninformative, such as the number of participants who respond to the intervention in the opposite direction of the average, sometimes known as the number of defiers. I can also use the same procedure to conduct inference on other quantities, such as the average intervention effect and the fraction affected in either direction, for which previous methods are informative but restricted in the quantities they can consider. I demonstrate the value of general finite sample inference using data from hypothetical drug trials. In one trial, the estimated average intervention effect shows that the lives of 40 out of 100 participants would be saved on average. I reject the null hypothesis that no participants would be killed at the 3 confidence that at least 3 participants would be killed.
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