A Finite Population Likelihood Ratio Test of the Sharp Null Hypothesis for Compliers
Advisor: Thomas Richardson
Randomized experiments are often employed in order to determine whether a treatment X has a causal effect on an outcome Y. However, patients do not always comply with their assigned treatment. For example, patients in a randomized clinical trial may choose not to take their prescribed treatment, possibly due to side-effects. In such randomized experiments with noncompliance, scientific interest is often in testing whether the treatment exposure X has an effect on the final outcome Y, among the subset of 'Compliers' who take the treatment only if assigned to do so and would not if assigned not to do so.
We propose a finite population significance test of the sharp null hypothesis that X has no effect on Y, within the principal stratum of Compliers, using a generalized likelihood ratio test. The resulting p-value may be interpreted as a summary of the strength of evidence against the null hypothesis. I will present new algorithms that solve integer programs required for evaluation of the generalized likelihood ratio.