Efficient Principally Stratified Treatment Effect Estimation in Crossover Studies with Absorbent Binary Endpoints
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Suppose one wishes to estimate the effect of a binary treatment on a binary endpoint conditional on a post-randomization quantity in a counterfactual world in which all subjects received treatment. It is generally difficult to identify this parameter without strong, untestable assumptions. It has been shown that identifiability assumptions become much weaker under a crossover design in which subjects not receiving treatment are later given treatment. Under the assumption that the post-treatment biomarker observed in these crossover subjects is the same as would have been observed had they received treatment at the start of the study, one can identify the treatment effect with only mild additional assumptions. This remains true if the endpoint is absorbent, i.e. an endpoint such as death or HIV infection such that the post-crossover treatment biomarker is not meaningful if the endpoint has already occurred. In this work, we review identifiability results for a parameter of the distribution of the data observed under a crossover design with the principally stratified treatment effect of interest. We describe situations in which these assumptions would be falsifiable, and show that these assumptions are not otherwise falsifiable. We then provide a targeted minimum loss-based estimator for the setting that makes no assumptions on the distribution that generated the data. When the semiparametric efficiency bound is well defined, for which the primary condition is that the biomarker is discrete-valued, this estimator is efficient among all regular and asymptotically linear estimators. We also present a version of this estimator for situations in which the biomarker is continuous. Implications to closeout designs for vaccine trials are discussed.
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