Efficient principally stratified treatment effect estimation in crossover studies with absorbent binary endpoints
We consider the estimation of the effect of a binary treatment on a binary endpoint conditional on a post-randomization quantity in a counterfactual world where all individuals received treatment. It is generally difficult to identify this effect without strong, untestable assumptions. It has been shown that identifiability assumptions become weaker under a crossover design where individuals not receiving treatment are later provided treatment. Under the assumption that the post-treatment biomarker observed in these crossover individuals is the same as would have been observed had they received treatment at the start of the study, the treatment effect can be identified with only mild additional assumptions. This remains true if the endpoint is absorbent, that is, if the post-crossover treatment biomarker is not meaningful if the endpoint has already occurred. Examples of absorbent endpoints include death and HIV infection. We provide identifiability conditions for the principally stratified treatment effect of interest when the data arise from a crossover design and describe situations where these conditions would be falsifiable given a large sample from the observed data distribution. We then introduce a nonparametric estimator for this effect. When the biomarker is discrete, this estimator is efficient among all regular and asymptotically linear estimators.