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Suppose one wishes to estimate the effect of a binary treatment on a binaryendpoint conditional on a post-randomization quantity in a counterfactual worldin which all subjects received treatment. It is generally difficult to identifythis parameter without strong, untestable assumptions. It has been shown thatidentifiability assumptions become much weaker under a crossover design inwhich subjects not receiving treatment are later given treatment. Under theassumption that the post-treatment biomarker observed in these crossoversubjects is the same as would have been observed had they received treatment atthe start of the study, one can identify the treatment effect with only mildadditional assumptions. This remains true if the endpoint is absorbent, i.e. anendpoint such as death or HIV infection such that the post-crossover treatmentbiomarker is not meaningful if the endpoint has already occurred. In this work,we review identifiability results for a parameter of the distribution of thedata observed under a crossover design with the principally stratifiedtreatment effect of interest. We describe situations in which these assumptionswould be falsifiable, and show that these assumptions are not otherwisefalsifiable. We then provide a targeted minimum loss-based estimator for thesetting that makes no assumptions on the distribution that generated the data.When the semiparametric efficiency bound is well defined, for which the primarycondition is that the biomarker is discrete-valued, this estimator is efficientamong all regular and asymptotically linear estimators. We also present aversion of this estimator for situations in which the biomarker is continuous.Implications to closeout designs for vaccine trials are discussed.

Efficient Principally Stratified Treatment Effect Estimation in Crossover Studies with Absorbent Binary Endpoints