Semiparametric estimation of treatment effects given base-line covariates on an outcome measured after a post-randomization event occurs.

We consider estimation, from a double-blind randomized trial, of treatment effect within levels of base-line covariates on an outcome that is measured after a post-treatment event E has occurred in the subpopulation 𝒫(E,E) that would experience event E regardless of treatment. Specifically, we consider estimation of the parameters γ indexing models for the outcome mean conditional on treatment and base-line covariates in the subpopulation 𝒫(E,E). Such parameters are not identified from randomized trial data but become identified if additionally it is assumed that the subpopulation 𝒫(Ē,E) of subjects that would experience event E under the second treatment but not under the first is empty and a parametric model for the conditional probability that a subject experiences event E if assigned to the first treatment given that the subject would experience the event if assigned to the second treatment, his or her outcome under the second treatment and his or her pretreatment covariates. We develop a class of estimating equations whose solutions comprise, up to asymptotic equivalence, all consistent and asymptotically normal estimators of γ under these two assumptions. In addition, we derive a locally semiparametric efficient estimator of γ. We apply our methods to estimate the effect on mean viral load of vaccine versus placebo after infection with human immunodeficiency virus (the event E) in a placebo-controlled randomized acquired immune deficiency syndrome vaccine tri.