Semiparametric methods for inferring treatment effects on outcomes defined only if a post-randomization event occurs

Sometimes in a randomized study, interest may reside in inferring a treatment effect on an outcome only defined if an event E has occurred. For instance, in an HIV vaccine trial, the investigator may want to learn about the effect of treatment on viral load, but this outcome is only measurable in subjects who become infected (the event E) during the course of the trial. Arguing within the framework of causal inference theory, the relevant treatment effect Delta here is defined in the subpopulation PE,E of individuals for whom the outcome would exist regardless of treatment assignment.; In the first chapter, Delta is shown to be non-identifiable from the observed data. This has important implications concerning the inferential approach to this problem. These are discussed and two inferential strategies are proposed: (1) to place sharp bounds on Delta that contain a range of plausible values for the treatment effect in the subpopulation PE,E , and (2) to describe a set of identifying assumptions in the form of user-specified variation independent parameters which permit the estimation of Delta. Since these parameters are not identified from the data, a sensitivity analysis approach is recommended.; The second chapter delves into the inferential problem of estimating a treatment effect Delta in the subpopulation PE,E conditional on baseline covariates. In particular, it considers estimation of parameters gamma indexing models for the outcome mean conditional on treatment and covariates in the subpopulation for which the outcome would be defined regardless of treatment assignment. Such parameters are not identified from randomized trial data but become so if it is additionally assumed (a) that the subpopulation PE&d1;,E of subjects that would experience event E under the second treatment but not under the first is empty and (b) 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/her outcome under the second treatment, and his/her pre-treatment covariates. A class of estimating equations whose solutions comprise, up to asymptotic equivalence, all consistent and asymptotically normal estimators of gamma under (a) and (b) is proposed and a locally semiparametric efficient estimator of gamma is derived.; Finally, the third chapter discusses the peculiar behavior of an estimator proposed by Gilbert, Bosch and Hudgens (2003) for estimating Delta in the absence of baseline covariates. It is shown that this estimator is the maximum likelihood estimator under a model with a boundary condition. Its limiting distribution is derived and convergence to it is shown to be non uniform over all laws allowed by the model. An important negative consequence of this result is that Wald confidence intervals do not have coverage probabilities equal to the prescribed level, regardless of whether an analytic variance estimator or the non-parametric bootstrap variance estimator is used. Also it is argued that conditional coverage, rather than overall coverage probabilities, are the relevant measures of confidence in this problem.