Sensitivity Analyses Comparing Time-to-Event Outcomes Existing Only in a Subset Selected Postrandomization

In some randomized studies, researchers are interested in determining the effect of treatment assignment on outcomes that may exist only in a subset chosen after randomization. For example, in preventative human immunodeficiency virus (HIV) vaccine efficacy trials, it is of interest to determine whether randomization to vaccine affects postinfection outcomes that may be right-censored. Such outcomes in these trials include time from infection diagnosis to initiation of antiretroviral therapy and time from infection diagnosis to acquired immune deficiency syndrome. Here we present sensitivity analysis methods for making causal comparisons on these postinfection outcomes. We focus on estimating the survival causal effect, defined as the difference between probabilities of not yet experiencing the event in the vaccine and placebo arms, conditional on being infected regardless of treatment assignment. This group is referred to as the always-infected principal stratum. Our key assumption is monotonicity—that subjects randomized to the vaccine arm who become infected would have been infected had they been randomized to placebo. We propose nonparametric, semiparametric, and parametric methods for estimating the survival causal effect. We apply these methods to the first Phase III preventative HIV vaccine trial, VaxGen's trial of AIDSVAX B/B.