Comparing competing risk outcomes within principal strata, with application to studies of mother-to-child transmission of HIV.

In randomized trials to prevent breast milk transmission of human immunodeficiency virus (HIV) from mother to infant, investigators are often interested in assessing the effect of a treatment or intervention on the cumulative risk of HIV infection by time (age) t in infants who are alive and uninfected at a certain time point τ(0)  < t. Such comparisons are challenging for two reasons. First, infants are typically randomized at birth (time 0 < τ(0) ) such that comparisons between trial arms among the subset of infants alive and uninfected at τ(0) are subject to selection bias. Second, in most mother-to-child transmission (MTCT) trials competing risks are often present, such as death or cessation of breastfeeding prior to HIV infection. In this paper, we present methods for assessing the causal effect of a treatment on competing risk outcomes within principal strata. In MTCT trials, the causal effect of interest is that of treatment on the risk of HIV infection by time t > τ(0) within the principal stratum of infants who would be alive and uninfected by τ(0) regardless of randomization assignment. We develop large sample nonparametric bounds and a semiparametric sensitivity analysis model for drawing inference about this causal effect. We present a simulation study demonstrating that the proposed methods perform well in finite samples. We apply the proposed methods to a large, recent MTCT trial.