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 τ0τ0 within the principal stratum of infants who would be alive and uninfected by τ0 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. © 2012 John Wiley & Sons, Ltd.
