Analysis of a randomized trial to prevent vertical transmission of HIV-1

We analyze data from a randomized trial of breastfeeding versus formula feeding in HIV-1-infected mothers and their infants. Estimates of infant HIV-l-free survival and the timing of vertical transmission of HIV-1 are complicated by the fact that the infants' HIV-1 status at death may be unknown, the time of HIV-1 infection may be interval censored, and the tests used to detect HIV-1 infection in the infants may be less than 100% sensitive or specific. To address these problems we develop nonparametric and semiparametric approaches to estimating the joint distribution of HIV-1 infection time and death time. The nonparametric estimator is based on a self-consistency algorithm and, in the current application, provides a unique estimate of the HIV-1-free survival at 24 months old. However, the estimate of the cumulative probability of HIV-I infection over time is nonunique. To resolve the nonuniqueness of the nonparametric estimator a semiparametric approach is proposed in which the joint distribution of HIV-1 infection time and death time is decomposed into the marginal distribution of death time, f(t), and the conditional distribution of HIV-1 infection time given the death time, g(s\t). f(t) is estimated nonparametrically while a Weibull distribution is used to model g(s\t). The parameters of the Weibull distribution are allowed to vary slowly in t using splines. The two approaches are shown to be complimentary Using these methods we find that the probability of HIV-I infection is significantly lower and the 24-month HIV-l-free survival is significantly higher in the formula-feeding group.