An imputation method for interval censored time-to-event with auxiliary information: analysis of the timing of mother-to-child transmission of HIV

Abstract

The timing of mother-to-child transmission (MTCT) of HIV is critical in understanding the dynamics of MTCT. It has a great implication to developing any effective treatment or prevention strategies for such transmissions. In this paper, we develop an imputation method to analyze the censored MTCT timing in presence of auxiliary information. Specifically, we first propose a statistical model based on the hazard functions of the MTCT timing to reflect three MTCT modes: in utero, during delivery and via breastfeeding, with different shapes of the baseline hazard that vary between infants. This model also allows that the majority of infants may be immuned from the MTCT of HIV. Then, the model is fitted by MCMC to explore marginal inferences via multiple imputation. Moreover, we propose a simple and straightforward approach to take into account the imperfect sensitivity in imputation step, and study appropriate censoring techniques to account for weaning. Our method is assessed by simulations, and applied to a large trial designed to assess the use of antibiotics in preventing MTCT of HIV.

Figure 1

Cumulative rates of MTCT of HIV (solid black) and detection of MTCT of HIV. The dashed lines represents the time to detection based on MI with m=2. The step curve represents time to detection based on the observed data with cross hairs indicating censoring times).

Figure 2

Curves of the cumulative proportion of late postnatal infections for the observed data analysis (black) and each of the augmented data sets with time to first positive test (red) and timing of infection adjusted for imperfect sensitivity (grey). The vertical lines represent the centers of the visit windows. The crosses on the solid line indicate where infants had a last negative test and then were subsequently lost to follow-up.