Adjusting for Misclassified Outcomes in a Multistate Model

Abstract

In this dissertation, we present a new model that accounts for time-dependent sensitivity in multivariate outcome survival models. Our problem was motivated by an interest in estimating baseline risk and associated covariates of time to postnatal transmission of HIV from mother to child (MTCT). Studies of postnatal transmission may be subject to bias due to several factors, including informative censoring due to death, the competing risk of weaning, and imperfect sensitivity of diagnostic testing for HIV in infants. While these issues have been partially addressed in previous literature, no single approach addresses all three. We propose to jointly model time to postnatal infection, time to death, and time to weaning as three separate outcomes in a multistate model, which is a framework often used to describe the progression of a process through successive events. Conditional on the underlying multistate model, we define an additional random variable to measure the probability of detection as a function of time since infection, and the cumulative distribution of this random variable serves as a sensitivity function that increases over time. We focus first on jointly modeling time to postnatal infection and time to death as two outcomes of an illness-death model. To incorporate sensitivity, we define an exponential random variable for the delay in detection, with the exponential rate determined a priori from the literature. We specify a full likelihood by parameterizing the baseline transition intensities as flexible penalized spline functions and numerically calculate maximum likelihood estimates for all spline parameters and covariates of interest. We next expand the illness-death model to include time to weaning as an additional outcome of the model. As before, we specify an exponential delay random variable and define spline-based baseline transition intensities. To estimate the parameters, we implement a Bayesian MCMC algorithm, using the prior for the spline coefficients to impose smoothness. Finally, we compare the extended illness-death model to the simpler illness-death model and to ad-hoc methods often used in the applied literature.