Analyzing doubly censored data with covariates, with application to AIDS

This paper proposes a method for incorporating covariate information in the analysis of survival data when both the time of the originating event and the failure event can be right- or interval-censored. This method generalizes the one-sample estimation results of De Gruttola and Lagakos by allowing the distribution of time between the two events to be a function of covariates under a proportional hazards model. Estimates for the model coefficients, as well as the underlying distributions, are obtained by an iterative fitting procedure based on Turnbull's self-consistency algorithm in combination with the Newton-Raphson algorithm. The method is illustrated with data from a study of hemophiliacs infected with the human immunodeficiency virus.