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 (1989, Biometrics 45, 1-11) 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 (1976, Journal of the Royal Statistical Society, Series B 38, 290-295) 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.