A discrete-time survival model to handle interval-censored covariates, with applications to HIV cohort studies

Methods are lacking to handle the problem of survival analysis in the presence of an interval-censored covariate, specifically the case in which the conditional hazard of the primary event of interest depends on the occurrence of a secondary event, the observation time of which is subject to interval-censoring. We propose and study a flexible class of discrete-time parametric survival models that handle the censoring problem through simultaneous modelling of the interval-censored secondary event, the outcome, and the censoring mechanism. We apply this model to the research question that motivated the methodology, estimating the hazard ratio of all-cause mortality between HIV-positive and HIV-negative individuals as a function of age and calendar time for males and females in a prospective cohort study in South Africa, which allows for insight into which HIV-positive demographic groups are at highest risk of excess mortality.