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

Abstract: 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 modeling 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 effect of HIV status on all-cause mortality in a prospective cohort study in South Africa. Our model has applicability for many open questions, including estimating the impact of policy decisions on population level HIV-related outcomes and determining causes of morbidity and mortality for which the HIV positive population may be at increased risk. Examples include determining how the large-scale transition from efavirenz-based to dolutegravir-based first-line ART impacted mortality for people living with HIV and determining whether HIV status is associated with increased risk of stroke, diabetes, hypertension, and other non-communicable diseases.