🤖 AI Summary
In survival analysis, interval censoring of covariates—such as HIV infection time known only to lie within a follow-up interval—induces bias in causal effect estimation. Method: We propose the first identifiable discrete-time parametric joint model that simultaneously characterizes the interval-censored covariate, the primary event (all-cause mortality), and the censoring mechanism. Our approach integrates discrete-time survival modeling, a joint likelihood framework, the EM algorithm, and Monte Carlo integration to ensure strict parameter identifiability. Contribution/Results: Applied to a South African prospective cohort, the model yields an accurate estimate of the causal effect of HIV status on all-cause mortality (HR = 2.17, 95% CI: 1.83–2.57), substantially outperforming ad hoc alternatives—including ignoring censoring or using proxy variables. This work establishes a theoretically sound and practically viable paradigm for causal inference under interval-censored covariates.
📝 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 joint 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.