Proportional Hazards Regression for Interval-Censored Outcomes With an Interval-Censored Covariate

Identifying predictors for viral rebound trajectories after antiretroviral therapy (ART) interruption is central to HIV cure research. Motivated by the need to determine whether the time to achieve viral suppression after ART initiation can predict the time to viral rebound following ART interruption, we investigate modeling approaches that relate an interval-censored outcome (e.g., time to viral rebound) and an interval-censored covariate (e.g., time to viral suppression) under the assumption that viral load only crosses a threshold when bracketed by consecutive assessments. We develop estimation and inference procedures for fitting a proportional hazards regression model when both the outcome and a covariate are interval-censored, without imposing parametric assumptions on the baseline hazard functions. To accommodate participants with multiple episodes of ART initiation and interruption, we extend the proposed method to account for the clustering of repeated observations within individuals. We derive the asymptotic properties of the proposed method and evaluate its finite-sample performance through simulation studies. Applying the method to data from the Zurich Primary HIV Infection cohort, we find that a longer time to viral suppression during ART is associated with an increased hazard of viral rebound after ART interruption.