The Botswana Combination Prevention Project was a cluster-randomized HIV prevention trial whose follow-up period coincided with Botswana’s national adoption of a universal test-and-treat strategy for HIV management. Of interest is whether, and to what extent, this change in policy (i) modified the observed preventative effects of the study intervention and (ii) was associated with a reduction in the population-level incidence of HIV in Botswana. To address these questions, we propose a stratified proportional hazards model for clustered interval-censored data with time-dependent covariates and develop a composite expectation maximization algorithm that facilitates estimation of model parameters without placing parametric assumptions on either the baseline hazard functions or the within-cluster dependence structure. We show that the resulting estimators for the regression parameters are consistent and asymptotically normal. We also propose and provide theoretical justification for the use of the profile composite likelihood function to construct a robust sandwich estimator for the variance. We characterize the finite-sample performance and robustness of these estimators through extensive simulation studies. Finally, we conclude by applying this stratified proportional hazards model to a re-analysis of the Botswana Combination Prevention Project, with the national adoption of a universal test-and-treat strategy now modeled as a time-dependent covariate.
Cook, Kaitlyn; Lu, Wenbin; and Wang, Rui, "Marginal Proportional Hazards Models for Clustered Interval-Censored Data with Time-Dependent Covariates" (February 2022). Harvard University Biostatistics Working Paper Series. Working Paper 234.