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Marginal Proportional Hazards Models for Clustered Interval-Censored Data with Time-Dependent Covariates

Marginal Proportional Hazards Models for Clustered Interval-Censored Data with Time-Dependent Covariates

The Botswana Combination Prevention Project was a cluster-randomized trial evaluating the impact of combination HIV prevention on the 3-year cumulative incidence of HIV in Botswana. The trial's follow-up period coincided with Botswana's national adoption of a universal test-and-treat strategy for HIV management. In this talk, we set out to determine 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 incidence of HIV in Botswana. To address these questions, we propose a marginal proportional hazards model for clustered interval-censored data with time-dependent covariates. We develop a composite expectation maximization algorithm that facilitates estimation of the model parameters without placing parametric assumptions on either the baseline hazard functions or the within-cluster dependence structure. We also develop a robust profile composite likelihood-based sandwich estimator for the variance. We discuss both the theoretical properties of these estimators and their performance in a series of simulation studies. We conclude by applying them 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.

## Department of Mathematics and Statistics