Marginal proportional hazards models for clustered interval-censored data with time-dependent covariates

Abstract

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 modified the preventative effects of the study intervention. To address such questions, we adopt 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.

Keywords: HIV; clustered failure time data; composite em algorithm; composite likelihood; interval censoring; marginal models; nonparametric likelihood; proportional hazards; semiparametric regression; time-dependent covariates.

Figure 1.

Comparison of 100 randomly selected estimated stratum-specific baseline survival functions (in gray) with the true data-generating functions (in color) under model (10) (column A), model (11) (column B), and model (12) (column C) with $M=100$, $S=4$, and a hierarchical within-cluster dependence structure.

Figure 2.

Duration of follow-up for each community in the Botswana Combination Prevention Project, measured as the time from the earliest recorded study visit to the last recorded study visit across all community members. Intervention assignment is indicated by line type (standard of care, solid; combination prevention, dashed) and pair membership by color; the shaded region corresponds to the time during which the national universal test and treat (UTT) policy was in effect.

Figure 3.

Estimated cumulative probability of HIV seroconversion in the standard-of-care communities (in red) and combination prevention communities (in blue), both before (solid line) and after (dotted line) universal test and treat adoption in Botswana.