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

Area of Science:

• Epidemiology
• Biostatistics
• Public Health

Background:

• The Botswana Combination Prevention Project (BCP) was a cluster-randomized trial for HIV prevention.
• Its follow-up coincided with Botswana's national adoption of a universal test and treat (UTT) strategy.
• The study aimed to assess the impact of this policy shift on the intervention's effectiveness.

Purpose of the Study:

• To develop and validate a statistical methodology for analyzing clustered, interval-censored data with time-dependent covariates.
• To evaluate the influence of Botswana's universal test and treat strategy on HIV prevention outcomes within the BCP trial.

Main Methods:

• A stratified proportional hazards model for clustered interval-censored data was employed.
• A composite expectation maximization algorithm was developed for parameter estimation.
• The model accommodates time-dependent covariates and makes no parametric assumptions on baseline hazards or within-cluster dependence.

Main Results:

• The developed estimators for regression parameters were shown to be consistent and asymptotically normal.
• A robust sandwich estimator for variance was proposed and theoretically justified using a profile composite likelihood function.
• Extensive simulation studies confirmed the finite-sample performance and robustness of the estimators.

Conclusions:

• The novel statistical model provides a robust framework for analyzing complex epidemiological data influenced by policy changes.
• The re-analysis of the Botswana Combination Prevention Project using this model incorporates the UTT strategy as a time-dependent covariate.
• This approach allows for a more nuanced understanding of intervention effectiveness in real-world public health policy contexts.