Methods for Meta-Analysis and for Modeling HIV Viral Rebound

Abstract

In Chapter 1, we develop methods for random-effects meta-analysis of combined outcomes. In clinical practice, treatment decision-making typically depends on an overall assessment of outcomes balancing benefits in various domains and potential risks. When individual patient data (IPD) are available from all studies, combined outcomes can be calculated for each individual and standard meta-analysis methods would apply. However, IPD are usually difficult to obtain. We propose a method to estimate the overall treatment effect for combined outcomes based on first reconstructing pseudo IPD from available summary statistics and then pooling estimates from multiple reconstructed datasets. Chapter 2 and 3 focus on methods for modeling the HIV viral rebound following interruption of antiretroviral therapy. In Chapter 2, we develop the Smoothed Simulated Pseudo Maximum Likelihood Estimation (S-SPMLE) approach for fitting nonlinear mixed effects models with censored responses. In addition, we derive hypothesis tests for the correlation among random effects and for the distributional assumptions of random effects. In Chapter 3, we propose a proportional hazards regression model relating an interval-censored outcome to an interval-censored covariate, and develop an Expectation-Maximization algorithm for parameter estimation. The approach is further extended to settings where observations are clustered. We apply it to estimate the effect of the time to viral suppression on the time to subsequent viral rebound.