Statistical methods for surrogacy and hypothesis testing in HIV research

Abstract

This dissertation focuses on the estimation of surrogacy for biomarkers in time-to-event setting and hypothesis testing for mixed-effects models. In the first part, we develop a new measure to evaluate the proportion of treatment effect explained by surrogate markers in the time-to-event setting, with an application to HIV clinical trials. In the second part, we develop a hypothesis testing procedure for random-effects meta-analysis. We consider the exact likelihood ratio tests for two hypotheses with boundary problems, including testing the global null and homogeneity. The proposed method works well regardless of the number of studies. We apply the methodology to assess the association between circumcision and HIV among men who have sex with men. In the third part, we develop a general hypothesis testing framework in mixed-effects models. We are interested in testing the hypothesis that involves both fixed-effects parameters and random-effects variance component and we propose a novel construction of independent score statistics from both components. We consider the linear combinations of two score statistics. We illustrate the power tradeoff between different linear combination weights and propose to choose the weight based on Bayes and Minimax criteria so that power can be balanced well across the alternative space. We apply the methodology to random-effects meta-analysis, set-based genetic association analysis and time-varying treatment effect in survival analysis.