Statistical Methods for Assessing Complex Multi-Exposure Data in HIV and Genetic Epidemiology
Abstract
Complex, multi-exposure problems arise in many forms. In this dissertation, we delve into three disparate forms of complex, multi-exposure questions, from the safety of combination antiretroviral (ARV) regimens to the complexities arising from repeated measures data to statistical genetics.In Chapter 1, we evaluate a hierarchical model that groups ARVs by drug class, while still providing individual ARV effect estimates, to screen for the safety of ARV exposures during pregnancy. In simulations, we compare the statistical operating characteristics of the hierarchical approach to the standard approaches of separate regression models for each ARV and a full, fixed effect model. We illustrate the characteristics of the hierarchical approach in an application evaluating risk of preterm delivery using a study including over 2,000 pregnancies representing over 100 antiretroviral combinations, each involving up to three drug classes.
Chapter 2 explores estimation of the relative excess risk due to interaction (RERI) in clustered data settings. The RERI is a measure of additive interaction for binary outcomes that can be calculated from multiplicative regression models. We evaluate the RERI for the setting of clustered data using both population-averaged and cluster-conditional models. In simulation studies, we find that estimation and inference for the RERI using population-averaged models is straightforward. However, frequentist implementations of cluster-conditional models including random intercepts often fail to converge or produce degenerate variance estimates. We develop a Bayesian implementation of log binomial random intercept models, which represents an attractive alternative for estimating the RERI in cluster-conditional models. We apply the methods to an observational study of adverse birth outcomes in mothers with HIV infection, in which mothers are clustered within clinical research sites.
In Chapter 3, we introduce a computationally efficient algorithm for permutation testing between a single rare genetic variant and affection status which also allows for adjustment of covariates. To demonstrate the feasibility of the algorithm, we apply the method to a study of chronic obstructive pulmonary disease. In simulations, we show that the permutation test maintains a Type I error rate closer to the nominal level than the asymptotic and saddlepoint approximation tests for rare variants.
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