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Inverse Probability Weighting in Survival Analysis and Network Analysis

Inverse probability weighting is a popular technique to accommodate selection bias due to non-random sampling and missing data. In the first chapter, we develop an inverse probability weighted estimator and an augmented inverse probability weighted estimator of regression coefficients for a linear model with randomly censored covariates, when the censoring mechanism may be dependent on the outcome. We investigate the asymptotic properties of both estimators and evaluate their finite sample performance through extensive simulation studies. We apply the proposed methods to an Alzheimer’s disease study. In the second chapter, we present an application of network analysis in a study of metabolites associated with moderate or severe hearing loss in the Nurses’ Health Study. In this first large population-based investigation the metabolomics of hearing loss, we successfully identified a set of metabolites and derived a corresponding network-informed metabolite score that was associated with the moderate or severe hearing loss in women. In the third chapter, we propose inverse probability weighted methods for covariance network estimation of a Gaussian random vector under matched case-control study designs. We show that the direct covariance estimate is biased when matching is ignored in both low and high dimensional settings. We propose a weighted covariance estimator for low dimensional settings and a likelihood-based estimation procedure for high dimensional settings, applicable in matched or highly stratified study designs. We applied our methods to existing data from a coronary heart disease case-control metabolomics study, nested within the prospective Women’s Health Initiative cohorts. The fourth chapter focuses on network aggregation using multiple datasets. We provide a summary of existing methods for network aggregation and investigate their performance under varying network structures, size and sparsity through simulation studies.
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