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Mixed Effects Models and their Applications

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Title: Mixed Effects Models and their Applications
Author: Wang, Weiqiang
Department: Department of Mathematics and Statistics
Program: Mathematics and Statistics
Advisor: Feng, ZenyDeardon, Rob
Abstract: Due to the flexibility and easy application, mixed effects models have been widely applied in medical studies. The first piece of my doctoral work involves modeling multiple events and their times to event using mixed effects models. Many diseases progress toward multiple outcomes after onset and patients may or may not be susceptible to the outcomes of interest. Interest in analyzing such disease data arises because statistical models must account for the mixture of susceptible and non-susceptible uncertainty, intra-correlation among multiple outcomes and intra-correlation among times of occurrence within each patient. We propose a mixed effects model nested within a mixture model to account for those issues. An EM algorithm is used to estimate parameters. Analytical forms of standard errors of each estimated parameters are derived based on the Louis' formula. Simulation studies are conducted to assess the performance of our proposed method. In the second paper of my thesis, a 2-step method is proposed to analyze genetic association between a single nucleotide polymorphism (SNP) and multiple longitudinal traits. In the first step, mixed effects models are used to analyze each longitudinal trait focusing on the estimated random effects. In the second step, we test the genetic association between each SNP with multiple estimated random effects simultaneously. The method is validated and evaluated through simulation studies and applied to the Framingham Heart Study data. The method is proved to be more powerful to detect the genetic pleiotropic effects than the union of testing each trait individually. The third paper focuses on the identification of gene and environment interactions. A random slope is introduced to the mixed effects model to model the genetic interactions with environmental factors. Both random intercepts and slopes will be treated as phenotypes to be tested. The method is validated and evaluated through simulation studies and real data application.
Date: 2014-04

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