AbstractsMathematics

In chapter one a Liability Threshold Mixed Linear Model (LTMLM) association statistic is introduced for ascertained case-control studies that increases power vs. existing mixed model methods for diseases with low prevalence, with a well-controlled false-positive rate. Using a chi-square score statistic computed from posterior mean liabilities (PML) under the liability threshold model. Each individual’s PML is conditional not only on that individual’s case-control status, but also on every individual’s case-control status and on the genetic relationship matrix obtained from the data estimated using a multivariate Gibbs sampler. In a Welcome Trust Case Control Consortium 2 (WTCCC2) multiple sclerosis data set LTMLM attained a 4.3% improvement (P=0.005) in chi-square statistics (vs. existing mixed model methods) at 75 known associated SNPs. Family-biased ascertainment is considered in chapter 2, where cases and controls are ascertained non-randomly with respect to family relatedness. We introduce a family based association statistic (LT-Fam) that is robust to this problem. For type 2 diabetes cases and controls (in the Jackson Heart Study) we down-sampled to increase relatedness among cases and observed: ATT was inflated and MLM was deflated, while LT-Fam was properly calibrated. Finally, in chapter three, we propose a 2-Step Bayesian Model Averaging (2-Step BMA) method with Propensity Score (PS) adjustment that targets the primary treatment of interest characterizing the treatment effect while controlling for a high dimensional set of unknown confounders including metabolites and other epidemiological factors. This method improves on existing methods by averaging over the entire model space of both the treatment and outcome models to control for cofounding while targeting treatment effect and without need of an arbitrary number of confounders to include a priori. Biostatistics Advisors/Committee Members: Price, Alkes (committee member), Zigler, Corwin (committee member), liang, liming (committee member).