Genome-wide association studies (GWAS) have been widely used to identify single-nucleotide polymorphisms (SNPs) that are responsible for diseases. A challenging aspect of this study is to resolve the multiple testing issue. We propose a new Bayesian method to measure statistical significance in these genome-wide studies based on the concept of false discovery rate (FDR). Our proposed method provides a convenient way to integrate prior knowledge obtained from external resources into current study. By controlling Bayesian FDR at a given level, the realized FDR is controlled. Our simulations show that the power can be substantially improved with precise prior information while the FDR is controlled at the desired level. When prior information is imprecise, our method can still improve the power of detecting signals and while keeping the FDR under control. The proposed Bayesian method is applied to a GWAS for schizophrenia. Meta-analysis is another approach to utilize information from multiple sources by combining results from multiple independent studies. A major concern in carrying out meta-analysis involves the proper characterization of heterogeneity (refers to the variation in results among studies) among populations. To account for heterogeneity, the most commonly used approach is to implement a random-effects model, where the random-effects are assumed to be normally distributed with an unknown population mean and an unknown variance. We relax the normality assumption and show that a broad class of distributions can be approximated by a class of mixture distributions. The population mean and variance estimates based on the mixture density are then obtained by the EM algorithm. Our results show that the proposed method greatly improves the accuracy in estimating the overall mean effect and heterogeneity variance in various realistic cases. We illustrate our method to combine results from six association studies on C957T polymorphism in DRD2 gene with schizophrenia. Dynamic systems defined by ordinary differential equations are important tools for modeling complicated biology system. To estimate parameters in a dynamic system for which the analytic, closed form solution is not available and involves missing or censored data, we extend the Bayesian Euler's Approximation method based on data augmentation algorithm. Our simulation study shows the method is robust in both cases. The proposed method is applied to analyze a HIV viral load dataset, which enables us to retrieve information from the censored data.
Number Of Pages: 118
Published: 30th September 2011
Dimensions (cm): 25.4 x 20.3 x 0.8
Weight (kg): 0.249