Bayesian Approach for Nonlinear Dynamic System and Genome-Wide Association Study

Abstract

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 various issues related to multiple tests. 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 positive FDR at a given level, the realized FDR is controlled. Our simulations show that the power can be substantially improved with correct 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, while keeping the FDR under control. The modified 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 among population. 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 overall mean effect and heterogeneity variance in various realistic cases. We illustrate our method to a study on DRD2 gene in multiple association studies with schizophrenia.

Dynamic system defined by ordinary differential equations is an important tool to modeling complicated biology system. To estimate parameters in the dynamic system which analytic, close form solution is not available and involving missing or censored data, we extend Bayesian Euler's Approximation method based on data augmentation algorithm. Our simulation study shown the method is robust in both cases. The proposed method is applied to analyze HIV viral load dataset, which enable us to retrieve information from the censored data.