Statistical Methods for the Analysis of Genomic and Survival Data

Genome-wide association studies (GWAS) have become popular tools for gene discovery in human disease research. While GWAS are becoming common, statistical methods for GWAS are in a bottleneck stage. In this dissertation, statistical methods are developed to help efficiently identify associated genetic markers.;The power of an association test depends on the underlying genetic models of the functional loci. It is of great importance to develop powerful goodness-of-fit tests for genetic models using case-control data. We develop a likelihood ratio test to test goodness-of-fit for either a recessive or dominant model without the requirement of known disease prevalence in the population. The test statistic has a closed-form formula with a simple null asymptotic distribution; thus its implementation is easy even for GWAS.;Most existing association tests for case-control studies are not efficient in the presence of genetic heterogeneity. Zhou and Pan proposed a binomial mixture model based association test to account for the possible genetic heterogeneity in case-control studies. However, it is difficult to apply their method to GWAS due to the intensive computational burden. We develop a likelihood ratio test (LRT) based on a general binomial mixture model. Our proposed LRT statistic has a closed-form formula and an explicit asymptotic null distribution. Therefore, it is easy to implement for GWAS.;Testing for Hardy-Weinberg Disequilibrium (HWD) in the control group has been used in a quality control step for almost every GWAS. However, this procedure is based on a misconception that HWE generally holds in the control group. We demonstrate that SNPs associated with the disease often have small p-value for HWD test. And we recommend against the premature exclusions of SNPs simply based on HWD.;In addition, we also address the statistical analysis for the survival data, which are very common datasets in current biomedical applications. Melanoma is one common cause of brain metastasis. It is desirable to identify risk factors of brain metastasis in melanoma patients. By taking advantages of two cohort studies at NYU, we identify clinical factors that were associated with brain metastasis development with survival analysis.