Pure Likelihood-based Methods for Genetic Association Studies

In this thesis, we contribute to the growing literature on the Evidential methodology for genetic association studies. The Evidential Paradigm (EP) is an alternative statistical framework to the Frequentist and Bayesian paradigms for statistical inference, which uses likelihood ratios to measure the strength of statistical evidence. The EP has favorable operational characteristics, with small and bounded error probabilities, and the framework has been applied to genetic linkage and association studies. We discuss some of the well-recognized issues associated with the Frequentist framework in assessing association evidence in genetic association studies, and we develop novel approaches under the EP to address these issues. We first address the issue of prioritizing individual rare sequence variants within an associated region in case-control association studies. Rare variants are commonly ranked by Fisher's exact test p-values, however, depending on whether one- or two-sided p-values are used, the same set of rare variants can be ranked differently. Motivated by the EP, we propose a conditional likelihood ratio-based measure, maxLRc, to rank rare variants. We show analytically that the maxLRc is based on the same underlying model as Fisher's exact test, and it is always well-defined even when data is under separation. Through simulations, we show that the maxLRc outperforms the commonly used two-sided Fisher's exact p-values in most simulation settings. We then address another issue in large-scale genetic association studies: under the Frequentist paradigm, any small effect size could become statistically signicant with large enough sample size. We discuss an EP solution to this problem which extends the EP to accommodate composite hypotheses (EPc) and uses the generalized likelihood ratios (GLRs) to measure statistical evidence. To provide theoretical justication for the extension, we analytically derive the operational characteristics for the EPc. We show that the GLRs have small and bounded error probabilities for the Normal distribution and fixed-dimensional parametric models asymptotically. We show that the data can support either the null or the alternative hypothesis under the EPc, allowing association results to be more clearly demarcated; and the use of composite hypotheses can guard against statistically signicant but practically insignificant findings in large-scale association studies.Ph.D