Multivariate Statistical Methods for Analyzing Genetic Association Studies

Genetic association studies lead to simultaneous categorical data analysis. The sample for every genetic locus consists of a contingency table containing the numbers of observed genotype-phenotype combinations. The goal of the statistical analysis is to detect associations between the (potentially very large) set of genetic markers and the (typically binary) phenotype of interest. This is a particular multiple test problem which has several challenging aspects, for instance the high dimensionality of the statistical parameter and the discreteness of the statistical model. Furthermore, the locus-specific contingency tables exhibit strong dependencies, at least in blocks of loci which are in linkage disequilibrium (LD), due to the biological mechanism of inheritance. This makes a multivariate statistical analysis the method of choice. In the first part of the presentation, we will consider frequentist multiple test procedures which are based on the concept of the effective number of tests based on probability bounds, see [1,2] and Section 4.3 of [3]. Such procedures incorporate LD information in a relaxed multiplicity correction of Bonferronior Šidák-type. Due to the extended interpretation of LD provided in [4], this methodology is applicable for a variety of families of test statistics. The second part is based on [5] and deals with Bayesian approaches to contingency table inference for genetic association data. Here, the multiplicity correction is performed via an appropriate construction of the prior probabilities for the validity of the locus-specific null hypotheses of no association. Exploiting the conjugacy of Dirichlet and multinomial distributions, posterior probabilities for the nulls can exactly be computed for any finite sample size, and decision theoretic multiple test procedures can be applied.