Recursive Mixture Modeling and Nonparametric Testing of Association in Case-Control Studies

• Activity Number: 436
• Type: Invited
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Li Ma*+
• Companies: Duke University
• Keywords: Bayesian nonparametrics ; genome-wide association studies ; recursive partitioning ; contingency tables ; high-dimensional data ; two-sample problem

Abstract

In many case-control settings a central goal is to test for the association between the predictors and the response. In such studies relevant covariates need to be accounted for to avoid false detections and loss of power for detecting true associations. While it is relatively easy to incorporate covariates in a parametric framework such as the logistic regression, conditioning is more difficult for nonparametric tests. Classical methods such as the Cochran-Mantel-Haenszel test achieve that by dividing a marginal table into conditional ones. Such an approach is undesirable in many modern applications because there are often a huge number of conditional tables, most of which are sparse due to the multi-dimensionality of both the predictor space and the covariate space. In this work, we introduce a nonparametric test for association given covariates that is robust to such sparsity. The test is based on a recursive mixture formulation and it can be carried out through efficient closed-form computation without Markov Chain Monte Carlo. Lying at the core of the method is a nonparametric prior for conditional distributions based on recursive partitioning.