Adaptive Testing of Conditional Association Through Recursive Mixture Modeling

Abstract

In many case-control studies, a central goal is to test for association or dependence between the predictors and the response. Relevant covariates must be conditioned on to avoid false positives and loss in power. Conditioning on covariates is easy in parametric frameworks such as the logistic regression—by incorporating the covariates into the model as additional variables. In contrast, nonparametric methods such as the Cochran-Mantel-Haenszel test accomplish conditioning by dividing the data into strata, one for each possible covariate value. In modern applications, this often gives rise to numerous strata, most of which are sparse due to the multidimensionality of the covariate and/or predictor space, while in reality, the covariate space often consists of just a small number of subsets with differential response-predictor dependence. We introduce a Bayesian approach to inferring from the data such an effective stratification and testing for association accordingly. The core of our framework is a recursive mixture model on the retrospective distribution of the predictors, whose mixing distribution is a prior on the partitions on the covariate space. Inference under the model can proceed efficiently in closed form through a sequence of recursions, striking a balance between model flexibility and computational tractability. Simulation studies show that our method substantially outperforms classical tests under various scenarios. Supplementary materials for this article are available online.

KEY WORDS:

• Bayesian model comparison
• Case-control study
• Conditional independence
• Contingency table
• Genetic association study
• Recursive partitioning

Acknowledgments

This research is partly supported by NSF grant DMS-1309057. The author thanks the editors and three anonymous reviewers for helpful comments.