A Bayesian method for finding interactions.

Abstract

In genomic studies, datasets with a small sample size and a large number of potential predictors are common. Recently, gene-gene interactions (epistasis) and gene-environment interactions have been drawing increasing attention due to the etiology of complex diseases. If all possible pair wise interactions are to be explored, then this leads to a high dimensional model space. There is very little work to handle this common problem. The emphasis of my research is on selecting interactions and controlling the number of falsely discovered predictors with a limited sample size. The method I propose simultaneously satisfies the two properties for inclusion of interactions: interpretability and discovery. In addition, I develop a novel equivalence between variable selection procedures and the false discovery rate. One application of my research is the development of a model to aid the therapeutic decision by identifying prognostic factors or interactions among abundant variables from the clinical and molecular profiles of patients. Given a patient's profile, an optimal treatment involves a trade-off between efficacy and toxicity. My research also proposes a novel way to compare treatments with multiple endpoints.