A Bayesian Hierarchical Model for High-Dimensional Meta-analysis

Many biomedical applications are concerned with the problem of selecting important predictors from a high-dimensional set of candidates, with the gene expression data as one example. Due to the fact that the sample size in any single study is usually small, it is thus important to combine information from multiple studies. In this chapter, we introduce a Bayesian hierarchical modeling approach which models study-to-study heterogeneity explicitly to borrow strength across studies. Using a carefully formulated prior specification, we develop a fast approach to predictor selection and shrinkage estimation for high-dimensional predictors. The proposed approach, which is related to the relevance vector machine (RVM), relies on maximum a posteriori (MAP) estimation to rapidly obtain a sparse estimate. As for the typical RVM, there is an intrinsic thresholding property in which unimportant predictors tend to have their coefficients shrunk to zero. The method will be illustrated with an application of selecting genes as predictors of time to an event.