BOPA: A Bayesian hierarchical model for outlier expression detection

In many cancer studies, a gene may be expressed in some but not all of the disease samples, reflecting the complexity of the underlying disease. The traditional t-test assumes a mean shift for the tumor samples compared to normal samples and is thus not structured to capture partial differential expressions. More powerful tests specially designed for this situation can find genes with heterogeneous expressions associated with possible subtypes of the cancer. This article proposes a Bayesian model for cancer outlier profile analysis (BOPA). We build on the Gamma–Gamma model introduced in Newton et al. (2001), Kendziorski et al. (2003), and Newton et al. (2004), by using a five-component mixture model to represent various differential expression patterns. The hierarchical mixture model explicitly accounts for outlier expressions, and inferences are based on samples from posterior distributions generated from the Markov chain Monte Carlo algorithm we have developed. We present simulation and real-life dataset analyses to demonstrate the proposed methodology.