Application of the Bayesian MMSE estimator for classification error to gene expression microarray data

MOTIVATION With the development of high-throughput genomic and proteomic technologies, coupled with the inherent difficulties in obtaining large samples, biomedicine faces difficult small-sample classification issues, in particular, error estimation. Most popular error estimation methods are motivated by intuition rather than mathematical inference. A recently proposed error estimator based on Bayesian minimum mean square error estimation places error estimation in an optimal filtering framework. In this work, we examine the application of this error estimator to gene expression microarray data, including the suitability of the Gaussian model with normal-inverse-Wishart priors and how to find prior probabilities. RESULTS We provide an implementation for non-linear classification, where closed form solutions are not available. We propose a methodology for calibrating normal-inverse-Wishart priors based on discarded microarray data and examine the performance on synthetic high-dimensional data and a real dataset from a breast cancer study. The calibrated Bayesian error estimator has superior root mean square performance, especially with moderate to high expected true errors and small feature sizes. AVAILABILITY We have implemented in C code the Bayesian error estimator for Gaussian distributions and normal-inverse-Wishart priors for both linear classifiers, with exact closed-form representations, and arbitrary classifiers, where we use a Monte Carlo approximation. Our code for the Bayesian error estimator and a toolbox of related utilities are available at http://gsp.tamu.edu/Publications/supplementary/dalton11a. Several supporting simulations are also included. CONTACT ldalton@tamu.edu