Genomic outlier profile analysis: mixture models, null hypotheses, and nonparametric estimation.

In most analyses of large-scale genomic data sets, differential expression analysis is typically assessed by testing for differences in the mean of the distributions between 2 groups. A recent finding by Tomlins and others (2005) is of a different type of pattern of differential expression in which a fraction of samples in one group have overexpression relative to samples in the other group. In this work, we describe a general mixture model framework for the assessment of this type of expression, called outlier profile analysis. We start by considering the single-gene situation and establishing results on identifiability. We propose 2 nonparametric estimation procedures that have natural links to familiar multiple testing procedures. We then develop multivariate extensions of this methodology to handle genome-wide measurements. The proposed methodologies are compared using simulation studies as well as data from a prostate cancer gene expression study.