Detecting differential gene expression with a semiparametric hierarchical mixture method

Abstract

Mixture modeling provides an effective approach to the differential expression problem in microarray data analysis. Methods based on fully parametric mixture models are available, but lack of fit in some examples indicates that more flexible models may be beneficial. Existing, more flexible, mixture models work at the level of one-dimensional gene-specific summary statistics, and so when there are relatively few measurements per gene these methods may not provide sensitive detectors of differential expression. We propose a hierarchical mixture model to provide methodology that is both sensitive in detecting differential expression and sufficiently flexible to account for the complex variability of normalized microarray data. EM-based algorithms are used to fit both parametric and semiparametric versions of the model. We restrict attention to the two-sample comparison problem; an experiment involving Affymetrix microarrays and yeast translation provides the motivating case study. Gene-specific posterior probabilities of differential expression form the basis of statistical inference; they define short gene lists and false discovery rates. Compared to several competing methodologies, the proposed methodology exhibits good operating characteristics in a simulation study, on the analysis of spike-in data, and in a cross-validation calculation.

Variability-specific differential gene expression across reproductive stages in sows

“…As recently demonstrated at a gene-specific level (Lo and Gottardo, 2007), an accurate modeling of residual dispersion patterns allows for a more realistic fit of gene expression data, reducing the rate of false positives when differential gene expression is characterized in terms of mathematical expectations or their differences (Kendziorski et al, 2003;Newton et al, 2004;Lo and Gottardo, 2007). Moreover, the analysis of heterogeneous residual dispersion patterns opens up promising research possibilities within the gene expression framework, where heterogeneity in residual variability could be viewed as an alternative and plausible characterization of differential expression patterns.…”

“…Assuming null residual (co)variances (Kendziorski et al, 2003;Newton et al, 2004;, heteroskedasticity between physiological stages was analyzed by stating…”

Optimality of Gene Ranking Based on Univariate P-values for Detecting Differentially Expressed Genes

“…Theoretical connection among various ranking methods, including those based on hierarchical Bayesian models (Newton et al, 2004;Noma et al, 2010), and comparison of their performances are important research areas. Recently, Storey (2007) developed the optimal discovery procedure, an optimality criterion for ordering tests in multiple testing, which can be formulated as a multiple test extension of the Neyman-Pearson optimality for testing individual genes.…”

“…Optimality of gene ranking is, hence, an important research area in statistical analysis of microarray studies. Recently, Newton et al (2004) and McLachlan et al (2006) have shown a ranking based on the local false discovery rate (local FDR; Efron et al, 2001), which represents the posterior probability of non-differential expression of each gene, is optimal for selecting differentially expressed genes from the viewpoint of the Bayesian decision theory. More recently, Noma et al (2010) developed three empirical Bayes methods for gene ranking on the basis of differential expression, using hierarchical mixture models.…”

Statistical Validation of Peptide Identifications in Large-Scale Proteomics Using the Target-Decoy Database Search Strategy and Flexible Mixture Modeling

“…Using this scale-free, univariate probability score, one can call peptide assignments correct if posterior probability is above a certain threshold. This posterior probability is directly related to local false discovery rate (fdr) discussed in Efron et al 12 and Newton et al, 13 and thus specifying the minimum probability threshold automatically controls global FDR to a desired degree.…”