A full Bayesian hierarchical mixture model for the variance of gene differential expression

<p>Abstract</p> <p>Background</p> <p>In many laboratory-based high throughput microarray experiments, there are very few replicates of gene expression levels. Thus, estimates of gene variances are inaccurate. Visual inspection of graphical summaries of these data usually reveals that heteroscedasticity is present, and the standard approach to address this is to take a log₂transformation. In such circumstances, it is then common to assume that gene variability is constant when an analysis of these data is undertaken. However, this is perhaps too stringent an assumption. More careful inspection reveals that the simple log₂transformation does not remove the problem of heteroscedasticity. An alternative strategy is to assume independent gene-specific variances; although again this is problematic as variance estimates based on few replications are highly unstable. More meaningful and reliable comparisons of gene expression might be achieved, for different conditions or different tissue samples, where the test statistics are based on accurate estimates of gene variability; a crucial step in the identification of differentially expressed genes.</p> <p>Results</p> <p>We propose a Bayesian mixture model, which classifies genes according to similarity in their variance. The result is that genes in the same latent class share the similar variance, estimated from a larger number of replicates than purely those per gene, i.e. the total of all replicates of all genes in the same latent class. An example dataset, consisting of 9216 genes with four replicates per condition, resulted in four latent classes based on their similarity of the variance.</p> <p>Conclusion</p> <p>The mixture variance model provides a realistic and flexible estimate for the variance of gene expression data under limited replicates. We believe that in using the latent class variances, estimated from a larger number of genes in each derived latent group, the <it>p</it>-values obtained are more robust than either using a constant gene or gene-specific variance estimate.</p

Bayesian testing of many hypotheses ×\times many genes: A study of sleep apnea

Substantial statistical research has recently been devoted to the analysis of large-scale microarray experiments which provide a measure of the simultaneous expression of thousands of genes in a particular condition. A typical goal is the comparison of gene expression between two conditions (e.g., diseased vs. nondiseased) to detect genes which show differential expression. Classical hypothesis testing procedures have been applied to this problem and more recent work has employed sophisticated models that allow for the sharing of information across genes. However, many recent gene expression studies have an experimental design with several conditions that requires an even more involved hypothesis testing approach. In this paper, we use a hierarchical Bayesian model to address the situation where there are many hypotheses that must be simultaneously tested for each gene. In addition to having many hypotheses within each gene, our analysis also addresses the more typical multiple comparison issue of testing many genes simultaneously. We illustrate our approach with an application to a study of genes involved in obstructive sleep apnea in humans.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS241 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

An Empirical Bayes Approach for Multiple Tissue eQTL Analysis

Expression quantitative trait loci (eQTL) analyses, which identify genetic markers associated with the expression of a gene, are an important tool in the understanding of diseases in human and other populations. While most eQTL studies to date consider the connection between genetic variation and expression in a single tissue, complex, multi-tissue data sets are now being generated by the GTEx initiative. These data sets have the potential to improve the findings of single tissue analyses by borrowing strength across tissues, and the potential to elucidate the genotypic basis of differences between tissues. In this paper we introduce and study a multivariate hierarchical Bayesian model (MT-eQTL) for multi-tissue eQTL analysis. MT-eQTL directly models the vector of correlations between expression and genotype across tissues. It explicitly captures patterns of variation in the presence or absence of eQTLs, as well as the heterogeneity of effect sizes across tissues. Moreover, the model is applicable to complex designs in which the set of donors can (i) vary from tissue to tissue, and (ii) exhibit incomplete overlap between tissues. The MT-eQTL model is marginally consistent, in the sense that the model for a subset of tissues can be obtained from the full model via marginalization. Fitting of the MT-eQTL model is carried out via empirical Bayes, using an approximate EM algorithm. Inferences concerning eQTL detection and the configuration of eQTLs across tissues are derived from adaptive thresholding of local false discovery rates, and maximum a-posteriori estimation, respectively. We investigate the MT-eQTL model through a simulation study, and rigorously establish the FDR control of the local FDR testing procedure under mild assumptions appropriate for dependent data.Comment: accepted by Biostatistic

Bayesian Gene Set Analysis

Gene expression microarray technologies provide the simultaneous measurements of a large number of genes. Typical analyses of such data focus on the individual genes, but recent work has demonstrated that evaluating changes in expression across predefined sets of genes often increases statistical power and produces more robust results. We introduce a new methodology for identifying gene sets that are differentially expressed under varying experimental conditions. Our approach uses a hierarchical Bayesian framework where a hyperparameter measures the significance of each gene set. Using simulated data, we compare our proposed method to alternative approaches, such as Gene Set Enrichment Analysis (GSEA) and Gene Set Analysis (GSA). Our approach provides the best overall performance. We also discuss the application of our method to experimental data based on p53 mutation status

Non-parametric Bayesian modelling of digital gene expression data

Next-generation sequencing technologies provide a revolutionary tool for generating gene expression data. Starting with a fixed RNA sample, they construct a library of millions of differentially abundant short sequence tags or "reads", which constitute a fundamentally discrete measure of the level of gene expression. A common limitation in experiments using these technologies is the low number or even absence of biological replicates, which complicates the statistical analysis of digital gene expression data. Analysis of this type of data has often been based on modified tests originally devised for analysing microarrays; both these and even de novo methods for the analysis of RNA-seq data are plagued by the common problem of low replication. We propose a novel, non-parametric Bayesian approach for the analysis of digital gene expression data. We begin with a hierarchical model for modelling over-dispersed count data and a blocked Gibbs sampling algorithm for inferring the posterior distribution of model parameters conditional on these counts. The algorithm compensates for the problem of low numbers of biological replicates by clustering together genes with tag counts that are likely sampled from a common distribution and using this augmented sample for estimating the parameters of this distribution. The number of clusters is not decided a priori, but it is inferred along with the remaining model parameters. We demonstrate the ability of this approach to model biological data with high fidelity by applying the algorithm on a public dataset obtained from cancerous and non-cancerous neural tissues