Improved statistical tests for differential gene expression by shrinking variance components estimates

Abstract

Combining information across genes in the statistical analysis of microarray data is desirable because of the relatively small number of data points obtained for each individual gene. Here we develop an estimator of the error variance that can borrow information across genes using the James-Stein shrinkage concept. A new test statistic (FS) is constructed using this estimator. The new statistic is compared with other statistics used to test for differential expression: the gene-specific F test (F1), the pooled-variance F statistic (F3), a hybrid statistic (F2) that uses the average of the individual and pooled variances, the regularized t-statistic, the posterior odds statistic B, and the SAM t-test. The FS-test shows best or nearly best power for detecting differentially expressed genes over a wide range of simulated data in which the variance components associated with individual genes are either homogeneous or heterogeneous. Thus FS provides a powerful and robust approach to test differential expression of genes that utilizes information not available in individual gene testing approaches and does not suffer from biases of the pooled variance approach.

A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics

“…Shrinking the variances to a common mean is standard practice in in genomic case-control studies (e.g. Cui et al, 2005). It is particular helpful if there are so few samples that the gene-specific variances are difficult to obtain.…”

“…Greenland, 2000). Shrinkage formalizes the idea of "borrowing strength across variables" and has proved beneficial in the problem of differential expression (e.g., Smyth, 2004;Cui et al, 2005) and classification of transcriptome data (e.g., Tibshirani et al, 2002;Zhu and Hastie, 2004). In this paper we particularly highlight the shrinkage approach of Ledoit and Wolf (2003) that allows fitting of all necessary tuning parameters in a simple analytical fashion.…”

The influence of parental effects on transcriptomic landscape during early development in brook charr (Salvelinus fontinalis, Mitchill)

“…This model included 'Array' as a random term and 'Dye' and 'Cross type' as fixed terms. A permutation-based F test (Fs, with 1000 sample ID permutations) was then performed and restricted maximum likelihood was used to solve the mixed model equations (Cui et al, 2005). We tested the presence of cross type effects with the ANOVA model and used the P-values to determine the significance of inter-cross differential expression.…”

Integrating biological information into the statistical analysis and design of microarray experiments

“…Most of the strategies available in the literature to overcome this situation refer to some sort of shrinkage estimation of variance components, to borrow information across genes (e.g. Smyth, 2004 andCui et al, 2005). However, those approaches are still based on the assumption of independence among genes, and they do not take advantage of prior genomic or biological knowledge.…”