Unequal group variances in microarray data analyses

Abstract

Motivation: In searching for differentially expressed (DE) genes in microarray data, we often observe a fraction of the genes to have unequal variability between groups. This is not an issue in large samples, where a valid test exists that uses individual variances separately. The problem arises in the small-sample setting, where the approximately valid Welch test lacks sensitivity, while the more sensitive moderated t-test assumes equal variance. Methods: We introduce a moderated Welch test (MWT) that allows unequal variance between groups. It is based on (i) weighting of pooled and unpooled standard errors and (ii) improved estimation of the gene-level variance that exploits the information from across the genes. Results: When a non-trivial proportion of genes has unequal variability, false discovery rate (FDR) estimates based on the standard t and moderated t-tests are often too optimistic, while the standard Welch test has low sensitivity. The MWT is shown to (i) perform better than the standard t, the standard Welch and the moderated t-tests when the variances are unequal between groups and (ii) perform similarly to the moderated t, and better than the standard t and Welch tests when the group variances are equal. These results mean that MWT is more reliable than other existing tests over wider range of data conditions. Availability: R package to perform MWT is available at http://www.meb.ki.se/~yudpaw Contact: yudi.pawitan@ki.se Supplementary information: Supplementary data are available at Bioinformatics online.

Integrating mean and variance heterogeneities to identify differentially expressed genes

“…Thus, the current IMVT is suitable for large samples other than small samples. By our simulation studies and the work of Demissie et al [6], the MWT could outperform the WT, especially for extremely small sample sizes. Novel parametric methods, i.e., the LRT, are needed to mine expression files of low-replicate experiments.…”

“…To calibrate unequal variances, another alternative is the MWT [6], which would yield reliable condition-specific variance estimators for low-replicate experiments. For large-sample experiments, one can perform Student t test on standardized data (STSD), where the gene expression levels are divided by condition-specific sample standard deviations respectively.…”

“…This test calibrates potential variance heterogeneity as an impediment to identify differentially expressed genes. Demissie et al developed the MWT [6] to obtain more stable estimates of the error variance of a gene in a low-replicate microarray experiment. The MWT outperformed the Welch test to allow for variance heterogeneity.…”

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“…To provide optimal statistical tools for selection of discriminative spectral components the Lilliefors's test was applied to assess for distribution normality and Bartlett's test was employed to check homogeneity of variances. Because the statistically significant heteroscedasticity of spectral components was observed the modified welch statistics (MwT) (27) was chosen for selection of discriminating components. Due to numerous spectral components analyzed a correction for multiple testing was applied; Storey's q-values (28) with thresholds for fDR (false discovery rate) equal to 0.05 were used.…”

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