Abstract
BackgroundMany analyses of gene expression data involve hypothesis tests of an interaction term between two fixed effects, typically tested using a residual variance. In expression studies, the issue of variance heteroscedasticity has received much attention, and previous work has focused on either between-gene or within-gene heteroscedasticity. However, in a single experiment, heteroscedasticity may exist both within and between genes. Here we develop flexible shrinkage error estimators considering both between-gene and within-gene heteroscedasticity and use them to construct F-like test statistics for testing interactions, with cutoff values obtained by permutation. These permutation tests are complicated, and several permutation tests are investigated here.ResultsOur proposed test statistics are compared with other existing shrinkage-type test statistics through extensive simulation studies and a real data example. The results show that the choice of permutation procedures has dramatically more influence on detection power than the choice of F or F-like test statistics. When both types of gene heteroscedasticity exist, our proposed test statistics can control preselected type-I errors and are more powerful. Raw data permutation is not valid in this setting. Whether unrestricted or restricted residual permutation should be used depends on the specific type of test statistic.ConclusionsThe F-like test statistic that uses the proposed flexible shrinkage error estimator considering both types of gene heteroscedasticity and unrestricted residual permutation can provide a statistically valid and powerful test. Therefore, we recommended that it should always applied in the analysis of real gene expression data analysis to test an interaction term.
Highlights
Many analyses of gene expression data involve hypothesis tests of an interaction term between two fixed effects, typically tested using a residual variance
Simulation studies The purpose of these simulation studies was to compare the performances of F1, F2, F3, FCui, FGen, FGen-gene, and FGen-grp in terms of type I error and power and to compare the results of a particular F-like statistic using four different permutation strategies: restricted/unrestricted residual permutation and restricted/unrestricted raw data permutation
The gene-specific analysis of variance (ANOVA) model in which data were generated from the model, yplr = Pp + Ll + RLrl + PLpl + plr, wp = 1, 2, l = 1,2, r = 1,2,3, where P, L, RL, and PL represent probe, line, replicates from a particular line, and the interaction between probe and line, respectively
Summary
Many analyses of gene expression data involve hypothesis tests of an interaction term between two fixed effects, typically tested using a residual variance. We develop flexible shrinkage error estimators considering both between-gene and within-gene heteroscedasticity and use them to construct F-like test statistics for testing interactions, with cutoff values obtained by permutation. These permutation tests are complicated, and several permutation tests are investigated here. Kerr et al constructed an ANOVA model that included the gene effect as a fixed effect This model assumes identically and independently distributed residual errors across genes. The advantage of this model is that the large number of genes involved in a microarray experiment results in huge degrees of freedom for the error estimate, which can lead to a very powerful test. One alternative is to use an ANOVA model for each gene, but the resulting test statistics from gene-specific models may have limited power because the biological sample size for each gene in a microarray experiment is usually small
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