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One of the most common analysis tasks in genomic research is to identifygenes that are differentially expressed (DE) between experimental conditions.Empirical Bayes (EB) statistical tests using moderated genewise variances havebeen very effective for this purpose, especially when the number of biologicalreplicate samples is small. The EB procedures can however be heavily influencedby a small number of genes with very large or very small variances. Thisarticle improves the differential expression tests by robustifying thehyperparameter estimation procedure. The robust procedure has the effect ofdecreasing the informativeness of the prior distribution for outlier geneswhile increasing its informativeness for other genes. This effect has thedouble benefit of reducing the chance that hypervariable genes will bespuriously identified as DE while increasing statistical power for the mainbody of genes. The robust EB algorithm is fast and numerically stable. Theprocedure allows exact small-sample null distributions for the test statisticsand reduces exactly to the original EB procedure when no outlier genes arepresent. Simulations show that the robustified tests have similar performanceto the original tests in the absence of outlier genes but have greater powerand robustness when outliers are present. The article includes case studies forwhich the robust method correctly identifies and downweights genes associatedwith hidden covariates and detects more genes likely to be scientificallyrelevant to the experimental conditions. The new procedure is implemented inthe limma software package freely available from the Bioconductor repository.

Robust hyperparameter estimation protects against hypervariable genes and improves power to detect differential expression