Simultaneous rank tests for detecting differentially expressed genes

Abstract

Rank tests are known to be robust to outliers and violation of distributional assumptions. Two major issues besetting microarray data are violation of the normality assumption and contamination by outliers. In this article, we formulate the normal theory simultaneous tests and their aligned rank transformation (ART) analog for detecting differentially expressed genes. These tests are based on the least-squares estimates of the effects when data follow a linear model. Application of the two methods are then demonstrated on a real data set. To evaluate the performance of the aligned rank transform method with the corresponding normal theory method, data were simulated according to the characteristics of a real gene expression data. These simulated data are then used to compare the two methods with respect to their sensitivity to the distributional assumption and to outliers for controlling the family-wise Type I error rate, power, and false discovery rate. It is demonstrated that the ART generally possesses the robustness of validity property even for microarray data with small number of replications. Although these methods can be applied to more general designs, in this article the simulation study is carried out for a dye-swap design since this design is broadly used in cDNA microarray experiments.

Keywords:

• microarray
• aligned rank transformation
• simultaneous tests
• bootstrap
• multiple testing
• robustness of validity

AMS Subject Classification:

• 62G09
• 62G10
• 62G35
• 62J
• 62P10

Acknowledgments

The authors thank Dr Philip W. Smith and Dr Jerry Perez of High Performance Computing at Texas Tech University for providing assistance with parallel computing.

Disclosure

No potential conflict of interest was reported by the authors.