Randomised P-values and nonparametric procedures in multiple testing

Abstract

The validity of many multiple hypothesis testing procedures for false discovery rate (FDR) control relies on the assumption that P-value statistics are uniformly distributed under the null hypotheses. However, this assumption fails if the test statistics have discrete distributions or if the distributional model for the observables is misspecified. A stochastic process framework is introduced that, with the aid of a uniform variate, admits P-value statistics to satisfy the uniformity condition even when test statistics have discrete distributions. This allows nonparametric tests to be used to generate P-value statistics satisfying the uniformity condition. The resulting multiple testing procedures are therefore endowed with robustness properties. Simulation studies suggest that nonparametric randomised test P-values allow for these FDR methods to perform better when the model for the observables is nonparametric or misspecified.

Keywords:

• multiple testing
• randomisation
• false discovery rate
• microarray
• P-value statistics

AMS Subject Classification:

• DMS-0805809
• DMS-0104016

Acknowledgements

The authors wish to thank the reviewers for their helpful and constructive comments. They also wish to thank Wensong Wu, Professor Joshua Tebbs, and Professor Phillip Dixon for helpful comments and discussions, and also thank Professor Peter Westfall for alerting them and providing them with relevant references. The authors also acknowledge NSF Grant DMS0805809; National Institutes of Health (NIH) Grant RR17698; and the Environmental Protection Agency (EPA) Grant RD-83241902-0 to the University of Arizona with subaward number Y481344 to the University of South Carolina. These grants partially supported this work.