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Abstract:
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We review two important and yet relatively unexplored aspects of multiple testing: internal cross-validation and increased variability under dependence. First, we discuss the problem of internal cross-validation due to Majumder et al (2009) and shed some light on the achieved false discovery rate (FDR) the outcomes of the Benjamini-Hochberg procedure (BH) are internally cross-validated. Secondly, we investigate the issue of dependence in massive genome-scale multiple testing literature and show that the popular BH procedure can be highly variable under dependence, indicating that inferences of one genome-scale association study may not replicate in a similar set of independent samples. We propose a new testing procedure that incorporates the dependence structure and improves the statistical power without substantial increase in the FDR. Compared to the BH method, the proposed method reduces the variability of inference and model misspecification has minimal effect on inferences, as assessed by the mean number of rejected hypotheses or the achieved FDR. We also evaluate our method on high-dimensional Genomic data to identify relevant biomarkers for cancer.
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