Hypotheses on a tree: new error rates and testing strategies

Author:

Bogomolov Marina1,Peterson Christine B2,Benjamini Yoav3,Sabatti Chiara4

Affiliation:

1. The William Davidson Faculty of Industrial Engineering and Management, Technion-Israel Institute of Technology, Technion City, Haifa 3200003, Israel

2. Department of Biostatistics, Division of Basic Science Research, The University of Texas, MD Anderson Cancer Center, Houston, Texas 77030 , USA

3. Department of Statistics and Operations Research, Tel-Aviv University, P.O. Box 39040, Tel-Aviv 6997801, Israel

4. Department of Statistics, Stanford University, 50 Governor’s Lane, Stanford, California 94305, USA

Abstract

Summary We introduce a multiple testing procedure that controls global error rates at multiple levels of resolution. Conceptually, we frame this problem as the selection of hypotheses that are organized hierarchically in a tree structure. We describe a fast algorithm and prove that it controls relevant error rates given certain assumptions on the dependence between the $p$-values. Through simulations, we demonstrate that the proposed procedure provides the desired guarantees under a range of dependency structures and that it has the potential to gain power over alternative methods. Finally, we apply the method to studies on the genetic regulation of gene expression across multiple tissues and on the relation between the gut microbiome and colorectal cancer.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Statistics, Probability and Uncertainty,General Agricultural and Biological Sciences,Agricultural and Biological Sciences (miscellaneous),General Mathematics,Statistics and Probability

Reference30 articles.

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5. Controlling the rate of GWAS false discoveries;Brzyski,;Genetics,2017

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