Jump to ContentJump to Main Navigation

Statistical Applications in Genetics and Molecular Biology

Editor-in-Chief: Stumpf, Michael P.H.

6 Issues per year

Increased IMPACT FACTOR 2012: 1.717
Rank 18 out of 117 in category Statistics & Probability in the 2012 Thomson Reuters Journal Citation Report/Science Edition
Mathematical Citation Quotient 2012: 0.07

VolumeIssuePage

Weighted Multiple Hypothesis Testing Procedures

Guolian Kang1 / Keying Ye2 / Nianjun Liu3 / David B. Allison4 / Guimin Gao5

1University of Alabama at Birmingham

2University of Texas at San Antonio

3University of Alabama at Birmingham

4University of Alabama at Birmingham

5University of Alabama at Birmingham

Citation Information: Statistical Applications in Genetics and Molecular Biology. Volume 8, Issue 1, Pages 1–22, ISSN (Online) 1544-6115, DOI: 10.2202/1544-6115.1437, April 2009

Publication History

Published Online:
2009-04-16

Multiple hypothesis testing is commonly used in genome research such as genome-wide studies and gene expression data analysis (Lin, 2005). The widely used Bonferroni procedure controls the family-wise error rate (FWER) for multiple hypothesis testing, but has limited statistical power as the number of hypotheses tested increases. The power of multiple testing procedures can be increased by using weighted p-values (Genovese et al., 2006). The weights for the p-values can be estimated by using certain prior information. Wasserman and Roeder (2006) described a weighted Bonferroni procedure, which incorporates weighted p-values into the Bonferroni procedure, and Rubin et al. (2006) and Wasserman and Roeder (2006) estimated the optimal weights that maximize the power of the weighted Bonferroni procedure under the assumption that the means of the test statistics in the multiple testing are known (these weights are called optimal Bonferroni weights). This weighted Bonferroni procedure controls FWER and can have higher power than the Bonferroni procedure, especially when the optimal Bonferroni weights are used. To further improve the power of the weighted Bonferroni procedure, first we propose a weighted Šidák procedure that incorporates weighted p-values into the Šidák procedure, and then we estimate the optimal weights that maximize the average power of the weighted Šidák procedure under the assumption that the means of the test statistics in the multiple testing are known (these weights are called optimal Šidák weights). This weighted Šidák procedure can have higher power than the weighted Bonferroni procedure. Second, we develop a generalized sequential (GS) Šidák procedure that incorporates weighted p-values into the sequential Šidák procedure (Scherrer, 1984). This GS Šidák procedure is an extension of and has higher power than the GS Bonferroni procedure of Holm (1979). Finally, under the assumption that the means of the test statistics in the multiple testing are known, we incorporate the optimal Šidák weights and the optimal Bonferroni weights into the GS Šidák procedure and the GS Bonferroni procedure, respectively. Theoretical proof and/or simulation studies show that the GS Šidák procedure can have higher power than the GS Bonferroni procedure when their corresponding optimal weights are used, and that both of these GS procedures can have much higher power than the weighted Šidák and the weighted Bonferroni procedures. All proposed procedures control the FWER well and are useful when prior information is available to estimate the weights.

Keywords: weight; multiple hypothesis testing; Bonferroni procedure; Šidák procedure; family-wise error rate

Comments (0)

Please log in or register to comment.
Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.