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ABSTRACT This article introduces a comprehensive framework to adjust a discrete test statistic for improving its hypothesis testing procedure. The adjustment minimizes the Wasserstein distance to a null‐approximating continuous distribution, tackling some fundamental challenges inherent in combining statistical significances derived from discrete distributions. The related theory justifies Lancaster's mid‐p and mean‐value chi‐squared statistics for Fisher's combination as special cases. To counter the conservative nature of Lancaster's testing procedures, we propose an updated null‐approximating distribution. It is achieved by further minimizing the Wasserstein distance to the adjusted statistics within an appropriate distribution family. Specifically, in the context of Fisher's combination, we propose an optimal gamma distribution as a substitute for the traditionally used chi‐squared distribution. This new approach yields an asymptotically consistent test that significantly improves Type I error control and enhances statistical power.
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The Generalized Fisher's Combination and Accurate P -Value Calculation under Dependence
Abstract Combining dependent tests of significance has broad applications but the related p-value calculation is challenging. For Fisher's combination test, current p-value calculation methods (eg, Brown's approximation) tend to inflate the type I error rate when the desired significance level is substantially less than 0.05. The problem could lead to significant false discoveries in big data analyses. This paper provides two main contributions. First, it presents a general family of Fisher type statistics, referred to as the GFisher, which covers many classic statistics, such as Fisher's combination, Good's statistic, Lancaster's statistic, weighted Z-score combination, and so forth. The GFisher allows a flexible weighting scheme, as well as an omnibus procedure that automatically adapts proper weights and the statistic-defining parameters to a given data. Second, the paper presents several new p-value calculation methods based on two novel ideas: moment-ratio matching and joint-distribution surrogating. Systematic simulations show that the new calculation methods are more accurate under multivariate Gaussian, and more robust under the generalized linear model and the multivariate t-distribution. The applications of the GFisher and the new p-value calculation methods are demonstrated by a gene-based single nucleotide polymorphism (SNP)-set association study. Relevant computation has been implemented to an R package GFisher available on the Comprehensive R Archive Network.
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- PAR ID:
- 10485788
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 79
- Issue:
- 2
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 1159-1172
- Size(s):
- p. 1159-1172
- Sponsoring Org:
- National Science Foundation
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