Open Access
March 2020 TFisher: A powerful truncation and weighting procedure for combining $p$-values
Hong Zhang, Tiejun Tong, John Landers, Zheyang Wu
Ann. Appl. Stat. 14(1): 178-201 (March 2020). DOI: 10.1214/19-AOAS1302


The $p$-value combination approach is an important statistical strategy for testing global hypotheses with broad applications in signal detection, meta-analysis, data integration, etc. In this paper we extend the classic Fisher’s combination method to a unified family of statistics, called TFisher, which allows a general truncation-and-weighting scheme of input $p$-values. TFisher can significantly improve statistical power over the Fisher and related truncation-only methods for detecting both rare and dense “signals.” To address wide applications, analytical calculations for TFisher’s size and power are deduced under any two continuous distributions in the null and the alternative hypotheses. The corresponding omnibus test (oTFisher) and its size calculation are also provided for data-adaptive analysis. We study the asymptotic optimal parameters of truncation and weighting based on Bahadur efficiency (BE). A new asymptotic measure, called the asymptotic power efficiency (APE), is also proposed for better reflecting the statistics’ performance in real data analysis. Interestingly, under the Gaussian mixture model in the signal detection problem, both BE and APE indicate that the soft-thresholding scheme is the best, the truncation and weighting parameters should be equal. By simulations of various signal patterns, we systematically compare the power of statistics within TFisher family as well as some rare-signal-optimal tests. We illustrate the use of TFisher in an exome-sequencing analysis for detecting novel genes of amyotrophic lateral sclerosis. Relevant computation has been implemented into an R package TFisher published on the Comprehensive R Archive Network to cater for applications.


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Hong Zhang. Tiejun Tong. John Landers. Zheyang Wu. "TFisher: A powerful truncation and weighting procedure for combining $p$-values." Ann. Appl. Stat. 14 (1) 178 - 201, March 2020.


Received: 1 April 2019; Revised: 1 September 2019; Published: March 2020
First available in Project Euclid: 16 April 2020

zbMATH: 07200167
MathSciNet: MR4085089
Digital Object Identifier: 10.1214/19-AOAS1302

Keywords: $P$-value combination , genetic association studies , global hypothesis testing , optimal test , signal detection , statistical power

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.14 • No. 1 • March 2020
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