Cauchy combination test: a powerful test with analytic p-value calculation under arbitrary dependency structures

08/27/2018
by   Yaowu Liu, et al.
0

Combining individual p-values to aggregate multiple small effects has a long-standing interest in statistics, dating back to the classic Fisher's combination test. In modern large-scale data analysis, correlation and sparsity are common features and efficient computation is a necessary requirement for dealing with massive data. To overcome these challenges, we propose a new test that takes advantage of the Cauchy distribution. Our test statistic has a very simple form and is defined as a weighted sum of Cauchy transformation of individual p-values. We prove a non-asymptotic result that the tail of the null distribution of our proposed test statistic can be well approximated by a Cauchy distribution under arbitrary dependency structures. Based on this theoretical result, the p-value calculation of our proposed test is not only accurate, but also as simple as the classic z-test or t-test, making our test well suited for analyzing massive data. We further show that the power of the proposed test is asymptotically optimal in a strong sparsity setting. Extensive simulations demonstrate that the proposed test has both strong power against sparse alternatives and a good accuracy with respect to p-value calculations, especially for very small p-values. The proposed test has also been applied to a genome-wide association study of Crohn's disease and compared with several existing tests.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/13/2021

Cauchy Combination Test for Sparse Signals

Aggregating multiple effects is often encountered in large-scale data an...
research
10/06/2017

Set-Based Tests for Genetic Association Using the Generalized Berk-Jones Statistic

Studying the effects of groups of Single Nucleotide Polymorphisms (SNPs)...
research
03/24/2021

Heavy-tailed distribution for combining dependent p-values with asymptotic robustness

The issue of combining individual p-values to aggregate multiple small e...
research
01/12/2018

TFisher Tests: Optimal and Adaptive Thresholding for Combining p-Values

For testing a group of hypotheses, tremendous p-value combination method...
research
03/03/2020

Accurate p-Value Calculation for Generalized Fisher's Combination Tests Under Dependence

Combining dependent tests of significance has broad applications but the...
research
08/15/2020

Generalized Spacing-Statistics and a New Family of Non-Parametric Tests

Random divisions of an interval arise in various context, including stat...
research
01/09/2014

Efficient unimodality test in clustering by signature testing

This paper provides a new unimodality test with application in hierarchi...

Please sign up or login with your details

Forgot password? Click here to reset