Evaluating the Cauchy Combination Test for Count Data

The Cauchy combination test (CCT) is a $p$-value combination method used in multiple-hypothesis testing and is robust under dependence structures. This study aims to evaluate the CCT for independent and correlated count data where the individual $p$-values are derived from tests based on Normal approximation to the negative binomial distribution. The correlated count data are modelled via copula methods. The CCT performance is evaluated in a simulation study to assess the type 1 error rate and the statistical power and compare it with existing methods. In addition, we consider the influence of factors such as the success parameter of the negative binomial distribution, the number of individual $p$-values, and the correlation strength. Our results indicate that the negative binomial success parameter and the number of combined individual $p$-values may influence the type 1 error rate for the CCT under independence or weak dependence. The choice of copula method for modelling the correlation between count data has a significant influence on type 1 error rates for both the CCT and MinP tests. The CCT has more control over managing the type 1 error rate as the strength increases in the Gumbel-Hougaard copula. This knowledge may have significant implications for practical applications.