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. Our results indicate that the number of combined tests, the negative binomial success parameter, and sample size significantly affect the type 1 error rate of the CCT under independence or moderate correlation. The CCT has more control over managing the type 1 error rate as the strength increases in the Gumbel-Hougaard copula. In general, the choice of copula and the strength of its correlation have a significant influence on type 1 error rates for both the CCT and MinP tests. Our simulation findings support the broader applications of the CCT under multivariate copulas that model upper-tail dependence with higher correlations. This knowledge may have significant implications for practical applications.