The poolr Package for Combining Independent and Dependent p Values

Abstract

The poolr package provides an implementation of a variety of methods for pooling (i.e., combining) p values, including Fisher's method, Stouffer's method, the inverse chisquare method, the binomial test, the Bonferroni method, and Tippett's method. More importantly, the methods can be adjusted to account for dependence among the tests from which the p values have been derived assuming multivariate normality among the test statistics. All methods can be adjusted based on an estimate of the effective number of tests or by using an empirically-derived null distribution based on pseudo replicates that mimics a proper permutation test. For the Fisher, Stouffer, and inverse chi-square methods, the test statistics can also be directly generalized to account for dependence, leading to Brown's method, Strube's method, and the generalized inverse chi-square method. In this paper, we describe the various methods, discuss their implementation in the package, illustrate their use based on several examples, and compare the poolr package with several other packages that can be used to combine p values.