Weighted inverse chi-square method for correlated significance tests

Fisher's inverse chi-square method for combining independent significance tests is extended to cover cases of dependence among the individual tests. A weighted version of the method and its approximate null distribution are presented. To illustrate the use of the proposed method, two tests for the overall treatment efficacy are combined, with the resulting test procedure exhibiting good control of the type I error probability. Two examples from clinical trials are given to illustrate the applicability of the procedures to real-life situations.