Permutation-based global rank test with adaptive weights for multiple primary endpoints

Multiple efficacy endpoints are investigated in clinical trials, and selecting the appropriate primary endpoints is key to the study's success. The global test is an analysis approach that can handle multiple endpoints without multiplicity adjustment. This test, which aggregates the statistics from multiple primary endpoints into a single statistic using weights for the statistical comparison, has been gaining increasing attention. A key consideration in the global test is determination of the weights. In this study, we propose a novel global rank test in which the weights for each endpoint are estimated based on the current study data to maximize the test statistic, and the permutation test is applied to control the type I error rate. Simulation studies conducted to compare the proposed test with other global tests show that the proposed test can control the type I error rate at the nominal level, regardless of the number of primary endpoints and correlations between endpoints. Additionally, the proposed test offers higher statistical powers when the efficacy is considerably different between endpoints or when endpoints are moderately correlated, such as when the correlation coefficient is greater than or equal to 0.5.