TYPE I ERROR INFLATION OF LOG-RANK TEST WITH SMALL SAMPLE SIZE: A PERMUTATION APPROACH AND SIMULATION STUDIES

Abstract

The log-rank test is a well-accepted nonparametric test in comparing the survival time between experimental and control group in regulatory settings. However, we have observed type I error inflation as high as 28% using the test in the simulation settings we have with even moderate sample sizes. In this paper, we explore several factors that potentially con-tribute to the inflation by simulation. Sample size, randomization ratio and significance levels are found to be influential factors. We propose an alternative log-rank test using an approximate permutation distribution instead of the standard normal distribution. It is shown that type I error is controlled when applying the approximate permutation test to both simple clinical trial designs and complicated group sequential designs.