A nonparametric test for equality of survival medians

Abstract

In clinical trials, researchers often encounter testing for equality of survival medians across study arms based on censored data. Even though Brookmeyer and Crowley introduced a method for comparing medians of several survival distributions, still some researchers misuse procedures that are designed for testing the homogeneity of survival curves. These procedures include the log-rank, Wilcoxon, and Cox models. This practice leads to inflation of the probability of a type I error, particularly when the underlying assumptions of these procedures are not met. We propose a new nonparametric method for testing the equality of several survival medians based on the Kaplan-Meier estimation from randomly right-censored data. We derive asymptotic properties of this test statistic. Through simulations, we compute and compare the empirical probabilities of type I errors and the power of this new procedure with those of the Brookmeyer-Crowley, log-rank, and Wilcoxon methods. Our simulation results indicate that the performance of these test procedures depends on the level of censoring and appropriateness of the underlying assumptions. When the objective is to test homogeneity of survival medians rather than survival curves and the assumptions of these tests are not met, some of these procedures severely inflate the probability of a type I error. In these situations, our test statistic provides an alternative to the Brookmeyer-Crowley test.

Figure 1

The survival curves of the four groups from Kaplan-Meier estimates. The estimated median survival times in weeks are 18, 29, 19, and 14 for breast cancer, lung cancer, colon cancer, and other cancer, respectively.

Figure 2

The estimated hazard functions of the four groups.