Median tests for censored survival data; a contingency table approach

The median failure time is often utilized to summarize survival data because it has a more straightforward interpretation for investigators in practice than the popular hazard function. However, existing methods for comparing median failure times for censored survival data either require estimation of the probability density function or involve complicated formulas to calculate the variance of the estimates. In this article, we modify a K-sample median test for censored survival data (Brookmeyer and Crowley, 1982, Journal of the American Statistical Association 77, 433-440) through a simple contingency table approach where each cell counts the number of observations in each sample that are greater than the pooled median or vice versa. Under censoring, this approach would generate noninteger entries for the cells in the contingency table. We propose to construct a weighted asymptotic test statistic that aggregates dependent χ(2)-statistics formed at the nearest integer points to the original noninteger entries. We show that this statistic follows approximately a χ(2)-distribution with k-1 degrees of freedom. For a small sample case, we propose a test statistic based on combined p-values from Fisher's exact tests, which follows a χ(2)-distribution with 2 degrees of freedom. Simulation studies are performed to show that the proposed method provides reasonable type I error probabilities and powers. The proposed method is illustrated with two real datasets from phase III breast cancer clinical trials.