A new method for the comparison of survival distributions

The assessment of overall homogeneity of time-to-event curves is a key element in survival analysis in biomedical research. The currently commonly used testing methods, e.g. log-rank test, Wilcoxon test, and Kolmogorov-Smirnov test, may have a significant loss of statistical testing power under certain circumstances. In this paper we propose a new testing method that is robust for the comparison of the overall homogeneity of survival curves based on the absolute difference of the area under the survival curves using normal approximation by Greenwood's formula. Monte Carlo simulations are conducted to investigate the performance of the new testing method compared against the log-rank, Wilcoxon, and Kolmogorov-Smirnov tests under a variety of circumstances. The proposed new method has robust performance with greater power to detect the overall differences than the log-rank, Wilcoxon, and Kolmogorov-Smirnov tests in many scenarios in the simulations. Furthermore, the applicability of the new testing approach is illustrated in a real data example from a kidney dialysis trial.