Combination-Based Permutation Testing in Survival Analysis

In survival analysis, it is very common to test whether two survival time distributions are equal. In the framework of random censorship model, two of the most frequently used procedures in order to compare samples of right-censored survival data are the asymptotic weighted log-rank test (WLR; Mantel, 1966) and the weighted Kaplan-Meier test (WKM; Kaplan and Meier, 1958). In this work we present a novel permutation combination-based testing approach for survival analysis. Within permutation methodology, censored data problems can be thought within a missing data setting. In this sense, it is possible to take into consideration a Multidimensional Permutation Test based on the theory of permutation testing with missing data. A comparative Monte Carlo simulation study has been performed, along with an application to a real case study, in order to evaluate the behaviour of the permutation procedures, with respect to some other asymptotic nonparametric methods proposed in the recent literature. The aim of this work is to point out a possible flexible and robust procedure, in terms of power, among the investigated methods. In general, the achieved results mainly suggest the use of a multidimensional permutation methodology in case of equal censoring.