Using integrated weighted survival difference for the two-sample censored data problem

For the two-sample censored data problem, Pepe and Fleming [Pepe, M.S., Fleming, T.R., 1989. Weighted Kaplan–Meier statistics: A class of distance tests for censored survival data. Biometrics 45, 497–507] introduced the weighted Kaplan–Meier (WKM) statistics. From these statistics we define stochastic processes which can be approximated by zero-mean martingales. Conditional distributions of the processes, given data, can be easily approximated through simulation techniques. Based on comparison of these processes, we construct a supremum test to assess the model adequacy. Monte Carlo simulations are conducted to evaluate and compare the size and power properties of the proposed test to the WKM and the log-rank tests. The procedures are illustrated using real data.