Modified Kolmogorov-Smirnov Test Procedures with Application to Arbitrarily Right-Censored Data

Abstract

The classical Kolmogorov one-sample goodness-of-fit and Smirnov two-sample test procedures are modified in an attempt to obtain increased power when applied to uncensored data. Both are then generalized for use with arbitrarily right-censored data. Motivation for the formulation of the generalized procedures is provided heuristically by appealing to the basic concept upon which the procedures for uncensored data are based; a theoretical motivation is provided by asymptotic weak convergence results. The size and power of the generalized Smirnov two-sample procedure are evaluated for small and moderate sample sizes using Monte Carlo simulations. Results of the simulations are also used to make comparisons with the Gehan-Wilcoxon and logrank two-sample test procedures. The generalized Smirnov procedure is found to maintain the size of the test in nearly all the cases studied, although it is conservative in small samples of heavily censored data. It is found to be more powerful than both the Gehan-Wilcoxon and the logrank procedures for the non-Lehmann alternatives considered.