A simulation-based goodness-of-fit test for survival data

To check the validity of a parametric model for survival data, a number of supremum-type tests have been proposed in the literature using Khmaladze's (1993, Ann. Statist. 18, 582-602) transformation of a test process. However, such a transformation is usually very complicated and lacks a clear interpretation. Information could also be lost through transformation. In this note, we propose a simulation-based supremum-type test directly from the original test process using an idea originally introduced by Lin et al. (1993, Biometrika 80, 557-572). The test is developed under the framework of Aalen's (1978, Ann. Statist. 6, 701-726) multiplicative intensity counting process model, and therefore applies to a number of survival models including those with very general forms of censoring and truncation. By comparing the observed test process with a set of simulated realizations of an approximating process, our method can be used as a graphical tool as well as a formal test for checking the adequacy of the assumed parametric model. We establish consistency of the resulting test under any fixed alternative. Its performance is investigated in a simulation study. Illustrations are given using some real data sets. (C) 2000 Elsevier Science B.V. All rights reserved.