Use of Schoenfeld's global test to test the proportional hazards assumption in the Cox proportional hazards model: an application to a clinical study

Cox proportional hazards (PH) model is one of the finest techniques in identifying combined effects of several covariates on the relative risk (hazard). This model assumes that the hazards of the different strata formed by the levels of the covariates are proportional. The primary objective of this paper is to illustrate the usefulness of a global goodness-of-fit test proposed by Schoenfeld for testing the PH assumption. Though several classical methods have been discussed in previous studies there is no one research paper that compares Schoenfeld's method with these. Moreover, programmes are developed in SAS for constructing this global goodness-of-fit test. In this paper the proposed test is applied to a real, large scale data set that involves several covariates, whereas Schoenfeld has used only a small data set with only one covariate to illustrate this new test. Using Kaplan-Meier curves, a preliminary analysis was conducted on the survival data. Then, a Cox PH model was fitted to the data. All the methods and residual analysis including the global goodness-of-fit test indicated that for the data set used the assumption of PH is violated. However, other than for the global goodness-of-fit test all other techniques are based on graphical methods and are thus subjective. Hence, for cases where the violation of the PH assumption is marginal these graphical methods may be inadequate to detect this departure. However, as the global goodness-of-fit test is an objective test it is recommended as the best among the methods compared.