A Simple Test for Goodness of Fit of Cox's Proportional Hazards Model

Cox's proportional hazards model for survival analysis (1972) has gained widespread attention from both applied and theoretical statisticians and is central to most work on survival analysis. To verify the assumption of proportional hazards underlying the model, several methods have recently been put forward (Cox, 1979; Schoenfeld, 1980; Andersen, 1982; Kalbfleisch and Prentice, 1980). These methods consist either of graphical techniques designed so as to visualize departures from the proportional hazards (PH) assumption or of formal tests based on parameterizing the interaction between covariates and time. In this paper a simple test statistic is proposed for detecting departures from the PH assumption. The proposed test is computationally and conceptually straightforward. Expressions for the first two moments of the test statistic are presented.