Abstract: A new goodness-of-fit test for Cox's proportional hazards model is introduced. The test is based on a transformation of the difference between nonparametric and Cox model specific estimators of the doubly-cumulative hazard function used by McKeague and Utikal (1991). The transformation is designed to give an asymptotically distribution-free test. The test is shown to be consistent against all alternatives except those in which the baseline hazard is linearly dependent on the covariate.
Key words and phrases: Brownian sheet, martingale methods, nonparametrics, proportional hazards.