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Checking the Short-Term and Long-Term Hazard Ratio Model for Survival Data


Song Yang, PhD, Office of Biostatistics Research, Division of Cardiovascular Sciences, National Heart, Lung and Blood Institute, NIH, DHHS, 6701 Rockledge Dr. MSC 7913, Bethesda, MD 20892, USA. E-mail:


Abstract.  The short-term and long-term hazard ratio model includes the proportional hazards model and the proportional odds model as submodels, and allows a wider range of hazard ratio patterns compared with some of the more traditional models. We propose two omnibus tests for checking this model, based, respectively, on the martingale residuals and the contrast between the non-parametric and model-based estimators of the survival function. These tests are shown to be consistent against any departure from the model. The empirical behaviours of the tests are studied in simulations, and the tests are illustrated with some real data examples.