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

• Activity Number: 405
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Song Yang*+ and Yichuan Zhao
• Companies: National Heart, Lung, and Blood Institute and Georgia State University
• Keywords: censoring ; goodness of fit ; martingale residuals ; omnibus test ; survival data

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 nonparametric and model-based estimators of the survival function. The martingale residual-based test is analogous to the well known test in the literature for the Cox proportional regression model, and the contrast-based test uses the nonparametric survivor function estimate. These tests are shown to be consistent against any departure from the model. The empirical behaviors of the tests are studied in simulations, and the tests are illustrated with some real data examples.