Hosmer-Lemeshow Goodness-of-Fit Test: Translations to the Cox Proportional Hazards Model

• Activity Number: 77
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Biometrics Section
• Author(s): Danielle Guffey*+ and Susanne May and David W. Hosmer
• Companies: University of Washington and University of Washington and University of Massachusetts Amherst
• Keywords: lack of fit ; calibration ; omnibus test ; liftime data analysis ; model checking

Abstract

Background: The goodness-of-fit (GOF) of a statistical model is often assessed by describing how well the model fits the observed data. We evaluate two translations of the Hosmer-Lemeshow GOF test for logistic regression to the Cox proportional hazards model, the Cook-Ridker (CR) and D'Agostino-Nam (DAN) tests. These translations are compared to a test designed specifically for survival data, the Gronnesby and Borgan (GB) test. Methods: The sizes of these tests are investigated via simulations by varying the baseline hazard function, effect size, percentage of censoring, sample size, number of groups, and the choice of fixed time. Results: The sizes of the CR and DAN tests are near the nominal level in very few of the simulated scenarios. In addition, numerical issues can occur when the estimated survival probability is zero and the estimated expected number of events is close to zero or one. Conclusions: Although the CR and DAN translations of the Hosmer-Lemeshow GOF test to the Cox proportional hazards regression are conceptually intuitive they appear to have an incorrect size and numerical issues can occur. The GB test should be used instead because of a more appropriate size.