There are few readily-implemented tests for goodness-of-fit for the Cox proportional hazards model with time-varying covariates. Through simulations, we assess the power of tests by Cox (J R Stat Soc B (Methodol) 34(2):187–220, 1972), Grambsch and Therneau (Biometrika 81(3):515–526, 1994), and Lin et al. (Biometrics 62:803–812, 2006). Results show that power is highly variable depending on the time to violation of proportional hazards, the magnitude of the change in hazard ratio, and the direction of the change. Because these characteristics are unknown outside of simulation studies, none of the tests examined is expected to have high power in real applications. While all of these tests are theoretically interesting, they appear to be of limited practical value.
Survival analysis Lack of fit Time-dependent covariates
This is a preview of subscription content, log in to check access.
Aitkin M, Laird N, Francis B (1983) A reanalysis of the Stanford heart transplant data. J Am Stat Assoc 78:264–274CrossRefGoogle Scholar
Altman DG, de Stavola BL (1994) Practical problems in fitting a proportional hazards model to data with updated measurements of the covariates. Stat Med 13:301–341CrossRefGoogle Scholar
Andersen PK (1992) Repeated assessment of risk factors in survival analysis. Stat Methods Med Res 1:297–315CrossRefGoogle Scholar
Bender R, Augustin T, Blettner M (2005) Generating survival times to simulate Cox proportional hazards models. Stat Med 24:1713–1723CrossRefMathSciNetGoogle Scholar
Clark DA, Stinson EB, Griepp RB, Schroeder JS, Shumway NE, Harrison DC (1971) Cardiac transplantation in man, VI. Prognosis of patients selected for cardiac transplantation. Ann Internal Med 75:15–21CrossRefGoogle Scholar
Cox DR (1972) Regression models and life tables. J R Stat Soc B (Methodol) 34(2):187–220zbMATHGoogle Scholar
Crowley J, Hu M (1977) Covariance analysis of heart transplant survival data. J Am Stat Assoc 72:27–36CrossRefGoogle Scholar
Fisher LD, Lin DY (1999) Time-dependent covariates in the Cox proportional-hazards regression model. Ann Rev Public Health 20:145–157CrossRefGoogle Scholar