American Journal of Epidemiology Vol. 150, No. 11: 1188-1200
Copyright © 1999 by The Johns Hopkins University School of Hygiene and Public Health
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Variation Over Time of the Effects of Prognostic Factors in a Population-based Study of Colon Cancer: Comparison of Statistical Models
1Department of Biostatistics and Medical Informatics, Teaching Hospital of Dijon France
2Department of Epidemiology and Biostatistics, McGill University, Division of Clinical Epidemiology, Montreal General Hospital
3Department of Epidemiology and Biostatistics (U472), French Institute for Medical Research (INSERM) Villejuif, France
4International Agency for Research on Cancer, ECP Lyon, France
5The Children's Hospital Research Institute of Denver and Pediatric Clinical Research Center and Department of Preventive Medicine and Biometrics, University of Colorado, CO
6Registry of Digestive Tumors, Burgundy University Dijon, France
7Department of Mathematics and Statistics, McGill University Montréal, Québec, Canada
Reprint requests to Dr. Michal Abrahamowicz, Division of Clinical Epidemiology Montreal General Hospital, 1650 Cedar Ave., Montréal, Québec H3G 1A4, Canada.
The authors compare the performance of different regression models for censored survival data in modeling the impact of prognostic factors on all-cause mortality in colon cancer. The data were for 1,951 patients, who were diagnosed in 1977-1991, recorded by the Registry of Digestive Tumors of Cote d'Or, France, and followed for up to 15 years. Models include the Cox proportional hazards model and its three generalizations that allow for hazard ratio to change over time: 1) the piecewise model where hazard ratio is a step function; 2) the model with interaction between a predictor and a parametric function of time; and 3) the non-parametric regression spline model. Results illustrate the importance of accounting for non-proportionality of hazards, and some advantages of flexible non-parametric modeling of time-dependent effects. The authors provide empirical evidence for the dependence of the results of piecewise and parametric models on arbitrary a priori choices, regarding the number of time intervals and specific parametric function, which may lead to biased estimates and low statistical power. The authors demonstrate that a single, a priori selected spline model recovers a variety of patterns of changes in hazard ratio and fits better than other models, especially when the changes are nonmonotonic, as in the case of cancer stages. Am J Epidemiol 1999; 150:1188–1200.
colonic neoplasms; Cox regression; goodness-of-fit; models, statistical; multivariate analysis; regression analysis; risk factors; survival analysis
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