Variation over time of the effects of prognostic factors in a population-based study of colon cancer: Comparison of statistical models

The authors compare the performance of different regression models for cens ored survival data in modeling the impact of prognostic factors on all-caus e mortality in colon cancer. The data were for 1,951 patients, who were dia gnosed 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 propor tional hazards model and its three generalizations that allow for hazard ra tio to change over time: 1) the piecewise model where hazard ratio is a ste p function; 2) the model with interaction between a predictor and a paramet ric function of time; and 3) the non-parametric regression spline model. Re sults illustrate the importance of accounting for non-proportionality of ha zards, and some advantages of flexible non-parametric modeling of time-depe ndent effects. The authors provide empirical evidence for the dependence of the results of piecewise and parametric models on arbitrary a priori choic es, 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 varie ty of patterns of changes in hazard ratio and fits better than other models , especially when the changes are non-monotonic, as in the case of cancer s tages.