A relative survival regression model using B‐spline functions to model non‐proportional hazards

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Abstract
Relative survival, a method for assessing prognostic factors for disease‐specific mortality in unselected populations, is frequently used in population‐based studies. However, most relative survival models assume that the effects of covariates on disease‐specific mortality conform with the proportional hazards hypothesis, which may not hold in some long‐term studies. To accommodate variation over time of a predictor's effect on disease‐specific mortality, we developed a new relative survival regression model using B‐splines to model the hazard ratio as a flexible function of time, without having to specify a particular functional form. Our method also allows for testing the hypotheses of hazards proportionality and no association on disease‐specific hazard. Accuracy of estimation and inference were evaluated in simulations. The method is illustrated by an analysis of a population‐based study of colon cancer. Copyright © 2003 John Wiley & Sons, Ltd.

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