Flexible modeling of the effects of continuous prognostic factors in relative survival

Abstract

Relative survival methods permit separating the effects of prognostic factors on disease‐related ‘excess mortality’ from their effects on other‐causes ‘natural mortality’, even when individual causes of death are unknown. As in conventional ‘crude’ survival, accurate assessment of prognostic factors requires testing and possibly modeling of non‐proportional effects and, for continuous covariates, of non‐linear relationships with the hazard. We propose a flexible extension of the additive‐hazards relative survival model, in which the observed all‐causes mortality hazard is represented by a sum of disease‐related ‘excess’ and natural mortality hazards. In our flexible model, the three functions representing (i) the baseline hazard for ‘excess’ mortality, (ii) the time‐dependent effects, and (iii) for continuous covariates, non‐linear effects, on the logarithm of this hazard, are all modeled by low‐dimension cubic regression splines. Non‐parametric likelihood ratio tests are proposed to test the time‐dependent and non‐linear effects. The accuracy of the estimated functions is evaluated in multivariable simulations. To illustrate the new insights offered by the proposed model, we apply it to re‐assess the effects of patient age and of secular trends on disease‐related mortality in colon cancer. Copyright © 2011 John Wiley & Sons, Ltd.