Comparison of Cox's and relative survival models when estimating the effects of prognostic factors on disease-specific mortality: a simulation study under proportional excess hazards.

In many prognostic studies focusing on mortality of persons affected by a particular disease, the cause of death of individual patients is not recorded. In such situations, the conventional survival analytical methods, such as the Cox's proportional hazards regression model, do not allow to discriminate the effects of prognostic factors on disease-specific mortality from their effects on all-causes mortality. In the last decade, the relative survival approach has been proposed to deal with the analyses involving population-based cancer registries, where the problem of missing information on the cause of death is very common. However, some questions regarding the ability of the relative survival methods to accurately discriminate between the two sources of mortality remain open. In order to systematically assess the performance of the relative survival model proposed by Esteve et al., and to quantify its potential advantages over the Cox's model analyses, we carried out a series of simulation experiments, based on the population-based colon cancer registry in the French region of Burgundy. Simulations showed a systematic bias induced by the 'crude' conventional Cox's model analyses when individual causes of death are unknown. In simulations where only about 10 per cent of patients died of causes other than colon cancer, the Cox's model over-estimated the effects of male gender and oldest age category by about 17 and 13 per cent, respectively, with the coverage rate of the 95 per cent CI for the latter estimate as low as 65 per cent. In contrast, the effect of higher cancer stages was under-estimated by 8-28 per cent. In contrast to crude survival, relative survival model largely reduced such problems and handled well even such challenging tasks as separating the opposite effects of the same variable on cancer-related versus other-causes mortality. Specifically, in all the cases discussed above, the relative bias in the estimates from the Esteve et al.'s model was always below 10 per cent, with the coverage rates above 81 per cent.

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

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.