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.