Commentary: Secular trends in the context of competing risks.

Abstract

Cancer mortality is increasing while the mortality rates of ischaemic heart disease (IHD) and cerebro-vascular disease (CVD) are decreasing, so it is natural to speculate that the increase in cancer mortality may partly be explained by new cancer cases among those avoiding or surviving IHD and CVD. Llorca and Delgado-Rodriguez present an approach based on Markov chains to evaluate this question of competing risks. 1 The statistical theory behind the use of Markov chains in the analyses of competing risks is well described 2 (textbox). The merit of their paper is therefore to illustrate that the different approaches previously used on this subject in the epidemiological literature can be unified. They analyse the secular trend of cancer mortality from 1981 to 1994 in Spain in the context of competing risks from IHD and CVD using both an ‘elimination model’ 2 (‘What would have happened if IHD and/or CVD had been eradicated’) and a ‘constant model’ 3 (‘What would have happened if the mortality of IHD and/or CVD had remained constant’). Under both of these scenarios, the estimated lifetime risks of cancer are very much the same as observed in 1994. Based on these findings it is tempting to conclude that the secular trends of IHD and CVD have had little influence on the secular trends of cancer mortality from 1981 to 1994. It might seem puzzling that one has to perform a simulation of different hypothetical scenarios in the evaluation of the past. If the question was whether an increase in cancer mortality from 1981 to 1994 was due to an increase in smoking, say, this could—in a cohort with smoking information—be evaluated by examining the secular trend among non-smokers only. However, the constant model can be viewed in the same way as an ‘everything-else-equal’ comparison (i.e. within the stratum of people where new survivors due to decrease in IHD and CVD since 1981 are excluded). In 1981 this stratum is just the total population, in 1994 this is estimated using the higher mortality rates of 1981. If cancer mortality is increasing even in this stratum, then it is unlikely that competing risks are the cause, because in this stratum the competing risk effect is constant. In other words, evaluating historical secular trends in the context of competing risks, as in the paper by Llorca and DelgadoRodriguez, does not have to be interpreted using different hypothetical scenarios, nor does one model have to be judged as more unrealistic than others. When evaluating past secular trends the most attractive model is the constant model because it gives an ‘everything-else-equal’ comparison based on external information. The flexible continuum of models presented by the authors is, in this situation, of little use. By contrast, when the question is about secular trends in the future, the realism and multitude of models are important considerations and the framework described by Llorca and DelgadoRodriguez is well suited for this purpose with the elimination model as the chief example. Another model mentioned in the epidemiological literature which could also be included in this framework is the cause-delay model. 4 In the cause-delay model one assumes that each generation approaches the age-specific force of mortality from IHD and CVD later than observed currently, e.g. the current mortality-specific rate for people aged 50‐54 years, say, is applied in the future scenario for people aged 55‐59 years. A crucial assumption in these analyses is that one can estimate the cancer mortality among survivors using the general agespecific cancer mortality, i.e. the assumption of ‘independent competing risks’. 5 If the assumption is not fulfilled then it