Analysis of cause of death: Competing risks or progressive illness-death model?

The analysis of cause of death is increasingly becoming a topic in oncology. It is usually distinguished between disease-related and disease-unrelated death. A frequently used approach is to define death as disease-related when a progression to advanced phases has occurred before, otherwise as disease-unrelated. The data are often analyzed as competing risks, while a progressive illness-death model might in fact describe the situation more precisely. In this study, we investigated under which circumstances this misspecification leads to biased estimations of the state occupation probabilities. We simulated data according to the progressive illness-death model in various settings, analyzed them with a competing risks model and with a progressive illness-death model and compared them to the true state occupation probabilities. Censoring was either added independently of the status or based on the patients' status. The simulations showed that the censoring mechanism was decisive for the bias while neither the progression hazard nor the Markov property was important. Further, we found a slightly increased standard deviation for the competing risk estimator when censoring was independent of the patients' status. For illustration, both methods were applied to two practical examples of chronic myeloid leukemia (CML): one randomized controlled trial and one registry data set. While in the first case both estimators yielded almost identical results, in the latter case, visible differences were found between both methods.