Simulating competing risks data in survival analysis.

Competing risks analysis considers time-to-first-event ('survival time') and the event type ('cause'), possibly subject to right-censoring. The cause-, i.e. event-specific hazards, completely determine the competing risk process, but simulation studies often fall back on the much criticized latent failure time model. Cause-specific hazard-driven simulation appears to be the exception; if done, usually only constant hazards are considered, which will be unrealistic in many medical situations. We explain simulating competing risks data based on possibly time-dependent cause-specific hazards. The simulation design is as easy as any other, relies on identifiable quantities only and adds to our understanding of the competing risks process. In addition, it immediately generalizes to more complex multistate models. We apply the proposed simulation design to computing the least false parameter of a misspecified proportional subdistribution hazard model, which is a research question of independent interest in competing risks. The simulation specifications have been motivated by data on infectious complications in stem-cell transplanted patients, where results from cause-specific hazards analyses were difficult to interpret in terms of cumulative event probabilities. The simulation illustrates that results from a misspecified proportional subdistribution hazard analysis can be interpreted as a time-averaged effect on the cumulative event probability scale.