Estimating sample size in the presence of competing risks - Cause-specific hazard or cumulative incidence approach?

In designing randomised clinical trials involving competing risks endpoints, it is important to consider competing events to ensure appropriate determination of sample size. We conduct a simulation study to compare sample sizes obtained from the cause-specific hazard and cumulative incidence (CMI) approaches, by first assuming exponential event times. As the proportional subdistribution hazard assumption does not hold for the CMI exponential (CMIExponential) model, we further investigate the impact of violation of such an assumption by comparing the results obtained from the CMI exponential model with those of a CMI model assuming a Gompertz distribution (CMIGompertz) where the proportional assumption is tenable. The simulation suggests that the CMIExponential approach requires a considerably larger sample size when treatment reduces the hazards of both the main event, A, and the competing risk, B. When treatment has a beneficial effect on A but no effect on B, the sample sizes required by both methods are largely similar, especially for large reduction in the main risk. If treatment has a protective effect on A but adversely affects B, then the sample size required by CMIExponential is notably smaller than cause-specific hazard for small to moderate reduction in the main risk. Further, a smaller sample size is required for CMIGompertz as compared with CMIExponential. The choice between a cause-specific hazard or CMI model in competing risks outcomes has implications on the study design. This should be made on the basis of the clinical question of interest and the validity of the associated model assumption.