Sample size for a noninferiority clinical trial with time-to-event data in the presence of competing risks

The analysis and planning methods for competing risks model have been described in the literature in recent decades, and noninferiority clinical trials are helpful in current pharmaceutical practice. Analytical methods for noninferiority clinical trials in the presence of competing risks (NiCTCR) were investigated by Parpia et al., who indicated that the proportional sub-distribution hazard (SDH) model is appropriate in the context of biological studies. However, the analytical methods of the competing risks model differ from those appropriate for analyzing noninferiority clinical trials with a single outcome; thus, a corresponding method for planning such trials is necessary. A sample size formula for NiCTCR based on the proportional SDH model is presented in this paper. The primary endpoint relies on the SDH ratio. A total of 120 simulations and an example based on a randomized controlled trial verified the empirical performance of the presented formula. The results demonstrate that the empirical power of sample size formulas based on the Weibull distribution for noninferiority clinical trials with competing risks can reach the targeted power.