  The analysis and planning methods for competing risks model have been
described in the literatures in recent decades, and non-inferiority clinical
trials are helpful in current pharmaceutical practice. Analytical methods for
non-inferiority clinical trials in the presence of competing risks were
investigated by Parpia et al., who indicated that the proportional
sub-distribution hazard model is appropriate in the context of biological
studies. However, the analytical methods of competing risks model differ from
those appropriate for analyzing non-inferiority clinical trials with a single
outcome; thus, a corresponding method for planning such trials is necessary. A
sample size formula for non-inferiority clinical trials in the presence of
competing risks based on the proportional sub-distribution hazard model is
presented in this paper. The primary endpoint relies on the sub-distribution
hazard 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 non-inferiority clinical trials with competing
risks can reach the targeted power.
