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

**Authors:** Dong Han, Zheng Chen, Yawen Hou  
**arXiv:** [1802.10245](https://arxiv.org/abs/1802.10245)  
**Date:** 2018-02-28  
**Summary page:** https://www.summarizepaper.com/en/paper/1802.10245v1/

## Key points

- Literature has described analysis and planning methods for competing risks models in recent decades.
- Non-inferiority clinical trials are increasingly important in current pharmaceutical practice.
- Parpia et al. found that the proportional sub-distribution hazard model is appropriate in biological studies for non-inferiority clinical trials with competing risks.
- This paper presents a sample size formula based on the sub-distribution hazard ratio and the Weibull distribution to plan such trials accurately.
- The formula was verified through 120 simulations and an example based on a randomized controlled trial, demonstrating its ability to reach targeted power for non-inferiority clinical trials with competing risks.
- Considering competing risks is important when designing these types of trials.

## Summary

In recent decades, literature has described analysis and planning methods for competing risks models. Non-inferiority clinical trials are becoming increasingly important in current pharmaceutical practice. Parpia et al. investigated analytical methods for non-inferiority clinical trials in the presence of competing risks and found that the proportional sub-distribution hazard model is appropriate in biological studies. To address the need for a corresponding method for planning such trials, this paper presents a sample size formula based on the sub-distribution hazard ratio and the Weibull distribution. The empirical performance of this formula was verified through 120 simulations and an example based on a randomized controlled trial. The results demonstrate that it can reach targeted power for non-inferiority clinical trials with competing risks. This study contributes to advancing statistical methodology by providing a new approach to plan these types of trials accurately and emphasizes the importance of considering competing risks when designing them.