Restricted Time Win Ratio: From Estimands to Estimation

Abstract

The win ratio is a novel approach to analyzing prioritized composite endpoints in clinical trials. The win ratio has grown increasingly popular and has been applied in many ongoing cardiovascular clinical trials. Despite the intuitive interpretation of win ratio statistics, the traditionally used win ratio estimands are heavily influenced by the pattern of censoring. Treating missing values or censored data as ties is generally not a reliable way of handling missing values even in the estimation procedure. To avoid this complication, we propose the restricted time win ratio, which is the win ratio at a pre-specified time point $\tau$ and can be written in terms of the expectations of potential outcomes. To estimate the proposed estimand, we develop an approximately fully conditional specification algorithm which imputes the missing data of longitudinal and clinical outcomes jointly up to $\tau$. The imputation algorithm can be easily revised to adjust a different hierarchical structure of the sequential comparisons specified by the users. Simulation studies in realistic settings show that the proposed imputation algorithm provides an unbiased and robust estimation of the restricted time win ratio. Finally, real data from a cardiovascular clinical trial are used to illustrate the proposed method.

Keywords:

• Composite endpoints
• Fully conditional specification
• Missing data
• Multiple imputation

Acknowledgments

All authors are employees and minor shareholder of Eli Lilly and Company.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.