The stratified win statistics (win ratio, win odds, and net benefit).

Area of Science:

• Biostatistics
• Clinical Trial Methodology
• Statistical Analysis

Background:

• The win ratio is a statistical measure used in clinical trials since 2018.
• Existing research highlights the relationship between win odds, net benefit, and win ratio.
• These statistics assess the same null hypothesis of equal win probabilities between groups.

Purpose of the Study:

• To demonstrate the direct and indirect relationships between win odds, net benefit, and win ratio, including their variances.
• To generalize the stratified win ratio methodology to win odds and net benefit.
• To confirm that the statistical test equivalencies and relationships hold for stratified win statistics.

Main Methods:

• Comparative statistical analysis of win odds, net benefit, and win ratio.
• Examination of the relationships between the estimated variances of these win statistics.
• Generalization of the stratified win ratio method to other win statistics.

Main Results:

• Win odds and net benefit are directly related, and indirectly related to the win ratio through ties.
• The estimated variances of these win statistics are also directly or indirectly related.
• The approximate equivalence of statistical tests and observed relationships hold for stratified win statistics.

Conclusions:

• The relationships between win odds, net benefit, and win ratio are mathematically established and extend to stratified versions.
• These findings support the complementary use of these statistics to evaluate treatment effect strength.
• The generalization of the stratified method enhances its applicability in clinical trial design and analysis.