Sample size formula for a win ratio endpoint

Area of Science:

• Clinical Trials Methodology
• Biostatistics
• Health Research Methods

Background:

• The win ratio composite endpoint is increasingly utilized in late-stage clinical trials for its hierarchical comparison of outcomes.
• Current sample size calculations for the win ratio method typically rely on complex simulations due to the absence of a simple formula.

Purpose of the Study:

• To derive and validate a straightforward formula for calculating sample sizes for trials employing the win ratio composite endpoint.
• To provide a method for sample size determination that utilizes summary-level data, contrasting with existing approaches requiring patient-level data.

Main Methods:

• A novel sample size formula was developed, incorporating the probabilities of one group's patient outperforming another and the likelihood of a tie.
• The formula's performance was assessed by comparing confidence intervals derived from it with those calculated using patient-level data across 17 composite or single win ratio endpoints.
• Simulations were conducted to evaluate the formula's accuracy and reliability.

Main Results:

• The sample size formula produced results comparable to those obtained using patient-level data for confidence intervals.
• Simulations confirmed the formula's robust performance.
• The formula demonstrated that adding even low-power endpoints to the hierarchy can enhance statistical power.

Conclusions:

• The developed formula offers a practical and accessible method for determining sample sizes for win ratio composite endpoints, simplifying a previously complex process.
• This formula facilitates quicker trial size determination for non-specialists and aids in modifying ongoing blinded trials.
• The insights from the formula support strategic endpoint selection to maximize trial power.