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Longitudinal Extension of the Win Odds for Ordinal Repeated Measurements.
Yongxi Long1, Bart C Jacobs2,3, Ewout W Steyerberg4
1Biomedical Data Sciences, Leiden University Medical Center, Leiden, the Netherlands.
Statistics in Medicine
|April 10, 2026
Summary
Win odds, a measure for comparing ordinal outcomes, are extended for repeated measurements. This statistical method provides a reliable way to analyze longitudinal data, enhancing clinical trial analysis.
Area of Science:
- Statistics
- Biostatistics
- Longitudinal Data Analysis
Background:
- Win odds are increasingly used for ordinal outcome analysis.
- They represent the odds of a better outcome for one group over another.
- Existing methods adjust for covariates using the probabilistic index model.
Purpose of the Study:
- To extend the probabilistic index model for analyzing repeated ordinal outcomes.
- To adapt win odds for longitudinal data with within-subject correlation.
- To provide a robust statistical tool for longitudinal ordinal data.
Main Methods:
- Modified estimation equations of the probabilistic index model.
- Accounting for within-subject correlation in longitudinal data.
- Parameter estimation using data restructuring and the R package geepack.
- Implementation of a sandwich-type estimator for variance-covariance matrix estimation.
Main Results:
- Simulations demonstrate consistent estimation of win odds.
- Confidence interval coverage is close to nominal levels.
- The extended model is effective for analyzing longitudinal ordinal outcomes.
Conclusions:
- The extended probabilistic index model is a promising method for comparing longitudinal ordinal outcomes.
- Win odds serve as a valuable summary measure in repeated measures studies.
- The R package 'lwo' facilitates the implementation of this statistical approach.
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