Longitudinal Extension of the Win Odds for Ordinal Repeated Measurements

Initially proposed for analyzing composite endpoints, the win odds have recently received increasing interest for the analysis of ordinal outcomes. When comparing an ordinal outcome between two groups, the win odds are the odds that a randomly selected subject from the first group has a better outcome than a randomly selected subject from the second group. As such, the win odds are an effect size that is closely related to the Mann-Whitney U test. The win odds can be adjusted for covariates by the probabilistic index model. Here, we aim to extend this model for repeated measurements. We modify the estimation equations of the probabilistic index model to account for within-subject correlation. Parameter estimation can be conveniently done via some data re-structuring and the R package geepack. We implement a sandwich-type estimator to estimate the variance-covariance matrix. Simulations show that the estimation of the win odds is consistent and the coverage of confidence intervals is close to nominal. We provide an application by reanalyzing a neurological trial for the treatment of Guillain-Barré syndrome (SID-GBS trial). This extension establishes the win odds as a promising summary measure to compare longitudinal ordinal outcomes. R package lwo is available on GitHub for implementing the proposed method.