Model-Assisted Bayesian Estimators of Transparent Population Level Summary Measures for Ordinal Outcomes in Randomized Controlled Trials

In randomized controlled trials, ordinal outcomes typically improve statistical efficiency over binary outcomes. The treatment effect on an ordinal outcome is usually described by the odds ratio from a proportional odds model, but this summary measure lacks transparency with respect to its emphasis on the components of the ordinal outcome when proportional odds is violated. We propose various summary measures for ordinal outcomes that are fully transparent in this regard, including 'weighted geometric mean' odds ratios and relative risks, and 'weighted mean' risk differences. We also develop and evaluate efficient model-assisted Bayesian estimators for these population level summary measures based on non-proportional odds models that facilitate covariate adjustment with marginalization via the Bayesian bootstrap. We propose a weighting scheme that engenders appealing invariance properties, including to whether the ordinal outcome is ordered from best to worst versus worst to best. Using computer simulation, we show that comparative testing based on the proposed population level summary measures performs well relative to the conventional proportional odds approach. We also report an analysis of the COVID-OUT trial, which exhibits evidence of non-proportional odds.