Enhanced precision in the analysis of randomized trials with ordinal outcomes

We present a general method for estimating the effect of a treatment on an ordinal outcome in randomized trials. The method is robust in that it does not rely on the proportional odds assumption. Our estimator leverages information in prognostic baseline variables, and has all of the following properties: (i) it is consistent; (ii) it is locally efficient; (iii) it is guaranteed to have equal or better asymptotic precision than both the inverse probability-weighted and the unadjusted estimators. To the best of our knowledge, this is the first estimator of the causal relation between a treatment and an ordinal outcome to satisfy these properties. We demonstrate the estimator in simulations based on resampling from a completed randomized clinical trial of a new treatment for stroke; we show potential gains of up to 39% in relative efficiency compared to the unadjusted estimator. The proposed estimator could be a useful tool for analyzing randomized trials with ordinal outcomes, since existing methods either rely on model assumptions that are untenable in many practical applications, or lack the efficiency properties of the proposed estimator. We provide R code implementing the estimator.