An Expected Score Approach to Ordinal Outcomes in a Bayesian, Response Adaptive, Randomized Trial

Abstract

Ordinal outcomes are common in medicine and can be analyzed in many ways, but the distribution of ordinal data can present unique challenges. The proposed KESETT study is a three-armed, randomized trial comparing two doses of ketamine plus levetiracetam to levetiracetam alone for treating patients with benzodiazepine-refractory status epilepticus. A Bayesian, adaptive clinical trial is proposed employing an ordinal primary outcome at 60 min ranging from 1 (improving consciousness and seizure cessation) to 5 (life-threatening event/death). Based on a previous study, the ordinal outcome is expected to have a bimodal distribution, with the effect of treatment expected to be nonproportional across the outcome scale. As such, approaches relying on assuming proportionality of the odds are not appropriate. We propose for this scenario an analytic approach to compare ordinal outcomes using the expected score derived from the posterior distribution for each treatment group. This approach requires minimal assumptions, maintains the benefit of using the full ordinal scale, is interpretable, and can be used in a Bayesian analysis framework. We compare this new approach under multiple simulated scenarios to three traditional frequentist approaches. The new approach controls Type I error and power, resulting in a sizable reduction in sample size relative to a nonparametric test.