Bayesian Inference of Causal Effects for an Ordinal Outcome in Randomized Trials

In randomized trials in which two treatment arms are compared with a binary outcome, the causal effect can be identified by assuming that the two treatment arms are exchangeable. In trials with an ordinal outcome, which is categorized as more than two, the causal effect can be identified by assuming that the potential outcomes are independent and that the two treatment arms are exchangeable. In this article, we propose a Bayesian approach to causal inference that does not rely on these two assumptions. To achieve this purpose, we use a randomization-based approach and response type. Then, the likelihood function is derived by physical randomization in which subjects who belong to a response type are randomly assigned to the treatment or control, with no modeling assumption on the outcome. Our approach can derive not only the posterior distribution of the causal effect but also that of the number of subjects in each response type. The proposed approach is illustrated with two examples from randomized clinical trials.