Beta-mapping and beta-regression for changes of ordinal-rating measurements on Likert scales: a comparison of the change scores among multiple treatment groups.

Patient reported outcome and observer evaluative studies in clinical trials and post-hoc analyses often use instruments that measure responses on ordinal-rating or Likert scales. We propose a flexible distributional approach by modeling the change scores from the baseline to the end of the study using independent beta distributions. The two shape parameters of the fitted beta distributions are estimated by matching-moments. Covariates and the interaction terms are included in multivariate beta-regression analyses under generalized linear mixed models. These methods are illustrated on the treatment satisfaction data in an overactive bladder drug study with four treatment arms. Monte-Carlo simulations were conducted to compare the Type 1 errors and statistical powers using a beta likelihood ratio test of the proposed method against its fully nonparametric or parametric alternatives.