Optimal design for dose response using beta distributed responses

Whenever a response is naturally confined to a finite interval (such as a visual analog scale for pain severity), the beta distribution provides a simple and flexible probability distribution to model such a response. The parameters of the distribution can then be related to covariates, such as dose, in a clinical trial through the generation of a beta regression model. In this article, we explore locally optimal designs for this class of regression models, focusing mainly on minimization of the generalized variance of maximum likelihood estimators (D-optimality). Optimal designs and sensitivity to misspecification of model parameters are examined using a candidate points searching algorithm. Although formally the model assumes that the response is continuous, it provides a parsimonious approximation for ordinal data when there is a relatively large number of categories. The resulting estimators and optimal designs are simpler and may offer more ease in interpretation than those derived from models for ordered categorical outcomes. The proposed methods are applied to data from a clinical trial.