Optimal Design for Beta Distributed Responses
Optimal Design for Beta Distributed Responses
Yuehui Wu, Valerii V. Fedorov, and Kathleen J. Propert
Abstract: Whenever a response is naturally con¯ned to a ¯nite set (such as a visual analog scale for pain severity) the Beta distribution provides a simple and °exible 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. 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 misspeci¯cation 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.
