Design for intervention studies with categorical outcomes

This thesis covers three related topics in the optimal design of experiments, with applications to clinical trials and rodent toxicology experiments. In general, optimal design theory provides guidelines for study design that maximize the efficiency of statistical estimates and hypothesis tests. This can in many settings provide substantial savings in required sample sizes and, thus, overall costs. The focus here is on optimal design for experiments with categorical outcomes, although many of the methods are directly extendable to other types of measures. The first topic addresses designs for dose-response experiments in which the outcome is an ordinal variable with many categories. Regression models based on the beta distribution are developed for these outcomes and D-optimal designs used to identify the optimal selection of doses. The methods are illustrated using data from a clinical trial. For the second topic, optimal designs are developed for animal experiments in regulated gene therapy. Four candidate dose-response models are explored that allow a dichotomous response to be a function of the doses of two simultaneous interventions, plus an interaction term. D-optimal designs are then identified for these models, and guidelines for the selection of doses provided. The final topic addresses two-stage sequential designs in which the goal is to select one of a number of candidate treatments in the first stage, for further testing in the second stage. The primary outcomes considered are Poisson outcomes, either independent, such as voiding frequency in urologic disorders, or paired, such as those seen in ophthalmology where one eye may be used as an internal control. First, under the assumption of normally-distributed outcomes, required sample sizes at each stage are identified, given assumptions about the true parameter values and error rates. These results then are extended to the Poisson outcome cases using variance-stabilizing transformations and the Poisson difference distribution.