Adaptive optimal design with application to a two drug combination trial based on efficiency-toxicity response

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] The first part of this dissertation develops an adaptive optimal design for dose-finding with combination therapies that accounts for both efficacy and toxicity. The bivariate probit model is used as a working model for the dose-response relationship. A desirable therapy is defined to be the dose combination that achieves a preset probability of efficacy and toxicity. The goal is to estimate the dose that exists closest to the desirable therapy, but within the therapeutic range. A-optimal designs that minimizes the variance of the estimate of this dose and D-optimal designs that minimize the (approximate) confidence ellipsoid for all model parameters are obtained. The next part addresses important outstanding questions concerning the information measure used in implementing adaptive optimal designs. Four measures of information are important in the literature on inference for stochastic processes. The measure used in adaptive optimal designs to construct treatment allocation procedures is none of these. I explore these information measures in the context of adaptive optimal designs.