| Dose response studies are customarily conducted in preclinical and phases 1 and 2 clinical trials to study the dose response curves of potential therapeutic drugs. Practical constraints on drug dose range, dose levels and dose allocation proportions/design weights due to drug efficacy, toxicity and FDA regulations have rendered the traditional optimal design approach obsolete. To incorporate these practical constraints, our group proposed the novel controlled optimal design concept and implemented a robust program for generating Bayesian optimal design for logit dose response model under the compound c- and D-optimality criteria using the cross-entropy method (Hu and Zhu et al., 2010). However, further work needs to be done to generalize these controlled optimal designs to accommodate more dose response models and to achieve better global optimality convergence. This is the primary objective of this thesis. To accomplish this goal, firstly, an exhaustive grid search method (EGS) is used to find the global optimal design. A complete set of possible design combinations of dosages and the corresponding design weights is generated, and the design objective function will be evaluated in each cell of the unit. Secondly, a general solution algorithm for linearly constrained global optimization (GLC, which stands for generalized linear constrained method) is adapted to derive the controlled optimal design. Our approach is accomplished by converting the constrained optimization problem to an unconstrained optimization problem through a parametric representation of its feasible region. In this thesis, all algorithms are extended to the entire family of the generalized linear regression models. In addition, we show that the closed-form expression of the optimal design can be found in some special cases using the GLC. Related implementation techniques are also covered in details in this work. |
