| This thesis is motivated by a study in which healthy volunteers were inoculated with different doses of nontypeable Haemophilus influenzae. The goal was to estimate the doses at which 50% and 90% of subjects became colonized, and these doses are denoted as the HCD50 and HCD90 respectively. A fifteen-subject study was designed in two stages, with the first six subjects allocated sequentially. The design was chosen based on scientific, practical, and statistical arguments, however, due to limited time, heuristic decisions were made for expedience. The design implemented in the study, together with a number of alternative designs based on specific algorithms or criteria, are evaluated in depth, under both Bayesian and frequentist paradigms.In particular, Bayesian myopic strategies with one-, two- and three-step-look-ahead procedures are investigated. The optimal sequential design strategy is that with minimum expected loss, where the expected loss is defined as the sum of the expected posterior variance of the HCD50 and HCD90. The higher the expected loss is, the worse is the performance of the design. In addition, a toxicity-response relationship may be appropriate, and can be incorporated into the design by putting a constraint on the posterior probability of toxicity at any dose. A new model considering both colonization (efficacy) and adverse event (toxicity) is proposed, and design procedures are developed incorporating this constraint.Monte Carlo simulations are used to estimate the expected loss for candidate design strategies for both univariate and bivariate models, and the results show that it is typically beneficial to look more steps ahead in determining designs, although the benefit may not be large. For the bivariate model, as the restriction becomes more conservative, the expected loss becomes larger and early stopping may occur since there are no acceptable doses available.Non-sequential designs are also found and examined. Criteria from optimal design theory are used by optimizing a function of the expected Fisher information matrix: the inverse of this matrix corresponds to the asymptotic covariance matrix of the parameters. An A-optimal design criterion is used which minimizes the sum of the asymptotic variances of the HCD50 and HCD90, or an expectation of the sum over a prior distribution. The corresponding sum of the exact posterior variances are estimated for the non-sequential designs, and compared with estimates from sequential strategies. These comparisons show that using sequential design strategies is better than non-sequential strategies, and the improvement may be large.Finally, some projects for future research in this area are proposed. |
