This thesis is motivated by an adaptive design which was developed to inoculate healthy volunteers with nontypeable Haemophilus influenzae. The goal was to estimate the doses at which 50% (HCD50) and 90% (HCD90) of subjects became colonized. A fifteen-subject study was designed in two stages, with the first six subjects allocated sequentially. The design was chosen based on scientific and statistical arguments, however, due to limited time, heuristic decisions were made for expedience. This design and a number of alternative designs are evaluated in depth by simulation, under both Bayesian and frequentist criteria. In this thesis, Bayesian myopic strategies with one-step- , two-step- and three-step-look-ahead procedures are investigated. The optimal design is defined as the one with minimum expected loss where the loss is the sum of the posterior variance of the HCD50 and HCD90. The higher the expected loss, the worse the design. Designs using different prior distribution are examined. In addition, the toxicity-response relationship can also be incorporated in selecting the optimal design. A new model considering both colonization (efficacy) and adverse event (toxicity) is proposed, and design procedures developed. Furthermore, restrictions on the probability of toxicity are implemented. The results from simulations show that it is beneficial to look more steps ahead in determining the optimal dose although the benefit may not be large. The is true for both univariate (colonization) and bivariate (colonization and toxicity) models. For the bivariate model, as the restriction becomes more conservative (the probability of toxicity is constrained to be smaller), the expected loss becomes larger and early stopping may occur. Non-sequential designs are also found and examined using D and A criteria for optimal design. The expected loss is computed to evaluate the designs and to compare with sequential strategies. From the simulation results, it shows that using sequential design strategies does improve the performance of the design compared to using non-sequential strategies, and the improvement may be large.

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