Sequential designs for estimating toxicity and efficacy in a dose-response setting

Phase I clinical trials are small, sequential studies designed to obtain information about toxicity profile of the experimental drug. Identification of appropriate dose levels of a drug in order to pass them for further testing is of importance. Hence the objective of the trial is to obtain maximum information about the relationship between the dose levels and probability of toxicity, called dose-response function. Optimal designs allocate the dose levels to patients in an efficient way. The efficiency is defined with respect to some optimality criteria which minimizes an appropriately chosen function of the information matrix of the model parameters. In this dissertation, we explore appropriate sequential designs based on certain optimality criteria. While such designs are applicable for phase I toxicity trials, they can also be used for efficacy studies or any other sequential study interested in efficient estimation of the dose-response relationship.;First, we enhance the performance and applicability of an existing two parameter model-based Bayesian sequential optimal design by re-implementing it using Markov Chain Monte Carlo methods. We develop and implement a new, multiparameter model-based optimal sequential procedure. In particular, a five parameter model building in a shape parameter and thresholds is explored. Both methods are extensively studied in simulations, under model misspecifications, of clinical trials mimicking real world situations. Ethical constraints, for protecting patients from the exposure to toxic dose levels, are incorporated as well. The methods are complementary and found to be very applicable in the trials where prior knowledge can be incorporated. Guidelines regarding which design should be used and how the models are to be constructed are discussed in detail.;The author also developed a new, completely nonparametric, sequential optimal design using isotonic spline estimation. The procedure is found to be useful for trials with a large number of dose levels, but less appropriate for trials with a small number of doses often found in phase I trials. For example, the method can be used in phase II trials, concerned primarily with efficacy of the experimental drug. The procedure also provides a venue for future improvements and development of mixture procedures.