OPTIMAL CROSSOVER DESIGNS IN CLINICAL TRIALS

Abstract

This thesis specializes in statistical issues involving crossover designs, a very popular design in clinical trials for comparing non-curative treatments for their efficacy. The popularity stems from the fact that each experimental subject receives a sequence of trial treatments rather than one single treatment as in parallel designs, and thereby requires fewer experimental subjects. Further, it reduces variability in treatment comparisons because subjects serve as their own controls and between-subject variations are eliminated. One distinct feature in crossover designs is that the treatment assigned to subjects may have lasting effects, called carryover effects, on their responses to treatments in subsequent applications. Crossover designs are well-deliberated for its controversy involving the non-orthogonal key parameters of direct and carryover treatments, which leads to completely different experimental designs depending on which is the primary interest. There are several issues that we address in this thesis. First, when building optimal designs, there are often competing objectives that the investigator desires to optimize. These multiple objectives can include two or more parameters or some functionals, ultimately requiring simultaneous considerations. We revisit the controversy from the point of view of constrained and compound designs for better understanding. Second, we focus on the construction of optimal designs to that of individual- based designs. Typically, designs were constructed to optimize the average subjects and not ideal in clinical and medical applications. N-of-1 trials are randomized multi-crossover experiments using two or more treatments on a single patient. They provide evidence and information on an individual patient, thus optimizing the management of the individual’s chronic illness. We build one sequence N-of-1 universally optimal designs. We also construct optimal N-of-1 designs for two treatments. Then, we discuss the extension to optimal aggregated N-of-1 designs, which will be optimal for an overall treatment effect. Third, we extend the response adaptive allocation strategy for continuous responses to construct those for binary responses with the goal of allocating more patients to better treatment sequences without sacrificing much estimation precision. Although design efficiency in terms of mean squared error may drop sharply, increase in allocated patients to the treatment with beneficial effect is evident. We show a balance can be achieved between various competing multiple objectives. Fourth, we advocate the convex optimization techniques to construct optimal crossover designs where analytic solutions are not feasible. Upon identifying the unique problems and conditions for constructing optimal designs to that of the convex optimization problem, we apply them to find optimal designs relatively simply.