Optimal biased coin designs for clinical trials

Adaptive designs have been used to randomize patients to treatments in comparative clinical trials. In this dissertation several response adaptive randomization schemes based on some optimal criteria are developed and properties of those designs are studied. In "Optimum Biased Coin Designs for Sequential Clinical Trials with Prognostic factors" Biometrika 69:61--67, Atkinson proposed a family of biased coins based on D-optimality and DA-optimality with the goal of balancing the number of patients across treatment arms. These allocation schemes are restricted to the case where outcome variances are equal and the paper gives no distributional properties for the resulting allocation proportions.; Here the optimal biased coins discussed by Atkinson are generalized to consider situations in which outcomes are heteroscedastic. Asymptotic properties of the designs suggested by Atkinson that do not consider prognostic factors are studied. New adaptive and response adaptive optimal biased coins are introduced that consider heteroscedastic outcomes in clinical trials having more than two treatments. It is shown that the allocation fractions tend almost surely to certain target allocations and the asymptotic distributions of the allocation fractions are given. It is shown that the D-optimal biased coins provide patient allocations that tend to Neyman allocation allowing for maximal power in some cases. Also, a new response adaptive biased coin that considers a binary prognostic factor is introduced and its asymptotic properties are studied.