Dynamic treatment allocation adjusting for prognostic factors for more than two treatments

Methods of sequential allocation of one of K treatments to patients, while controlling for important prognostic factors, are developed and compared. We focus on methods that are based on optimality theory (Begg and Iglewicz, 1980, Biometrics 36, 81-90; Atkinson, 1982, Biometrika 69, 61-67), the permuted block procedure (Zelen, 1974, Journal of Chronic Diseases 27, 365-375), and the compromise method (Faraggi and Reiser, 1991, Communication in Statistics, Simulation and Computation 20, 243-254). These methods are extended to the K treatments case and are evaluated in terms of efficiency and balance. It is shown that each method achieved the best results in the criterion it was designed to optimize, i.e., within stratum balance for the permuted block allocation and efficiency for the allocations that are based on optimality theory, but did not do well with other criteria. The compromise method, on the other hand, has good overall properties in terms of both balance and efficiency.