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Phase II Multi-Arm Clinical Trial Designs and Randomization with Covariates via Empirical Weighting

Yuan Ao, Alexander W Dromerick and Ming T. Tan

In phase II clinical trials, multiple competing treatments may be studied, and often we have information on covariates about the patients (characters, e.g., gender, age etc). In this case the goal of the design is to allocate each patient to one of the treatments such that the covariates values are as much balanced as possible while still maintaining randomization. However the two objectives often conflict each other. In addition, when there are three or more covariates, balance among covariates is difficult or impossible to achieve. There are numerous studies to address this topic under various situations and considerations, and each has its pros and cons. Motivated from a stroke rehabilitation trial, we propose a design that retains randomization and balances covariates, using the empirical weights to construct the design covariates
distribution, then maximizing the entropy of this empirical distribution over all possible designs subject to
suitable constraint(s). We propose to use empirical likelihood to assign weights of covariates and then derive the design by balancing their (empirical) entropy. The proposed method uses all the information in the covariates, as compared to methods using only the main covariates or their principal components. Different from existing methods, the proposed method achieves balance over the covariates without stratification, and is easy to use. We illustrate the method with simulated examples. The resulting multi-arm design is then used further to construct the optimal and minimax design in the presence of covariates in two-stage trials.