Optimal adaptive generalized Pَlya urn design for multi-arm clinical trials

A class of optimal adaptive multi-arm clinical trial designs is proposed based on an extended generalized Pَlya urn (GPU) model. The design is applicable to both the qualitative and quantitative responses and achieves, asymptotically, some pre-specified optimality criterion. Such criterion is specified by a functional of the response distributions and is implemented through the relationship between the design matrix and its first eigenvector. The asymptotic properties of the design are studied using the existing methods on GPU. Some examples for commonly used clinical designs are given as illustration.