A new tool for comparing adaptive designs; a posteriori efficiency

In this work, we consider an adaptive linear regression model designed to explain the patient’s response in a clinical trial. Patients are assumed to arrive sequentially. The adaptive nature of this statistical model allows the error terms to depend on the past which has not been permitted in other adaptive models in the literature. Some techniques of the theory of optimal designs are used in this framework to define new concepts: a-posteriori efficiency and mean a-posteriori efficiency. We then explicitly relate the variance of the allocation rule to the mean a-posteriori efficiency. These measures are useful for studying the comparative performance of adaptive designs. As an example, a comparative study is made among several design- adaptive designs to establish their properties with respect to a criterion of interest.