Asymptotic Properties of Adaptive designs for Clinical Trials with delayed Response

For adaptive clinical trials using a generalized Friedman’s urn design, we derive the limiting distribution of the urn composition under staggered entry and delayed response. The stochastic delay mechanism is assumed to depend on both the treatment assigned and the patient’s response. A very general setup is employed with K treatments and L responses. When $L = K =2$, one example of a generalized Friedman’s urn design is the randomized play-the-winner rule. An application of this rule occurred in a clinical trial of depression, which had staggered entry and delayed response. We show that maximum likelihood estimators from such a trial have the usual asymptotic properties.