Goodness-of-fit test for response adaptive clinical trials

Much attention has been given in recent years to adaptive designs of clinical trials as ethical alternatives when the traditional randomization becomes ethically infeasible. But such designs create dependency among the collected data, and hence statistical methods for adaptive clinical trials are more complex than those for traditional randomized clinical trials. In this paper, we examine some extensions of common statistical methods for independent data. Under regularity conditions, the logarithm of likelihood ratio statistic 2lnλ2lnλ for dependent data is shown to be asymptotically chi-square distributed, providing a foundation for asymptotic analysis of adaptive clinical trials with k treatments. We also discuss both the consistency and the asymptotic normality of the maximum likelihood estimators for a wide class of adaptive designs.