This article discusses the asymptotic optimality of statistical inference for response-adaptive designs, which has ethical advantages over traditional methods for clinical trials. The upper bound of statistical power of asymptotically level α tests is derived and the Wald statistic is shown to be asymptotically optimal in terms of achieving the upper bound of the asymptotic power. The rates of coverage error probability of the confidence interval are proven to depend on the convergence rate of the allocation proportions for non-normally distributed responses. When the response density functions are normal density functions, it is proven that the coverage error probability and type I error rate are of the order n−1. The Canadian Journal of Statistics 46: 458–469; 2018
Bibliographical noteFunding Information:
Yanqing Yi acknowledges research support from the Natural Sciences and Engineering Research Council of Canada (NSERC). Xuan Li acknowledges partial support from the Grant-in-Aid of Research, Artistry and Scholarship (GIA) awarded by the Office of the Vice President for Research, University of Minnesota.
- Confidence interval
- coverage error probability
- most powerful test
- order of type I error rate
- response adaptive designs