Response adaptive designs with asymptotic optimality

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  • Author: Yanqing Yi and Xuan Li
  • Date: 01 May 2019
  • Copyright: Image copyright of Patrick Rhodes

An article published in The Canadian Journal of Statistics 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 article is available via this link and the authors explain their findings in further detail below:

Response adaptive designs with asymptotic optimality

Yanqing Yi and Xuan Li

The Canadian Journal of Statistics, Volume 46, Issue 3, September 2018, pages 458-469

thumbnail image: Response adaptive designs with asymptotic optimality

Response adaptive designs use information from patient responses collected during clinical trials to modify treatment allocation probabilities in order to allocate a high proportion of patients to the potentially better treatment. The designs have ethical advantages over traditional randomized designs of clinical trials; however, the samples from response-adaptive designs are dependent due to the modification of treatment allocation probabilities. This dependency may reduce the statistical power of hypothesis testing when comparing treatment effects. The authors discussed the asymptotic optimality of statistical inference for response-adaptive designs in this article. They derived the upper bound of statistical power of asymptotically level α tests and proved that the Wald statistic is asymptotically optimal in terms of achieving the upper bound of asymptotic power.

They also showed that the order of the type I error rate in the approximation to the nominal level is o(n−1/2) for general distributions of responses and O(n−1) for normally distributed responses. Similar results were derived for the coverage error probability for asymptotic two-sided confidence intervals. The authors included a numerical study which demonstrated the ethical advantages of response adaptive designs; and also indicated that the simulated statistical power and type I error rate are close to the nominal levels for the size of 185. These results quantify the influence of adaptive randomization on the error probabilities and provide approximation accuracy in statistical power and type I error rate when planning an adaptive clinical trial.

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