Response adaptive designs with asymptotic optimality

Yanqing Yi; Xuan Li

doi:10.1002/cjs.11460

Response adaptive designs with asymptotic optimality

Yanqing Yi, Xuan Li

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English (US)
Pages (from-to)	458-469
Number of pages	12
Journal	Canadian Journal of Statistics
Volume	46
Issue number	3
DOIs	https://doi.org/10.1002/cjs.11460
State	Published - Sep 2018
Externally published	Yes

Bibliographical note

Funding 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.

Keywords

Confidence interval
coverage error probability
most powerful test
order of type I error rate
response adaptive designs

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abstract = "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",

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