Journal
ANNALS OF STATISTICS
Volume 39, Issue 1, Pages 643-671Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/10-AOS851
Keywords
Adaptive designs; asymptotic normality; clinical trial; urn model; branching process with immigration; birth and death urn; drop-the-loser rule
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Funding
- National Natural Science Foundation of China [11071214]
- Natural Science Foundation of Zhejiang Province [R6100119]
- Fundamental Research Funds for the Central University [2010QNA3032]
- NSF [DMS-03-49048, DMS-09-07297]
- Research Grants Council of the Hong Kong Special Administrative Region [CUHK400608]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0907297] Funding Source: National Science Foundation
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Urn models have been widely studied and applied in both scientific and social science disciplines. In clinical studies, the adoption of urn models in treatment allocation schemes has proved to be beneficial to researchers, by providing more efficient clinical trials, and to patients, by increasing the likelihood of receiving the better treatment. In this paper, we propose a new and general class of immigrated urn (IMU) models that incorporates the immigration mechanism into the urn process. Theoretical properties are developed and the advantages of the IMU models are discussed. In general, the IMU models have smaller variabilities than the classical urn models, yielding more powerful statistical inferences in applications. Illustrative examples are presented to demonstrate the wide applicability of the IMU models. The proposed IMU framework, including many popular classical urn models not only offers a unify perspective for us to comprehend the urn process, but also enables us to generate several novel urn models with desirable properties.
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