We investigate the optimal allocation design for response adaptive clinical trials, under the average reward criterion. The treatment randomization process is formatted as a Markov decision process and the Bayesian method is used to summarize the information on treatment effects. A span-contraction operator is introduced and the average reward generated by the policy identified by the operator is shown to converge to the optimal value. We propose an algorithm to approximate the optimal treatment allocation using the Thompson sampling and the contraction operator. For the scenario of two treatments with binary responses and a sample size of 200 patients, simulation results demonstrate efficient learning features of the proposed method. It allocates a high proportion of patients to the better treatment while retaining a good statistical power and having a small probability for a trial going in the undesired direction. When the difference in success probability to detect is 0.2, the probability for a trial going in the unfavorable direction is &lt; 1.5%, which decreases further to &lt; 0.9% when the difference to detect is 0.3. For normally distribution responses, with a sample size of 100 patients, the proposed method assigns 13% more patients to the better treatment than the traditional complete randomization in detecting an effect size of difference 0.8, with a good statistical power and a &lt; 0.7% probability for the trial to go in the undesired direction.

Yanqing Yi

Xikui Wang

Statistical Methods in Medical Research

STATISTICAL METHODS IN MEDICAL RESEARCH 是一份同行评审的学术期刊，是医学统计学所有主要领域文章的主要载体，也是所有医学统计学家的重要参考资料。这本独特的期刊只专注于统计和医学，旨在让专业人士了解医学界现在可以使用的许多强大的统计技术。该期刊是出版伦理委员会 (COPE) 的成员

Statistical Methods in Medical Research is a peer-reviewed academic journal that serves as a primary platform for articles in all major areas of medical statistics, making it an essential reference for all medical statisticians. This unique journal focuses exclusively on the intersection of statistics and medicine, aiming to inform professionals about the many powerful statistical techniques currently available in the medical field. Furthermore, the journal is a member of the Committee on Publication Ethics (COPE).

《Statistical Methods in Medical Research》是一本经过同行评审的学术期刊，涵盖医学统计学的所有主要领域，成为医学统计学家们的重要参考资料。这本独特的期刊专注于统计学与医学的结合，旨在帮助专业人士了解医学界当前可用的多种强大统计技术。此外，该期刊还是出版伦理委员会（COPE）的成员。

Category	Quartile
医学	3
医学, 数学与计算生物学	2
医学, 统计学与概率论	3
医学, 卫生保健与服务	4
医学, 医学信息	4

Approximation to the optimal allocation for response adaptive designs

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Journal Info

Category	Quartile
STATISTICS & PROBABILITY	1