AI 中文总结
针对临床试验中响应自适应设计的多方面困境，提出通用框架定义高效设计族，证明相关最优性。在此基础上给出多治疗临床试验的双自适应偏置硬币设计族，兼具随机性和效率优势，并推导其理论性质。
AI 中文摘要
在临床试验中，随机性、效率（功效和变异性）以及理想的分配比例是评估响应自适应设计的重要组成部分，且在应用中存在相互冲突的需求。本文旨在提供应对这些困境的设计。首先给出了一个通用框架，用于实现高效响应自适应随机化程序，能达到任意期望分配比例下分配方差的克拉美 - 罗下界。该框架灵活，可定义适用于双治疗和多治疗临床试验的具有良好性质的新的高效设计族。还证明了在具有相同极限分配比例的所有响应自适应随机化程序中，作为设计随机性度量的选择偏差和熵具有最优值。基于效率和随机性理论，提出了一种新的用于多治疗临床试验的双自适应偏置硬币设计族，其能针对任意分配比例，在随机性和效率方面渐近最优，即随机性渐近最优且渐近分配方差达到克拉美 - 罗下界。通过高斯近似和高斯比较定理技术推导了包括样本分配比例和分布参数估计量的强一致性、渐近正态性和泛函中心极限定理等理论性质。
英文摘要
The randomness, efficiency (power and variability), and desirable allocation proportions are important components for evaluating a response-adaptive design in clinical trials and conflicted demands in applications. The aim of this paper is to provide designs dealing with these dilemmas. We first give a general framework for efficient response-adaptive randomization procedures that attain the Cramér-Rao lower bounds of the allocation variances for any desired allocation proportions. The general framework is flexible for us to define new families of efficient designs with good properties for both two and multiple-treatment clinical trials. We also prove that, among all response-adaptive randomization procedures with the same limit allocation proportions, the selection biases and entropies as measures of the randomness of the designs have their optimal values. Basing on the theory on efficiency and randomness, we propose a new family of doubly adaptive biased coin designs for multi-treatment clinical trials that can target any allocation proportion and are asymptotically best in terms both the randomness and efficiency so that their randomness is asymptotic optimal and asymptotic allocation variance attains the Cramér-Rao lower bound. Theoretical properties, including the strong consistency, the asymptotic normality, and the functional central limit theorem for both the sample allocation proportions and the estimators of the distribution parameters, are developed by using the technique of Gaussian approximation and Gaussian comparing theorems.
Comments55 pages
