Abstract：
Doubly adaptive biased coin design (DBCD), a response-adaptive randomization scheme, aims to skew subject assignment probabilities based on accrued responses for ethical considerations. Recent years have seen substantial advances in understanding DBCD\'s theoretical properties, assuming correct model specification for the responses. However, concerns have been raised about the impact of model misspecification on its design and analysis. In this paper, we assess the robustness to both design model misspecification and analysis model misspecification under DBCD. On one hand, we confirm that the consistency and asymptotic normality of the allocation proportions can be preserved, even when the responses follow a distribution other than the one imposed by the design model during the implementation of DBCD. On the other hand, we extensively investigate three commonly used linear regression models for estimating and inferring the treatment effect, namely difference-in-means, analysis of covariance (ANCOVA) I, and ANCOVA II. By allowing these regression models to be arbitrarily misspecified, thereby not reflecting the true data generating process, we derive the consistency and asymptotic normality of the treatment effect estimators evaluated from the three models. The asymptotic properties show that the ANCOVA II model, which takes covariate-by-treatment interaction terms into account, yields the most efficient estimator. These results can provide theoretical support for using DBCD in scenarios involving model misspecification, thereby promoting the widespread application of this randomization procedure.
摘要：
双自适应偏置硬币设计(DBCD)，响应自适应随机化方案，旨在基于道德考虑的应计响应来扭曲主题分配概率。近年来，在理解DBCD的理论性质方面取得了重大进展，假设响应的模型规范正确。然而,有人担心模型规格错误对其设计和分析的影响。在本文中,我们评估了DBCD下设计模型错误规范和分析模型错误规范的鲁棒性。一方面,我们确认可以保持分配比例的一致性和渐近正态，即使响应遵循DBCD实施过程中设计模型所施加的分布以外的分布。另一方面,我们广泛研究了三种常用的线性回归模型来估计和推断治疗效果，即均值差异，协方差分析(ANCOVA)I，ANCOVAII。通过允许这些回归模型被任意错误指定，从而不能反映真实的数据生成过程，我们从三个模型中得出治疗效果估计的一致性和渐近正态。渐近性质表明，ANCOVAII模型，它考虑了协变量与治疗的相互作用项，产生最有效的估计器。这些结果可以为在涉及模型错误指定的场景中使用DBCD提供理论支持，从而促进了该随机化程序的广泛应用。
