We propose the covariate-balanced-and-adjusted response-adaptive randomization (CBARA) procedure for adaptive design in clinical trials, which integrates the complementary strengths of covariate-adjusted response-adaptive randomization (CARA) and covariate-adaptive randomization (CAR). The CBARA procedure updates the target allocation ratio according to observed responses and patient covariate profiles without requiring a correctly specified model, thereby retaining CARA's ethical and efficiency considerations while improving robustness. In addition, the CBARA procedure extends the CAR principle from fixed target allocation ratios to covariate-adjusted adaptive target allocation ratios, yet still pursues balance in treatment allocation with respect to covariate features. This integration is enabled by a newly defined imbalance vector and three interrelated components: the allocation function, parameter estimation and update mechanism. We establish the asymptotic properties of covariate imbalance and the estimators under the CBARA procedure. The results demonstrate that the CBARA procedure can improve balance for both observed and unobserved covariates while preserving the consistency of the allocation ratio. The theoretical analysis is developed through a pseudo-Markov chain framework, where a new discrepancy measure for transition kernels is introduced to handle the continuity of Poisson equation solutions with respect to parameters.

翻译：摘要：我们提出了协变量平衡调整响应自适应随机化（CBARA）程序，用于临床试验中的适应性设计，该程序整合了协变量调整响应自适应随机化（CARA）和协变量自适应随机化（CAR）的互补优势。CBARA程序根据观察到的反应和患者协变量概况更新目标分配比例，无需正确指定的模型，从而保留了CARA的伦理和效率考量，同时提高了鲁棒性。此外，CBARA程序将CAR原则从固定目标分配比例扩展到协变量调整自适应目标分配比例，但仍追求在协变量特征方面处理分配的平衡性。这种整合通过新定义的失衡向量和三个相互关联的组件实现：分配函数、参数估计和更新机制。我们建立了在CBARA程序下协变量失衡和估计量的渐近性质。结果表明，CBARA程序可以改善观测和未观测协变量的平衡性，同时保持分配比例的一致性。理论分析通过伪马尔可夫链框架展开，其中引入了转移核的新差异度量，以处理泊松方程解相对于参数的连续性。