We consider a formal statistical design that allows simultaneous enrollment of a main cohort and a backfill cohort of patients in a dose-finding trial. The goal is to accumulate more information at various doses to facilitate dose optimization. The proposed design, called Bi3+3, combines the simple dose-escalation algorithm in the i3+3 design and a model-based inference under the framework of probability of decisions (POD), both previously published. As a result, Bi3+3 provides a simple algorithm for backfilling patients to lower doses in a dose-finding trial once these doses exhibit safety profile in patients. The POD framework allows dosing decisions to be made when some backfill patients are still being followed with incomplete toxicity outcomes, thereby potentially expediting the clinical trial. At the end of the trial, Bi3+3 uses both toxicity and efficacy outcomes to estimate an optimal biological dose (OBD). The proposed inference is based on a dose-response model that takes into account either a monotone or plateau dose-efficacy relationship, which are frequently encountered in modern oncology drug development. Simulation studies show promising operating characteristics of the Bi3+3 design in comparison to existing designs.

翻译：我们提出一种正式的统计设计，允许在剂量探索试验中同时纳入主队列与回填队列患者，旨在收集不同剂量下的更多信息以促进剂量优化。该设计称为Bi3+3，结合了i3+3设计中的简单剂量递增算法与基于决策概率（POD）框架的模型推断（两者均为先前发表方法）。通过此设计，Bi3+3提供了一个简单算法，可在较低剂量经患者验证安全性后将其回填至剂量探索试验中。POD框架支持在部分回填患者的毒性结局尚不完全时做出剂量决策，从而有可能加速临床试验进程。试验结束时，Bi3+3利用毒性与有效性结果共同估算最佳生物学剂量（OBD）。该推断基于剂量-反应模型，该模型可考虑单调或平台型剂量-有效性关系，这是现代肿瘤药物开发中的常见情形。模拟研究表明，相比现有设计，Bi3+3设计具有令人满意的操作特性。