Recent years have seen increased interest in combining drug agents and/or schedules. Several methods for Phase I combination-escalation trials are proposed, among which, the partial ordering continual reassessment method (POCRM) gained great attention for its simplicity and good operational characteristics. However, the one-parameter nature of the POCRM makes it restrictive in more complicated settings such as the inclusion of a control group. This paper proposes a Bayesian partial ordering logistic model (POBLRM), which combines partial ordering and the more flexible (than CRM) two-parameter logistic model. Simulation studies show that the POBLRM performs similarly as the POCRM in non-randomised settings. When patients are randomised between the experimental dose-combinations and a control, performance is drastically improved. Most designs require specifying hyper-parameters, often chosen from statistical considerations (operational prior). The conventional "grid search'' calibration approach requires large simulations, which are computationally costly. A novel "cyclic calibration" has been proposed to reduce the computation from multiplicative to additive. Furthermore, calibration processes should consider wide ranges of scenarios of true toxicity probabilities to avoid bias. A method to reduce scenarios based on scenario-complexities is suggested. This can reduce the computation by more than 500 folds while remaining operational characteristics similar to the grid search.

翻译：近年来，药物联合治疗和/或联合给药方案的研究日益受到关注。针对I期联合剂量递增试验已提出多种方法，其中部分排序持续重评估法（POCRM）因其简洁性和良好的操作特性而备受关注。然而，POCRM的单参数特性使其在更复杂的场景中（如包含对照组时）具有局限性。本文提出一种贝叶斯部分排序逻辑模型（POBLRM），该模型结合了部分排序机制和比CRM更灵活的双参数逻辑模型。模拟研究表明，在非随机化设置中POBLRM的表现与POCRM相似。当患者在实验性剂量组合与对照组之间进行随机分配时，其性能得到显著提升。多数设计需要设定超参数，这些参数通常基于统计考量（运算先验）进行选择。传统的"网格搜索"校准方法需要大量模拟计算，计算成本高昂。本文提出一种新颖的"循环校准"方法，可将计算复杂度从乘性降低至加性。此外，校准过程应考虑真实毒性概率的广泛场景以避免偏差。本文提出一种基于场景复杂度的场景缩减方法，可在保持与网格搜索相近操作特性的同时，将计算量减少500倍以上。