Shrinkage Estimation for Dose–Response Modeling in Phase II Trials With Multiple Schedules

Recently, phase II trials with multiple schedules (frequency of administrations) have become more popular, for instance, in the development of treatments for atopic dermatitis. If the relationship of the dose and response is described by a parametric model, a simplistic approach is to scale doses from different schedules to a common unit and pool all rescaled doses. However, this approach ignores the potential heterogeneity in dose–response curves between schedules. A more reasonable approach is the partial pooling, that is, certain parameters of the dose–response curves are shared, while others are allowed to vary. Rather than using schedule-specific fixed-effects, we propose a Bayesian hierarchical model with random-effects to model the between-schedule heterogeneity with regard to certain parameters. Schedule-specific dose–response relationships can then be estimated using shrinkage estimation. Considering Emax models, the proposed method displayed desirable performance in terms of the mean absolute error and the coverage probabilities for the dose–response curve compared to the complete pooling. Furthermore, it outperformed the partial pooling with schedule-specific fixed-effects by producing lower mean absolute error and shorter credible intervals. The methods are illustrated using simulations and a phase II trial example in atopic dermatitis. A publicly available R package, ModStan, is developed to automate the implementation of the proposed method (https://github.com/gunhanb/ModStan).

近年来，采用多种给药方案的II期临床试验（phase II trials）愈发普遍，例如在特应性皮炎（atopic dermatitis）治疗药物的研发中。若剂量与反应的关系可通过参数模型（parametric model）描述，一种简易的处理方式是将不同方案下的剂量折算至统一单位后进行合并池化。但该方法未能考量不同方案间剂量-反应曲线潜在的异质性。更为合理的统计策略为部分池化（partial pooling）：即保留剂量-反应曲线的部分参数共享属性，同时允许其余参数存在个体差异。相较于仅采用方案专属固定效应的传统方法，本文提出一种带有随机效应（random-effects）的贝叶斯分层模型（Bayesian hierarchical model），以建模不同方案间部分参数的异质性。后续即可通过收缩估计（shrinkage estimation）得到各方案专属的剂量-反应关系。
针对Emax模型（Emax models），相较于完全池化方法，本文所提方法在剂量-反应曲线的平均绝对误差（mean absolute error）与覆盖概率（coverage probabilities）两项指标上均表现出更优的性能。此外，相较于采用方案专属固定效应的部分池化方法，所提方法可得到更低的平均绝对误差与更窄的可信区间（credible intervals）。
本文通过模拟试验与一项特应性皮炎的II期临床试验实例，对所提方法进行了验证与演示，并开发了一款公开可用的R包（R package）ModStan以实现该方法的自动化部署，相关代码仓库地址为：https://github.com/gunhanb/ModStan。