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（给药频率）的II期临床试验愈发流行，例如在特应性皮炎治疗药物的研发中。若剂量-反应关系可通过参数模型描述，一种简易方法是将不同给药方案下的剂量缩放至统一单位，并合并所有经重标后的剂量。但该方法忽略了不同给药方案间剂量-反应曲线可能存在的异质性。更为合理的方法为部分合并法（partial pooling），即保留剂量-反应曲线的部分参数共享，同时允许其余参数存在差异。相较于使用给药方案专属的固定效应模型，本文提出一种带有随机效应的贝叶斯分层模型，用于对特定参数下的给药方案间异质性进行建模。随后可通过收缩估计法，得到各给药方案专属的剂量-反应关系估计值。以Emax模型（Emax model）为例，相较于完全合并法（complete pooling），所提方法在平均绝对误差与剂量-反应曲线覆盖率两方面均表现优异。此外，相较于采用给药方案专属固定效应的部分合并法，该方法所得平均绝对误差更低、可信区间更窄，性能更优。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演示验证。本文还开发了一款公开可用的R软件包ModStan，可自动实现所提方法的落地运行（https://github.com/gunhanb/ModStan）。