The effects of treatments may differ between persons with different characteristics. Addressing such treatment heterogeneity is crucial to investigate whether patients with specific characteristics are likely to benefit from a new treatment. The current paper presents a novel Bayesian method for superiority decision-making in the context of randomized controlled trials with multivariate binary responses and heterogeneous treatment effects. The framework is based on three elements: a) Bayesian multivariate logistic regression analysis with a P\'olya-Gamma expansion; b) a transformation procedure to transfer obtained regression coefficients to a more intuitive multivariate probability scale (i.e., success probabilities and the differences between them); and c) a compatible decision procedure for treatment comparison with prespecified decision error rates. Procedures for a priori sample size estimation under a non-informative prior distribution are included. A numerical evaluation demonstrated that decisions based on a priori sample size estimation resulted in anticipated error rates among the trial population as well as subpopulations. Further, average and conditional treatment effect parameters could be estimated unbiasedly when the sample was large enough. Illustration with the International Stroke Trial dataset revealed a trend towards heterogeneous effects among stroke patients: Something that would have remained undetected when analyses were limited to average treatment effects.

翻译：不同特征的患者对治疗的反应可能不同。处理这种治疗异质性对于探究特定特征患者是否能从新疗法中获益至关重要。本文提出了一种新颖的贝叶斯方法，用于在具有多元二元响应及异质性治疗效应的随机对照试验中进行优劣决策。该框架基于三个要素：a) 基于Pólya-Gamma展开的贝叶斯多元逻辑回归分析；b) 将回归系数转换为更直观的多元概率尺度（即成功概率及其差异）的变换程序；c) 在预设决策错误率下用于治疗比较的兼容决策程序。文中还包含了非信息先验分布下的先验样本量估计步骤。数值评估表明，基于先验样本量估计做出的决策在试验总体及亚群中均能达到预期的错误率。此外，当样本量足够大时，平均及条件治疗效应参数可被无偏估计。通过国际卒中试验数据集的示例分析，揭示了卒中患者中存在异质性效应的趋势——若仅分析平均治疗效应，这一现象将无法被检测到。