In recent years, there has been growing research interest in addressing treatment hierarchy questions within network meta-analysis (NMA). In NMAs involving many treatments, the number of possible hierarchy questions becomes prohibitively large. To manage this complexity, previous work has recommended pre-selecting specific hierarchy questions of interest (e.g., ``among options A, B, C, D, E, do treatments A and B have the two best effects in terms of improving outcome X?") and calculating the empirical probabilities of the answers being true given the data. In contrast, we propose an efficient and scalable algorithmic approach that eliminates the need for pre-specification by systematically generating a comprehensive catalog of highly credible treatment hierarchy questions, specifically, those with empirical probabilities exceeding a chosen threshold (e.g., 95%). This enables decision-makers to extract all meaningful insights supported by the data. An additional algorithm trims redundant insights from the output to facilitate interpretation. We define and address six broad types of binary hierarchy questions (i.e., those with true/false answers), covering standard hierarchy questions answered using existing ranking metrics - pairwise comparisons and (cumulative) ranking probabilities - as well as many other complex hierarchy questions. We have implemented our methods in an R package and illustrate their application using real NMA datasets on diabetes and depression interventions. Beyond NMA, our approach is relevant to any decision problem concerning three or more treatment options.

翻译：近年来，针对网络荟萃分析（NMA）中治疗层次问题的研究兴趣日益增长。在涉及多种治疗的NMA中，可能的层次问题数量变得极其庞大。为应对这种复杂性，先前的研究建议预先选择特定的、感兴趣的层次问题（例如，“在选项A、B、C、D、E中，治疗A和B是否在改善结局X方面具有最好的两种效果？”），并计算给定数据下答案为真的经验概率。与之相反，我们提出了一种高效且可扩展的算法方法，通过系统地生成一个全面的高可信度治疗层次问题目录，特别是那些经验概率超过选定阈值（例如95%）的问题，从而无需预先指定。这使得决策者能够提取数据支持的所有有意义的见解。一个额外的算法会从输出中修剪冗余的见解，以方便解释。我们定义并解决了六种广泛的二元层次问题（即答案为真/假的问题），涵盖了使用现有排序指标（成对比较和（累积）排序概率）回答的标准层次问题，以及许多其他复杂的层次问题。我们已在R包中实现了我们的方法，并使用糖尿病和抑郁症干预措施的真实NMA数据集说明了其应用。除了NMA之外，我们的方法也适用于任何涉及三种或更多治疗方案的选择问题。