标题： 零膨胀贝叶斯多研究无限非负矩阵分解 显示英文标题

标题： Zero-Inflated Bayesian Multi-Study Infinite Non-Negative Matrix Factorization

摘要： 理解饮食模式与健康结果之间的关联，例如癌症风险，对于制定公共卫生指南和设计未来的饮食干预措施至关重要。 然而，饮食摄入数据存在多个统计挑战：它们是高维的，通常稀疏且含有过多的零值，并且由于个体层面的协变量而表现出异质性。 非负矩阵分解（NMF）通常用于估计高维计数数据中的模式，但通常依赖泊松假设，并缺乏充分应对这些复杂性的灵活性。 此外，整合多个研究的数据，例如癌症风险的病例对照研究，需要能够在不同来源之间共享信息的同时保留研究特异性结构的模型。 在本文中，我们引入了一种新颖的贝叶斯NMF模型，该模型（i）联合建模多研究计数数据以实现跨研究的信息共享，（ii）包含一个混合成分以处理零膨胀问题，并（iii）利用灵活的贝叶斯非参数先验来描述由个体协变量引起的模式得分的异质性。 这种结构允许根据饮食特征对个体进行聚类，从而进行下游与健康结果的关联分析。 通过广泛的模拟研究，我们证明与现有的贝叶斯NMF方法相比，我们的模型显著提高了估计准确性。 我们进一步通过在饮食与上呼吸道和消化道癌症的多个病例对照研究中的应用，展示了其适用性，识别出具有营养意义的饮食模式。 一个实现我们方法的R包可在https://github.com/blhansen/ZIMultiStudyNMF获取。 显示英文摘要

摘要： Understanding the association between dietary patterns and health outcomes, such as the cancer risk, is crucial to inform public health guidelines and shaping future dietary interventions. However, dietary intake data present several statistical challenges: they are high-dimensional, often sparse with excess zeros, and exhibit heterogeneity driven by individual-level covariates. Non-Negative Matrix Factorization (NMF), commonly used to estimate patterns in high-dimensional count data, typically relies on Poisson assumptions and lacks the flexibility to fully address these complexities. Additionally, integrating data across multiple studies, such as case-control studies on cancer risk, requires models that can share information across sources while preserving study-specific structure. In this paper, we introduce a novel Bayesian NMF model that (i) jointly models multi-study count data to enable cross-study information sharing, (ii) incorporate a mixture component to account for zero inflation, and (iii) leverage flexible Bayesian non-parametric priors for characterizing the heterogeneity in pattern scores induced by the individual covariates. This structure allows for clustering of individuals based on dietary profiles, enabling downstream association analyses with health outcomes. Through extensive simulation studies, we demonstrate that our model significantly improves estimation accuracy compared to existing Bayesian NMF methods. We further illustrate its utility through an application to multiple case-control studies on diet and upper aero-digestive tract cancers, identifying nutritionally meaningful dietary patterns. An R package implementing our approach is available at https://github.com/blhansen/ZIMultiStudyNMF.