Linked-Tucker Factorized Individualized Regression for Paired Multivariate Categorical Outcomes
配对多元分类结局的关联 Tucker 分解个体化回归AI 解读 ↓
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配对多元分类结局的关联 Tucker 分解个体化回归
- 研究问题
- 如何联合分析龋齿与氟斑牙这类配对、零膨胀的有序结局，同时刻画个体、牙齿位置和年龄之间的效应异质性？
- 方法与思路
- 作者提出联合门槛有序回归，以关联 Tucker 张量分解共享个体因子，结合马蹄先验和贝叶斯后验计算。
- 材料陈述的贡献
- 摘要称模型区分疾病出现与阳性结局严重程度，并在牙科纵向数据中发现氟暴露、饮食与两类结局的空间异质关联。
- 阅读关注点
- 应核对共享因子的可识别性、比例优势设定、先验敏感性和后验诊断，以及个体效应汇总与关联解释的边界。
- 阅读边界
- 依据所给 arXiv v3 预印本摘要，不能声称已同行评审或期刊接收；报告的是关联，摘要未建立暴露的因果效应。
原文摘要
We propose a joint individualized hurdle-ordinal regression model for paired zero-inflated ordinal outcomes with subject-specific, spatially varying, and time-varying covariate effects, motivated by the Iowa Fluoride Study (IFS). The two outcomes, dental caries and dental fluorosis, are measured repeatedly across ages at fine spatial resolution, yielding nested longitudinal data with substantial zero inflation, ordinality, and heterogeneity across individuals and locations. For each outcome, a hurdle component models disease presence, while a proportional-odds component models severity among positive observations. To parsimoniously represent the high-dimensional coefficient arrays, we introduce a linked Tucker tensor factorization. Shared subject-mode factors induce dependence between the caries and fluorosis coefficient tensors, while separate spatial factors accommodate the distinct measurement grids of tooth surfaces and tooth zones. A horseshoe prior on the core tensor elements encourages sparsity, and posterior computation is performed using the No-U-Turn Sampler in NumPyro. Population-level effect summaries are obtained by projecting individualized posterior linear predictors onto the design space, and Wasserstein barycenters aggregate these summaries across tooth locations and anatomical classes. Applied to the IFS, the model reveals spatially heterogeneous associations between early-life fluoride and dietary exposures and both outcomes. Fluoride exposure is associated with increased odds and severity of fluorosis, while soda intake consistently increases caries risk. These associations differ between presence and severity components and vary across tooth locations, ages, and subpopulations defined by prior caries status, highlighting the importance of the joint hurdle-ordinal framework for disentangling disease occurrence from disease progression in multilevel dental data.