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.

翻译：本文提出一种联合个性化障碍序数回归模型，用于处理配对零膨胀序数结果，该模型包含个体特异性、空间变化和时变协变量效应，受爱荷华氟化物研究（IFS）启发。两个结果变量——龋齿和氟斑牙——在不同年龄以精细空间分辨率重复测量，形成嵌套纵向数据，具有显著的零膨胀、序数性以及个体和位置间的异质性。针对每个结果，障碍部分建模疾病存在性，而比例优势部分建模阳性观测中的严重程度。为简洁表示高维系数数组，我们引入一种链接塔克张量分解。共享个体模式因子在龋齿和氟斑牙系数张量之间诱导依赖性，而独立的空间因子则适应牙齿表面和牙齿区域的不同测量网格。核心张量元素上的马蹄形先验促进稀疏性，后验计算使用NumPyro中的无U型转折采样器执行。通过将个体化后验线性预测投影到设计空间上获得总体效应摘要，并利用瓦瑟斯坦重心将这些摘要聚合到牙齿位置和解剖类别间。应用于IFS时，该模型揭示了早期氟化物和饮食暴露与两个结果之间的空间异质性关联。氟化物暴露与氟斑牙发生概率和严重程度增加相关，而苏打水摄入持续增加龋齿风险。这些关联在存在性和严重程度成分之间不同，且随牙齿位置、年龄和由先前龋齿状态定义的子群体变化，突出了联合障碍序数框架在多层次牙科数据中区分疾病发生与疾病进展的重要性。