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：我们提出了一种联合个性化障碍序数回归模型，用于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——龋齿和牙氟中毒——在不同年龄以精细空间分辨率重复测量，产生嵌套纵向数据，具有显著的零膨胀、序数性以及个体和位置间的异质性。对于每个结果，障碍部分模拟疾病存在性，而比例优势部分模拟阳性观测中的严重程度。为简洁表示高维系数数组，我们引入了一种链接Tucker张量分解。共享的主体模式因子诱导龋齿和氟中毒系数张量之间的依赖性，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型转弯采样器进行。通过将个性化后验线性预测投影到设计空间上获得总体效应总结，而Wasserstein重心则跨牙齿位置和解剖类别聚合这些总结。应用于IFS时，该模型揭示了早期氟化物和饮食暴露与两种结果之间的空间异质性关联。氟化物暴露与氟中毒的几率和严重程度增加相关，而苏打水摄入则持续增加龋齿风险。这些关联在存在性和严重性成分之间有所不同，并随牙齿位置、年龄及由既往龋齿状态定义的子群体而变化，突显了联合障碍序数框架在多层牙齿数据中区分疾病发生与疾病进展的重要性。