Linked-Tucker Factorized Individualized Regression for Paired Multivariate Categorical Outcomes

2026-05-07

AI Summary

This study addresses the modeling of two zero-inflated ordered dental outcomes—dental caries and fluorosis—accounting for individual, spatial (tooth position), and temporal (age) heterogeneity as well as their complex associations with early-life exposures. The authors propose a joint individualized two-part regression framework that separately models disease occurrence and severity. An innovative linked Tucker tensor decomposition is introduced to compress high-dimensional coefficient arrays: shared individual factors capture dependence between outcomes, while outcome-specific spatial factors accommodate distinct anatomical grids, and Wasserstein barycenters aggregate multiscale effects. Efficient Bayesian inference is achieved via horseshoe priors and NUTS sampling. Empirical results reveal that fluoride exposure significantly increases both the risk and severity of fluorosis, while carbonated beverage consumption persistently elevates caries risk, with pronounced heterogeneity across tooth positions, ages, and subpopulations.

Abstract

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.

Problem

• zero-inflated ordinal outcomes
• individualized regression
• paired multivariate categorical data
• spatially varying effects
• dental caries and fluorosis

Innovation

• linked Tucker factorization
• hurdle-ordinal regression
• zero-inflated ordinal outcomes
• spatially varying coefficients
• Wasserstein barycenter