An Interpretable Single-Index Mixed-Effects Model for Non-Gaussian National Survey Data

2025-09-24

AI Summary

Periodontal clinical metrics (e.g., clinical attachment loss, probing depth) often exhibit non-normality—specifically skewness and heavy-tailed heteroscedasticity—while national survey data introduce complex within-cluster correlations and sampling bias. Method: We propose an interpretable single-index mixed-effects model featuring skewed random effects, heavy-tailed residuals, a monotonic single-index link function, grouped horseshoe priors for sparse variable selection, and integrated survey weights to correct for complex sampling design. Contribution/Results: Compared to conventional Gaussian-based models, our approach substantially improves goodness-of-fit and biological interpretability for non-Gaussian, skewed, and heteroscedastic periodontal data. The method is implemented in the open-source R package MSIMST, enabling robust, transparent, and scalable modeling of large-scale complex medical survey data.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Kernel Methods

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Web data generation and simulation
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

This manuscript presents an innovative statistical model to quantify periodontal disease in the context of complex medical data. A mixed-effects model incorporating skewed random effects and heavy-tailed residuals is introduced, ensuring robust handling of non-normal data distributions. The fixed effect is modeled as a combination of a slope parameter and a single index function, constrained to be monotonic increasing for meaningful interpretation. This approach captures different dimensions of periodontal disease progression by integrating Clinical Attachment Level (CAL) and Pocket Depth (PD) biomarkers within a unified analytical framework. A variable selection method based on the grouped horseshoe prior is employed, addressing the relatively high number of risk factors. Furthermore, survey weight information typically provided with large survey data is incorporated to ensure accurate inference. This comprehensive methodology significantly advances the statistical quantification of periodontal disease, offering a nuanced and precise assessment of risk factors and disease progression. The proposed methodology is implemented in the extsf{R} package href{https://cran.r-project.org/package=MSIMST}{ extsc{MSIMST}}.

Problem

• Develops statistical model to quantify periodontal disease using complex medical survey data
• Handles non-normal data distributions with skewed random effects and heavy-tailed residuals
• Integrates multiple biomarkers and risk factors within unified analytical framework

Innovation

• Mixed-effects model with skewed random effects and heavy-tailed residuals
• Monotonic single index function combined with slope parameter for fixed effects
• Grouped horseshoe prior variable selection incorporating survey weights