Neural Network-based Partial-Linear Single-Index Models for Environmental Mixtures Analysis

2025-12-12

AI Summary

Assessing health effects of environmental mixtures faces challenges in model flexibility, interpretability, and compatibility with multiple outcome types. To address these, we propose the Neural Network-driven Partially Linear Single-Index Model (NN-PLSIM), the first framework to integrate deep learning’s representation capacity with the interpretability of semiparametric modeling. NN-PLSIM enables end-to-end learning of an exposure index and uniformly accommodates continuous, binary, and time-to-event outcomes under nonlinear exposure–response relationships. It incorporates bootstrap-based statistical inference to yield robust confidence intervals for estimated exposure weights. Extensive simulations and analyses of NHANES real-world data demonstrate high predictive accuracy, clear interpretability of exposure-weighted indices, and strong scalability. A fully open-source software package supports end-to-end implementation—including model fitting, visualization, and uncertainty quantification—facilitating reproducible mixture health effect assessment.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Evaluating the health effects of complex environmental mixtures remains a central challenge in environmental health research. Existing approaches vary in their flexibility, interpretability, scalability, and support for diverse outcome types, often limiting their utility in real-world applications. To address these limitations, we propose a neural network-based partial-linear single-index (NeuralPLSI) modeling framework that bridges semiparametric regression modeling interpretability with the expressive power of deep learning. The NeuralPLSI model constructs an interpretable exposure index via a learnable projection and models its relationship with the outcome through a flexible neural network. The framework accommodates continuous, binary, and time-to-event outcomes, and supports inference through a bootstrap-based procedure that yields confidence intervals for key model parameters. We evaluated NeuralPLSI through simulation studies under a range of scenarios and applied it to data from the National Health and Nutrition Examination Survey (NHANES) to demonstrate its practical utility. Together, our contributions establish NeuralPLSI as a scalable, interpretable, and versatile modeling tool for mixture analysis. To promote adoption and reproducibility, we release a user-friendly open-source software package that implements the proposed methodology and supports downstream visualization and inference ( exttt{https://github.com/hyungrok-do/NeuralPLSI}).

Problem

• Evaluates health effects of complex environmental mixtures
• Bridges interpretability with deep learning expressive power
• Accommodates diverse outcome types and supports inference

Innovation

• Neural network-based partial-linear single-index model for interpretability
• Flexible neural network models diverse health outcome types
• Bootstrap-based inference provides confidence intervals for parameters