Causal Inference in Biomedical Imaging via Functional Linear Structural Equation Models

2026-01-28

AI Summary

This study addresses the challenge of identifying causal effects between organ-specific functional features in medical imaging and clinical outcomes, particularly when infinite-dimensional exposures coexist with high-dimensional confounders—a setting where conventional methods fail. To tackle this, the authors propose the Functional Linear Structural Equation Model (FLSEM), which introduces, for the first time, an identifiable functional structural equation framework into biomedical causal inference. By leveraging a scalar instrumental variable, they establish formal identifiability conditions and develop the FGS-DAR algorithm, which achieves selection consistency for efficient variable selection and parameter estimation. Additionally, they formulate a hypothesis test for assessing the nullity of functional coefficients. Extensive simulations and real-data analyses using the UK Biobank demonstrate that the proposed method robustly identifies causal relationships while maintaining high estimation accuracy and variable selection precision.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Computer Vision: Medical and Biological Imaging

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Understanding the causal effects of organ-specific features from medical imaging on clinical outcomes is essential for biomedical research and patient care. We propose a novel Functional Linear Structural Equation Model (FLSEM) to capture the relationships among clinical outcomes, functional imaging exposures, and scalar covariates like genetics, sex, and age. Traditional methods struggle with the infinite-dimensional nature of exposures and complex covariates. Our FLSEM overcomes these challenges by establishing identifiable conditions using scalar instrumental variables. We develop the Functional Group Support Detection and Root Finding (FGS-DAR) algorithm for efficient variable selection, supported by rigorous theoretical guarantees, including selection consistency and accurate parameter estimation. We further propose a test statistic to test the nullity of the functional coefficient, establishing its null limit distribution. Our approach is validated through extensive simulations and applied to UK Biobank data, demonstrating robust performance in detecting causal relationships from medical imaging.

Problem

• causal inference
• biomedical imaging
• functional data
• structural equation model
• instrumental variables

Innovation

• Functional Linear Structural Equation Model
• Causal Inference
• Medical Imaging
• Instrumental Variables
• Variable Selection