[Paper Review] Multi-study factor regression model: an application in nutritional epidemiology

Roberta De Vito, Alejandra Avalos‐Pacheco|arXiv (Cornell University)|Apr 25, 2023

Nutritional Studies and DietMedicine3 citations

TL;DR

This paper introduces the Multi-Study Factor Regression (MSFR) model, a novel joint factor analysis framework that simultaneously identifies shared and group-specific dietary patterns across diverse populations while adjusting for covariates like gender, education, and lifestyle factors. The method improves estimation accuracy and prediction performance over standard approaches, revealing significant associations between dietary patterns and health outcomes in Hispanic/Latino communities.

ABSTRACT

Diet is a risk factor for many diseases. In nutritional epidemiology, studying reproducible dietary patterns is critical to reveal important associations with health. However, it is challenging: diverse cultural and ethnic backgrounds may critically impact eating patterns, showing heterogeneity, leading to incorrect dietary patterns and obscuring the components shared across different groups or populations. Moreover, covariate effects generated from observed variables, such as demographics and other confounders, can further bias these dietary patterns. Identifying the shared and group-specific dietary components and covariate effects is essential to drive accurate conclusions. To address these issues, we introduce a new modeling factor regression, the Multi-Study Factor Regression (MSFR) model. The MSFR model analyzes different populations simultaneously, achieving three goals: capturing shared component(s) across populations, identifying group-specific structures, and correcting for covariate effects. We use this novel method to derive common and ethnic-specific dietary patterns in a multi-center epidemiological study in Hispanic/Latinos community. Our model improves the accuracy of common and group dietary signals and yields better prediction than other techniques, revealing significant associations with health. In summary, we provide a tool to integrate different groups, giving accurate dietary signals crucial to inform public health policy.

Motivation & Objective

• To address the challenge of identifying reproducible dietary patterns across diverse ethnic and cultural groups in nutritional epidemiology.
• To correct for confounding effects of demographic and lifestyle variables that obscure true dietary signals in heterogeneous populations.
• To develop a unified statistical framework that jointly models common and study-specific dietary components across multiple studies.
• To improve the accuracy of dietary pattern estimation and prediction compared to existing factor analysis methods.
• To enable robust, interpretable, and policy-relevant insights into diet-disease associations in multi-ethnic populations.

Proposed method

• The MSFR model integrates Multi-Study Factor Analysis (MSFA) with latent factor regression to jointly model common and study-specific factors across multiple populations.
• It uses an efficient ECM algorithm with closed-form updates for deterministic estimation, enabling scalable computation.
• Covariate effects (e.g., gender, education, smoking, alcohol, BMI) are explicitly modeled and adjusted for in the factor structure.
• The model estimates both shared (common) and group-specific loading matrices and latent factors simultaneously.
• Factor cardinality is robustly estimated, reducing overfitting compared to unadjusted models.
• The method is publicly available via GitHub, supporting reproducibility and broader adoption.

Figure 1: Heatmap of the common (left panel) and study-specific (right panel) factor loadings in the HCHS/SOL.

Experimental results

Research questions

• RQ1 How can we jointly identify common and ethnic-specific dietary patterns across diverse Latino subgroups while adjusting for key confounders?
• RQ2 To what extent does covariate adjustment improve the accuracy and interpretability of dietary pattern estimation in multi-center studies?
• RQ3 How does the MSFR model compare to standard factor analysis and multi-study factor analysis in terms of prediction performance and factor estimation?
• RQ4 Which dietary patterns are most strongly associated with the Alternative Healthy Eating Index (AHEI-2010) in the Hispanic Community Health Study/Study of Latinos (HCHS/SOL)?
• RQ5 Can the MSFR model detect meaningful, interpretable dietary patterns that are both globally shared and locally specific across different Latino ethnic backgrounds?

Key findings

• The MSFR model significantly improved prediction accuracy and estimation robustness compared to MSFA and standard factor regression, especially under strong covariate effects.
• The common dietary patterns showed that plant-based and seafood patterns increased the AHEI-2010 score, while animal products and dairy products decreased it.
• The animal products pattern had a strong negative association with AHEI-2010, decreasing it from 49.7 (first quantile) to 45.2 (fifth quantile).
• The dairy products pattern slightly decreased AHEI-2010, from 48.1 (first quantile) to 46.7 (fifth quantile).
• Study-specific patterns revealed distinct associations: the Dominican pattern increased AHEI-2010 from 51.2 (first quantile) to 46.4 (third quantile), while the Cuban pattern slightly decreased it from 44.7 to 43.5.
• Standard errors for study-specific factors were very low, indicating high precision in estimation.

Figure 2: Association of each factor with each food group for each common factor (first box) and each study-specific factor (second box).