Bayesian Nonparametric Causal Inference for High-Dimensional Nutritional Data via Factor-Based Exposure Mapping

TL;DR

Addresses causal effects of high-dimensional dietary data by mapping $p$ nutrients into $J$ latent dietary patterns via a Bayesian factor model and discretizing each pattern to three ordered levels $T_j\in\{0,1,2\}$. It introduces $\text{BCF3L}$, a Bayesian Causal Forest extension for three ordered treatment levels, integrating exposure mapping and generalized propensity scores. In simulations and the HCHS/SOL application, six patterns are identified and show that increasing from low to medium adherence reduces BMI and fasting insulin for several patterns, with effects varying by pattern and outcome; high adherence often yields smaller or non-significant gains. The work provides an open-source R package implementing BCF3L and demonstrates practical impact for causal nutrition policy and personalized dietary guidance.

Abstract

Diet plays a crucial role in health, and understanding the causal effects of dietary patterns is essential for informing public health policy and personalized nutrition strategies. However, causal inference in nutritional epidemiology faces several challenges: (i) high-dimensional and correlated food/nutrient intake data induce massive treatment levels; (ii) nutritional studies are interested in latent dietary patterns rather than single food items; and (iii) the goal is to estimate heterogeneous causal effects of these dietary patterns on health outcomes. We address these challenges by introducing a sophisticated exposure mapping framework that reduces the high-dimensional treatment space via factor analysis and enables the identification of dietary patterns. We also extend the Bayesian Causal Forest to accommodate three ordered levels of dietary exposure, better capturing the complex structure of nutritional data and enabling estimation of heterogeneous causal effects. We evaluate the proposed method through extensive simulations and apply it to a multi-center epidemiological study of Hispanic/Latino adults residing in the US. Using high-dimensional dietary data, we identify six dietary patterns and estimate their causal link with two key health risk factors: body mass index and fasting insulin levels. Our findings suggest that higher consumption of plant lipid-antioxidant, plant-based, animal protein, and dairy product patterns is associated with reduced risk.

Figures (4)

• Figure 1: Bias of the estimated causal effects $\tau_{0,1}$ (medium vs. low) and $\tau_{1,2}$ (high vs. medium) across 50 simulated datasets. Panels (left to right) show: Scenario 1, Scenario 2, and Scenario 3 (factors 1-4). Colors denote methods: BCF3L (green), BLR‑HS (yellow), and BART (blue).
• Figure 2: Root mean squared error (RMSE) of the estimated causal effects $\tau_{0,1}$ (medium vs. low) and $\tau_{1,2}$ (high vs. medium). Panels (left to right) correspond to Scenario 1, Scenario 2, Scenario 3 (factors 1–4). Colors denote methods: BCF3L (green), BLR‑HS (yellow), and BART (blue).
• Figure 3: Varimax-rotated factor loadings for 53 nutrients in HCHS/SOL across the six dietary patterns.
• Figure 4: Posterior means and 90% credible intervals of the causal effects of the six identified dietary patterns on body mass index (BMI) and fasting insulin levels: $\tau_{0,1}$ (medium vs. low) and $\tau_{1,2}$ (high vs. medium). Estimates obtained from BCF3L adjusting for the covariates in Section \ref{['sub:HCHS']}

Theorems & Definitions (5)

• Definition 1: Exposure mapping characteristics
• Definition 2: Potential outcome under exposure mapping
• Corollary 1: Strong ignorability under exposure mapping
• proof
• Definition 3: Causal estimands: CATEs and FS-CATEs