Unveiling population heterogeneity in health risks posed by environmental hazards using regression-guided neural network.

As environmental hazards become more frequent, it is critically important to understand their health impacts and identify individuals at disproportionately higher risk. Moderated Multiple Regression (MMR) provides a straightforward approach for investigating population heterogeneity by incorporating interaction terms between hazard exposure and population characteristics into a regression model. However, when vulnerabilities are embedded within complex, high-dimensional covariate spaces, MMR often fails to adequately model complex population heterogeneity. Here, we introduce a hybrid method, Regression-Guided Neural Networks (ReGNN), which integrates the flexibility of artificial neural networks (ANNs) within the structural form of a regression model. Briefly, ReGNN embeds an ANN inside a regression equation to generate a latent representation that nonlinearly combines potential sources of heterogeneity and moderates the effect of an environmental hazard. Because the outer layer maintains a regression structure, it delivers statistically robust inference while preserving traditional interpretability if augmented with Double Machine Learning (DML)-style residualization and cross-fitting. Through extensive simulation studies, we demonstrate ReGNN's effectiveness in modeling complex heterogeneous effects. We further illustrate its utility by applying it to investigate population heterogeneity in the association of air pollution (PM2.5) with cognitive functioning scores. By comparing ReGNN's results with those from traditional MMR models, we show that ReGNN can uncover patterns of heterogeneity that would otherwise remain hidden.