A spatial random forest algorithm for population-level epidemiological risk assessment

TL;DR

This work tackles population-level causal inference in areal epidemiology by proposing SPAR-Forest-ERF, a framework that fuses random forests with Bayesian spatial smoothing to learn non-linear confounder–response relationships and estimate interpretable exposure–response functions with full uncertainty quantification. The method iteratively propagates uncertainty between the machine learning and spatial components, introduces an ERF-based stopping criterion, and supports both linear and nonlinear ERFs, including measurement-error adjustments. Simulation studies show substantial improvements in ERF estimation and uncertainty coverage over standard GLMMs when confounding is nonlinear and exposure is spatially structured; a one-iteration simplification underperforms. In the motivating Scotland study, PM$_{2.5}$ and PM$_{10}$ exhibit significant associations with self-rated health, with SPAR-Forest-ERF yielding more precise ERFs and demonstrating the practical utility of the approach for spatial epidemiology and risk assessment.

Abstract

Spatial epidemiology identifies the drivers of elevated population-level disease risks, using disease counts, exposures and known confounders at the areal unit level. Poisson regression models are typically used for inference, which incorporate a linear/additive regression component and allow for unmeasured confounding via a set of spatially autocorrelated random effects. This approach requires the confounder interactions and their functional relationships with disease risk to be specified in advance, rather than being learned from the data. Therefore, this paper proposes the SPAR-Forest-ERF algorithm, which is the first fusion of random forests for capturing non-linear and interacting confounder-response effects with Bayesian spatial autocorrelation models that can estimate interpretable exposure response functions (ERF) with full uncertainty quantification. Methodologically, we extend existing methods set in a prediction context by propagating uncertainty between both the ML and statistical models, developing a new stopping criteria designed to ensure the stability of the primary inferential target, and incorporating a range of different ERFs for maximum model flexibility. This methodology is motivated by a new study quantifying the impact of air pollution concentrations on self-rated health in Scotland, using data from the recently released 2022 national census.

Figures (2)

• Figure 1: Root mean square errors (boxplots and points) for the estimates of the linear ERFs corresponding to the spatially autocorrelated exposure. The top four panels relate to different disease prevalences (rare vs common) and control for confounding (good vs poor), while the bottom panel relates to where all the known confounders have simple linear relationships with disease risk. The numbers relate to the mean RMSE over the 100 simulated data sets.
• Figure 2: Estimates and pointwise 95% credible intervals for the exposure response functions $g[x(\mathcal{S}_k)]$ for PM$_{2.5}$ (left) and PM$_{10}$ (right) for bad (top) and good (bottom) self-rated health from the SPAR-Forest-ERF model. The ERFs are presented as RRs relative to the minimum pollutant concentration observed in the study. The red dashed line at a relative risk of one corresponds to no association.