Modeling Spatial Heterogeneity in Exposure Buffers and Risk: A Hierarchical Bayesian Approach

Abstract

Place-based epidemiology studies often rely on circular buffers to define ``exposure'' to spatially distributed risk factors, where the buffer radius represents a threshold beyond which exposure does not influence the outcome of interest. This approach is popular due to its simplicity and alignment with public health policies. However, buffer radii are often chosen relatively arbitrarily and assumed constant across the spatial domain. This may result in suboptimal statistical inference if these modeling choices are incorrect. To address this, we develop SVBR (Spatially-Varying Buffer Radii), a flexible hierarchical Bayesian spatial change points approach that treats buffer radii as unknown parameters and allows both radii and exposure effects to vary spatially. Through simulations, we find that SVBR improves estimation and inference for key model parameters compared to traditional methods. We also apply SVBR to study healthcare access in Madagascar, finding that proximity to healthcare facilities generally increases antenatal care usage, with clear spatial variation in this relationship. By relaxing rigid assumptions about buffer characteristics, our method offers a flexible, data-driven approach to accurately defining exposure and quantifying its impact. The newly developed methods are available in the R package EpiBuffer.

Figures (3)

• Figure 1: Map of Madagascar, with the study area, Toliara Province highlighted (Panel A), and map of the study area showing health facility locations (red circles) and cluster locations (squares), where cluster sample size is indicated by the size of the square and proportion of the sample that completed $\ge 4$ ANC visits is indicated by the color of the square (Panels B and C). Urban and rural designated clusters are plotted separately (Panel B, Urban; Panel C, Rural).
• Figure 2: Results from the Madagascar (Toliara Province) antenatal care case study for the counts exposure definition. Posterior median radii estimates (transparent circles) are presented for each competing model ((A) SVBR$\left[5, \theta\right]$, (B) SVBR$\left[\delta, \theta\right]$, (C) SVBR$\left[\delta\left(\textbf{s}_j\right), \theta\right]$, (D) SVBR$\left[\delta\left(\textbf{s}_j\right), \theta\left(\textbf{s}_j\right)\right]$). Clusters where the $95\%$ highest posterior density interval for $\text{z}\{\textbf{s}_j; \delta(\textbf{s}_j)\} \theta(\textbf{s}_j)$ includes $0$ are indicated with grey shading while clusters whose interval does not include $0$ are shaded based on the corresponding posterior median. Health facility locations are identified with solid red points.
• Figure 3: Distance buffer polygons mapping the cluster-level posterior median radius on walking road/path networks, where health facility exposure is defined as counts of facilities within distance $\delta(\textbf{s}_j)$. Buffers are colored based on the posterior median estimate of $\text{z}\{\textbf{s}_j; \delta(\textbf{s}_j)\}\theta$ obtained from applying SVBR$\left[\delta\left(\textbf{s}_j\right), \theta\right]$ to the Madagascar (Toliara Province) case study data. The map shows a subset of the larger study region for improved visibility.