Statistical software for analyzing the health effects of multiple concurrent exposures via Bayesian kernel machine regression

TLDR

Estimating health effects of multi‑pollutant mixtures is increasingly important, and while Bayesian kernel machine regression (BKMR) offers a flexible approach, its adoption has been hampered by limited software, lack of efficient interpretable outputs, and difficulty handling non‑continuous outcomes. The study introduces the open‑source bkmr R package, demonstrates visualization and summary methods for high‑dimensional exposure‑response functions, implements a probit regression for binary outcomes, and presents a fast Gaussian predictive process version of BKMR. BKMR flexibly estimates multivariable exposure‑response functions, performs variable selection—including grouped selection for correlated exposures—and the authors provide reproducible R code illustrating these methods. In demonstration studies, the bkmr package accurately estimated complex nonlinear mixture effects, the Gaussian predictive process version cut runtime substantially with minimal loss of precision, the probit BKMR correctly identified relevant variables and produced interpretable latent‑continuous or probability‑scale estimates, thereby extending BKMR’s accessibility to diverse epidemiologic analyses.

Abstract

Estimating the health effects of multi-pollutant mixtures is of increasing interest in environmental epidemiology. Recently, a new approach for estimating the health effects of mixtures, Bayesian kernel machine regression (BKMR), has been developed. This method estimates the multivariable exposure-response function in a flexible and parsimonious way, conducts variable selection on the (potentially high-dimensional) vector of exposures, and allows for a grouped variable selection approach that can accommodate highly correlated exposures. However, the application of this novel method has been limited by a lack of available software, the need to derive interpretable output in a computationally efficient manner, and the inability to apply the method to non-continuous outcome variables. This paper addresses these limitations by (i) introducing an open-source software package in the R programming language, the bkmr R package, (ii) demonstrating methods for visualizing high-dimensional exposure-response functions, and for estimating scientifically relevant summaries, (iii) illustrating a probit regression implementation of BKMR for binary outcomes, and (iv) describing a fast version of BKMR that utilizes a Gaussian predictive process approach. All of the methods are illustrated using fully reproducible examples with the provided R code. Applying the methods to a continuous outcome example illustrated the ability of the BKMR implementation to estimate the health effects of multi-pollutant mixtures in the context of a highly nonlinear, biologically-based dose-response function, and to estimate overall, single-exposure, and interactive health effects. The Gaussian predictive process method led to a substantial reduction in the runtime, without a major decrease in accuracy. In the setting of a larger number of exposures and a dichotomous outcome, the probit BKMR implementation was able to correctly identify the variables included in the exposure-response function and yielded interpretable quantities on the scale of a latent continuous outcome or on the scale of the outcome probability. This newly developed software, integrated suite of tools, and extended methodology makes BKMR accessible for use across a broad range of epidemiological applications in which multiple risk factors have complex effects on health.