Abstract
BackgroundEstimating 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.MethodsThis 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.ResultsApplying 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.ConclusionsThis 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.
Highlights
Estimating the health effects of multi-pollutant mixtures is of increasing interest in environmental epidemiology
Through simulation studies based on real-world datasets, we found that (i) Bayesian kernel machine regression (BKMR) could well estimate exposure-response functions that included both nonlinear and non-additive effects, (ii) BKMR could identify important mixture components through variable selection, and (iii) the hierarchical variable selection approach could detect important groups of highly correlated exposures even in situations where individual components could not be identified
We have found that when conducting BKMR with variable selection, the magnitudes of the posterior inclusion probabilities can be sensitive to the choice of the prior distribution on the rm parameters [15]
Summary
Estimating the health effects of multi-pollutant mixtures is of increasing interest in environmental epidemiology. Several statistical methods have been proposed for estimating the health effects of multiple exposures, including machine learning methods such as random forests [6]; clustering methods and other dimensional reduction methods such as principal components analysis, factor analysis, and structural equation models; and regression penalization methods such as the lasso [7]. These methods have typically addressed some but not all of the challenges and/ or scientific objectives described above. Reviews of prior methods and their limitations, as well as systematic comparisons of the performance of selected methods, have been published previously [1, 8,9,10,11,12]
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