Bayesian probability

Feature selection

Mathematics

Biology

Support vector machine

Data mining

Statistics

Machine learning

Kernel method

Paleontology

Probit

Artificial intelligence

Programming language

Environmental epidemiology

Software

Context (archaeology)

Computer science

Kriging

Probit model

Medicine

Environmental health

Environmental Health

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.

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