Bayesian kernel machine regression for estimating the health effects of multi-pollutant mixtures

Biostatistics. 2015 Jul;16(3):493-508. doi: 10.1093/biostatistics/kxu058. Epub 2014 Dec 22.


Because humans are invariably exposed to complex chemical mixtures, estimating the health effects of multi-pollutant exposures is of critical concern in environmental epidemiology, and to regulatory agencies such as the U.S. Environmental Protection Agency. However, most health effects studies focus on single agents or consider simple two-way interaction models, in part because we lack the statistical methodology to more realistically capture the complexity of mixed exposures. We introduce Bayesian kernel machine regression (BKMR) as a new approach to study mixtures, in which the health outcome is regressed on a flexible function of the mixture (e.g. air pollution or toxic waste) components that is specified using a kernel function. In high-dimensional settings, a novel hierarchical variable selection approach is incorporated to identify important mixture components and account for the correlated structure of the mixture. Simulation studies demonstrate the success of BKMR in estimating the exposure-response function and in identifying the individual components of the mixture responsible for health effects. We demonstrate the features of the method through epidemiology and toxicology applications.

Keywords: Air pollution; Bayesian variable selection; Environmental health; Gaussian process regression; Metal mixtures.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Animals
  • Bangladesh
  • Bayes Theorem*
  • Biostatistics
  • Child, Preschool
  • Developmental Disabilities / etiology
  • Dogs
  • Environmental Health / statistics & numerical data
  • Environmental Pollutants / adverse effects*
  • Female
  • Hemodynamics / drug effects
  • Humans
  • Infant
  • Machine Learning
  • Metals / adverse effects
  • Models, Statistical
  • Neurodevelopmental Disorders / etiology
  • Normal Distribution
  • Pregnancy
  • Regression Analysis


  • Environmental Pollutants
  • Metals