Send to

Choose Destination
Stat Med. 2019 Apr 30;38(9):1582-1600. doi: 10.1002/sim.8059. Epub 2018 Dec 26.

Selection of nonlinear interactions by a forward stepwise algorithm: Application to identifying environmental chemical mixtures affecting health outcomes.

Author information

Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, Illinois.
Department of Biostatistics, University of Michigan, Ann Arbor, Michigan.
Department of Psychology, University of Michigan, Ann Arbor, Michigan.
Department of Environmental Health Sciences, University of Michigan, Ann Arbor, Michigan.


In this paper, we propose a stepwise forward selection algorithm for detecting the effects of a set of correlated exposures and their interactions on a health outcome of interest when the underlying relationship could potentially be nonlinear. Though the proposed method is very general, our application in this paper remains to be on analysis of multiple pollutants and their interactions. Simultaneous exposure to multiple environmental pollutants could affect human health in a multitude of complex ways. For understanding the health effects of multiple environmental exposures, it is often important to identify and estimate complex interactions among exposures. However, this issue becomes analytically challenging in the presence of potential nonlinearity in the outcome-exposure response surface and a set of correlated exposures. Through simulation studies and analyses of test datasets that were simulated as a part of a data challenge in multipollutant modeling organized by the National Institute of Environmental Health Sciences (, we illustrate the advantages of our proposed method in comparison with existing alternative approaches. A particular strength of our method is that it demonstrates very low false positives across empirical studies. Our method is also used to analyze a dataset that was released from the Health Outcomes and Measurement of the Environment Study as a benchmark beta-tester dataset as a part of the same workshop.


environmental exposures; interaction selection; multipollutant research; nonlinear effects


Supplemental Content

Loading ...
Support Center