Lagged kernel machine regression for identifying time windows of susceptibility to exposures of complex mixtures

Shelley H. Liu, Jennifer F. Bobb, Kyu Ha Lee, Chris Gennings, Birgit Claus Henn, David Bellinger, Christine Austin, Lourdes Schnaas, Martha M. Tellez-Rojo, Howard Hu, Robert O. Wright, Manish Arora, Brent A. Coull

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


The impact of neurotoxic chemicalmixtures on children's health is a critical public health concern. It is well known that during early life, toxic exposures may impact cognitive function during critical time intervals of increased vulnerability, known as windows of susceptibility. Knowledge on time windows of susceptibility can help inform treatment and prevention strategies, as chemical mixtures may affect a developmental process that is operating at a specific life phase. There are several statistical challenges in estimating the health effects of time-varying exposures to multi-pollutant mixtures, such as: multi-collinearity among the exposures both within time points and across time points, and complex exposureresponse relationships. To address these concerns, we develop a flexible statistical method, called lagged kernel machine regression (LKMR). LKMR identifies critical exposure windows of chemical mixtures, and accounts for complex non-linear and non-additive effects of the mixture at any given exposure window. Specifically, LKMR estimates how the effects of a mixture of exposures change with the exposure time window using a Bayesian formulation of a grouped, fused lasso penalty within a kernel machine regression (KMR) framework. A simulation study demonstrates the performance of LKMR under realistic exposure-response scenarios, and demonstrates large gains over approaches that consider each time window separately, particularly when serial correlation among the time-varying exposures is high. Furthermore, LKMR demonstrates gains over another approach that inputs all time-specific chemical concentrations together into a single KMR. We apply LKMR to estimate associations between neurodevelopment and metal mixtures in Early Life Exposures in Mexico and Neurotoxicology, a prospective cohort study of child health in Mexico City.

Original languageEnglish
Pages (from-to)325-341
Number of pages17
Issue number3
StatePublished - 1 Jul 2018


  • Bayesian analysis
  • Environmental epidemiology
  • Hierarchical models
  • Statistical methods in epidemiology


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