The data BKMRfits10 is simulated data with 10
BKMRfits, each is a BKMR fit using multiple imputed data with size \(n = 500\).
This code assumes you have \(K\) BKMR fits and that each of these fits were ran for the same number if MCMC iterations.
All effects are calculated as the average change in the outcome for a change in the exposure elements from a particular quantile to another quantile calculated across ALL imputed datasets. If there are no missing values in the Z matrix (in the mixture exposure), this is same contrast considered when only using the observed Z.
All functions have the option to choose between an “approx” or “exact” method. The “exact” method combines the posterior samples from all MI fits and uses this posterior chain of length iterations times MI datasets for inference. The “approx” method uses the bkmr approx estimates and std errors from each MI fit and calculates an overall estimate and sd using Rubin’s 1987 method. (When using the “exact” method, the functions take a while to run, so make sure you save the data frames to be used for plotting).
This code can also be used with only 1 BKMR fit. The additional
flexibility with this code over what is included in the
bkmr package is that you have the option to fix specified
variables to a given quantile when creating overall risk and single
variable risk plots.
Bauer, Julia A., Katrina L. Devick, Jennifer F. Bobb, Brent A. Coull, David Bellinger, Chiara Benedetti, Giuseppa Cagna et al. “Associations of a metal mixture measured in multiple biomarkers with IQ: evidence from Italian adolescents living near ferroalloy industry.” Environmental health perspectives 128, no. 9 (2020): 097002.
Anglen Bauer J, Devick KL, Bobb JF, Coull BA, Zoni S, Fedrighi C, Benedetti C, Guazzetti S, White R, Bellinger D, Yang Q, Webster T, Wright RO, Smith D, Lucchini R, Claus Henn. Associations from a mixture of manganese, lead, copper and chromium and adolescent neurobehavior.
Bobb JF, Claus Henn B, Valeri L, Coull BA. 2018. Statistical software for analyzing the health effects of multiple concurrent exposures via Bayesian kernel machine regression. Environ Health 17:67; doi:10.1186/s12940-018-0413-y.
Bobb JF, Valeri L, Claus Henn B, Christiani DC, Wright RO, Mazumdar M, et al. 2015. Bayesian kernel machine regression for estimating the health effects of multi-pollutant mixtures. Biostatistics 16:493–508; doi:10.1093/biostatistics/kxu058.
Rubin DB. 1987. Multiple imputation for nonresponse in surveys. Wiley.
Valeri L, Mazumdar M, Bobb J, Claus Henn B, Sharif O, Al. E. 2017. The joint effect of prenatal exposure to metal mixtures on neurodevelopmental outcomes at 24 months: evidence from rural Bangladesh. Env Heal Perspect 125; doi:DOI: 10.1289/EHP614.