Bayesian Inference of Chemical Mixtures in Risk Assessment Incorporating the Hierarchical Principle

Kundu, Debamita; Kim, Sungduk; Albert, Paul S.

doi:10.51387/24-NEJSDS58

The New England Journal of Statistics in Data Science

Bayesian Inference of Chemical Mixtures in Risk Assessment Incorporating the Hierarchical Principle

Volume 2, Issue 3 (2024), pp. 284–295

Debamita Kundu Sungduk Kim Paul S. Albert

https://doi.org/10.51387/24-NEJSDS58

Pub. online: 23 February 2024 Type: Biomedical Research

Open Access

Accepted
10 October 2023

Published
23 February 2024

Abstract

Analyzing health effects associated with exposure to environmental chemical mixtures is a challenging problem in epidemiology, toxicology, and exposure science. In particular, when there are a large number of chemicals under consideration it is difficult to estimate the interactive effects without incorporating reasonable prior information. Based on substantive considerations, researchers believe that true interactions between chemicals need to incorporate their corresponding main effects. In this paper, we use this prior knowledge through a shrinkage prior that a priori assumes an interaction term can only occur when the corresponding main effects exist. Our initial development is for logistic regression with linear chemical effects. We extend this formulation to include non-linear exposure effects and to account for exposure subject to detection limit. We develop an MCMC algorithm using a shrinkage prior that shrinks the interaction terms closer to zero as the main effects get closer to zero. We examine the performance of our methodology through simulation studies and illustrate an analysis of chemical interactions in a case-control study in cancer.

References

[1]

Albert, J. H. and Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association 88(422) 669–679. MR1224394

[2]

Bien, J., Taylor, J. and Tibshirani, R. (2013). A lasso for hierarchical interactions. Annals of Statistics 41(3) 1111. https://doi.org/10.1214/13-AOS1096. MR3113805

[3]

Bobb, J. F., Valeri, L., Claus Henn, B., Christiani, D. C., Wright, R. O., Mazumdar, M., Godleski, J. J. and Coull, B. A. (2015). Bayesian kernel machine regression for estimating the health effects of multi-pollutant mixtures. Biostatistics 16(3) 493–508. https://doi.org/10.1093/biostatistics/kxu058. MR3365442

[4]

Carrico, C., Gennings, C., Wheeler, D. C. and Factor-Litvak, P. (2015). Characterization of weighted quantile sum regression for highly correlated data in a risk analysis setting. Journal of Agricultural, Biological, and Environmental Statistics 20(1) 100–120. https://doi.org/10.1007/s13253-014-0180-3. MR3334469

[5]

Casella, G., Ghosh, M., Gill, J. and Kyung, M. (2010). Penalized regression, standard errors, and Bayesian lassos. Bayesian Analysis 5(2) 369–411. https://doi.org/10.1214/10-BA607. MR2719657

[6]

Chiou, S. H., Betensky, R. A. and Balasubramanian, R. (2019). The missing indicator approach for censored covariates subject to limit of detection in logistic regression models. Annals of Epidemiology 38 57–64.

[7]

Chipman, H., Hamada, M. and Wu, C. (1997). A Bayesian variable-selection approach for analyzing designed experiments with complex aliasing. Technometrics 39 372–381.

[8]

Colt, J. S., Lubin, J., Camann, D., Davis, S., Cerhan, J., Severson, R. K., Cozen, W. and Hartge, P. (2004). Comparison of pesticide levels in carpet dust and self-reported pest treatment practices in four US sites. Journal of Exposure Science and Environmental Epidemiology 14(1) 74–83.

[9]

Griffin, J., Brown, P. et al. (2017). Hierarchical shrinkage priors for regression models. Bayesian Analysis 12(1) 135–159. https://doi.org/10.1214/15-BA990. MR3597570

[10]

Helsel, D. R. (1990). Less than obvious-statistical treatment of data below the detection limit. Environmental Science & Technology 24(12) 1766–1774.

[11]

Herring, A. H. (2010). Nonparametric Bayes shrinkage for assessing exposures to mixtures subject to limits of detection. Epidemiology (Cambridge, Mass.) 21(Suppl 4) 71.

[12]

Hwang, B. S., Chen, Z., M. Buck Louis, G. and Albert, P. S. (2019). A Bayesian multi-dimensional couple-based latent risk model with an application to infertility. Biometrics 75(1) 315–325. https://doi.org/10.1111/biom.12972. MR3953732

[13]

Lange, K. L., Little, R. J. and Taylor, J. M. (1989). Robust statistical modeling using the t distribution. Journal of the American Statistical Association 84(408) 881–896. MR1134486

[14]

Liu, C. (2004). Robit regression: a simple robust alternative to logistic and probit regression. In Applied Bayesian Modeling and Casual Inference from Incomplete-Data Perspectives 227–238. https://doi.org/10.1002/0470090456.ch21. MR2138259

[15]

McCullagh, P. and Nelder, J. A. (1989). Generalized linear models (2nd edition). Pp 511. č30. 1989. ISBN 0-412-31760-5 (Chapman and Hall). The Mathematical Gazette 74(469) 320–321. https://doi.org/10.2307/3619865.

[16]

Ortega-Villa, A. M., Liu, D., Ward, M. H. and Albert, P. S. (2021). New insights into modeling exposure measurements below the limit of detection. Environmental Epidemiology 5(1).

[17]

Polson, N. G. and Scott, J. (2010). Shrinkg globally, act locally: Sparse Bayesian regularization and prediction. In Bayesian Statistics (J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West, eds.) 9 501–538. https://doi.org/10.1093/acprof:oso/9780199694587.003.0017. MR3204017

[18]

Scosyrev, E., Messing, J., Noyes, K., Veazie, P. and Messing, E. (2012). Surveillance Epidemiology and End Results (SEER) program and population-based research in urologic oncology: an overview. In Urologic Oncology: Seminars and Original Investigations 30 126–132. Elsevier.

[19]

Stone, C. J. (1986). The dimensionality reduction principle for generalized additive models. The Annals of Statistics 590–606. https://doi.org/10.1214/aos/1176349940. MR0840516

[20]

Zahm, S. H., Ward, M. H. and Blair, A. (1997). Pesticides and cancer. Occupational Medicine (Philadelphia, PA) 12(2) 269–289.

[21]

Zhang, B., Chen, Z. and Albert, P. S. (2012). Latent class models for joint analysis of disease prevalence and high-dimensional semicontinuous biomarker data. Biostatistics 13(1) 74–88.

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Keywords

Chemical mixture Interaction Shrinkage Collapsed Gibbs

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