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September 2021 Bayesian joint modeling of chemical structure and dose response curves
Kelly R. Moran, David Dunson, Matthew W. Wheeler, Amy H. Herring
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Ann. Appl. Stat. 15(3): 1405-1430 (September 2021). DOI: 10.1214/21-AOAS1461


Today there are approximately 85,000 chemicals regulated under the Toxic Substances Control Act, with around 2,000 new chemicals introduced each year. It is impossible to screen all of these chemicals for potential toxic effects, either via full organism in vivo studies or in vitro high-throughput screening (HTS) programs. Toxicologists face the challenge of choosing which chemicals to screen, and predicting the toxicity of as yet unscreened chemicals. Our goal is to describe how variation in chemical structure relates to variation in toxicological response to enable in silico toxicity characterization designed to meet both of these challenges. With our Bayesian partially Supervised Sparse and Smooth Factor Analysis (BS3FA) model, we learn a distance between chemicals targeted to toxicity, rather than one based on molecular structure alone. Our model also enables the prediction of chemical dose-response profiles based on chemical structure (i.e., without in vivo or in vitro testing) by taking advantage of a large database of chemicals that have already been tested for toxicity in HTS programs. We show superior simulation performance in distance learning and modest to large gains in predictive ability compared to existing methods. Results from the high-throughput screening data application elucidate the relationship between chemical structure and a toxicity-relevant high-throughput assay. An R package for BS3FA is available online at

Funding Statement

This work was partially supported by the National Institute of Environmental Health Sciences of the United States National Institutes of Health (grants 1R01ES028804-01 and 5R01ES027498-02, and intramural funds) and the Department of Energy Computational Science Graduate Fellowship (grant DE-FG02-97ER25308). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.


The authors would like to thank Evan Poworoznek and Bora Jin for helpful comments.


Download Citation

Kelly R. Moran. David Dunson. Matthew W. Wheeler. Amy H. Herring. "Bayesian joint modeling of chemical structure and dose response curves." Ann. Appl. Stat. 15 (3) 1405 - 1430, September 2021.


Received: 1 December 2019; Revised: 1 March 2021; Published: September 2021
First available in Project Euclid: 23 September 2021

Digital Object Identifier: 10.1214/21-AOAS1461

Keywords: Dimension reduction , distance learning , functional prediction , high-throughput screening , QSAR , ToxCast , toxicity

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.15 • No. 3 • September 2021
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