{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T16:55:58Z","timestamp":1781542558912,"version":"3.54.5"},"reference-count":41,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T00:00:00Z","timestamp":1759708800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"name":"Government of British Columbia"},{"name":"Azimuth Consulting Group Inc."}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,5,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Ecological risk assessors can use concentration-response models to estimate the expected biological effect corresponding to a particular concentration or dose of a chemical or to derive a site-specific concentration or benchmark dose corresponding to a specific magnitude of effect. For toxicologists, fitting concentration-response relationships to data for individual experiments is routine work. For risk assessors, however, a focus on single experiments is usually inappropriate because of the desire to characterize risks accurately and to fully account for uncertainties. Use of a single experiment while excluding other good-quality experiments can result in estimates that do not accurately represent all available information. For a risk assessment, the full range of possible concentration-response relationships that reflect variation among experiments is relevant. For datasets comprising multiple concentration-response experiments, mixed-effects, or hierarchical models, collectively referred to herein as multilevel models, are suitable because they simultaneously fit a global mean relationship while accounting for variability among subsets of the data. Here, we demonstrate a case study of multilevel concentration-response modeling of the effects of copper on salmonids. Using studies compiled to support development of aquatic life guidelines and criteria in Canada and the United States, we extracted raw concentration-response data from either the publications or through contact with study authors. Our final dataset focused on survival as the endpoint and included 20 experiments from six studies. We fit several generalized linear mixed-effect models, allowing for varying intercepts or slopes among studies and experiments. Once a preferred random-effects structure was identified, we then incorporated known toxicity modifying factors of copper as covariates and identified a preferred final model. Last, to more fully account for uncertainties, we refit the preferred model in a Bayesian framework. The magnitude of random variation among studies and experiments was considerable, highlighting the potential pitfalls of estimating risks based on single experiments.<\/jats:p>","DOI":"10.1093\/inteam\/vjaf138","type":"journal-article","created":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T13:25:27Z","timestamp":1759757127000},"page":"717-726","source":"Crossref","is-referenced-by-count":1,"title":["Multilevel modeling of concentration-response data can improve risk assessment: a case study of copper effects on fish"],"prefix":"10.1093","volume":"22","author":[{"given":"Ryan","family":"Hill","sequence":"first","affiliation":[{"name":"Azimuth Consulting Group Inc , Vancouver,","place":["Canada"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Brian","family":"Pyper","sequence":"additional","affiliation":[{"name":"Azimuth Consulting Group Inc , Vancouver,","place":["Canada"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sean","family":"Engelking","sequence":"additional","affiliation":[{"name":"Azimuth Consulting Group Inc , Vancouver,","place":["Canada"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,10,6]]},"reference":[{"key":"2026061512340435000_vjaf138-B1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v067.i01","article-title":"Fitting linear mixed-effects models using lme4","volume":"67","author":"Bates","year":"2015","journal-title":"Journal of Statistical Software"},{"key":"2026061512340435000_vjaf138-B2","author":"British Columbia Ministry of Environment and Climate Change Strategy (BC ENV)","year":"2019"},{"key":"2026061512340435000_vjaf138-B3","volume-title":"Early life-stage toxicity of copper to engendered and surrogate fish species","author":"Besser","year":"2001"},{"key":"2026061512340435000_vjaf138-B4","doi-asserted-by":"publisher","first-page":"1657","DOI":"10.1897\/06-571R.1","article-title":"Sensitivity of mottled sculpins (Cottus bairdi) and rainbow trout (Oncorhynchus mykiss) to acute and chronic toxicity of cadmium, copper, and zinc","volume":"26","author":"Besser","year":"2007","journal-title":"Environmental Toxicology and Chemistry"},{"key":"2026061512340435000_vjaf138-B5","doi-asserted-by":"publisher","first-page":"2911","DOI":"10.1002\/etc.5483","article-title":"Adverse outcome pathways for chronic copper toxicity to fish and amphibians","volume":"41","author":"Brix","year":"2022","journal-title":"Environmental Toxicology and Chemistry"},{"key":"2026061512340435000_vjaf138-B6","doi-asserted-by":"publisher","first-page":"1649","DOI":"10.1002\/etc.5012","article-title":"Comparative performance of multiple linear regression and biotic ligand models for estimating the bioavailability of copper in freshwater","volume":"40","author":"Brix","year":"2021","journal-title":"Environmental Toxicology and Chemistry"},{"key":"2026061512340435000_vjaf138-B7","volume-title":"Model Selection and Multimodel Inference: a Practical Information-Theoretic Approach","author":"Burnham","year":"2002"},{"key":"2026061512340435000_vjaf138-B8","author":"Canadian Council of Ministers of the Environment (CCME)","year":"2007"},{"key":"2026061512340435000_vjaf138-B9","author":"Canadian Council of Ministers of the Environment (CCME)","year":"2020"},{"key":"2026061512340435000_vjaf138-B10","volume-title":"Toxicity of copper, cadmium and zinc to Pacific Northwest salmonids. National Environmental Research Center, Office of Research and Development","author":"Chapman","year":"1975"},{"key":"2026061512340435000_vjaf138-B11","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1198\/1085711032291","article-title":"A Bayesian hierarchical model for risk assessment of methylmercury","volume":"8","author":"Coull","year":"2003","journal-title":"Journal of Agricultural, Biological, and Environmental Statistics"},{"key":"2026061512340435000_vjaf138-B12","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1016\/j.aquatox.2017.07.013","article-title":"Experimentally derived acute and chronic copper biotic ligand models for rainbow trout","volume":"192","author":"Cremazy","year":"2017","journal-title":"Aquatic Toxicology"},{"key":"2026061512340435000_vjaf138-B13","author":"Environment and Climate Change Canada (ECCC)","year":"2021"},{"key":"2026061512340435000_vjaf138-B14","volume-title":"Uncertainties in estimating low effect concentrations in aquatic toxicity tests. Conference presentation at the SETAC North America 45th Annual Meeting, 20\u201324 October 2024","author":"Erickson","year":"2024"},{"key":"2026061512340435000_vjaf138-B15","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1002\/env.2339","article-title":"Bayesian benchmark dose analysis","volume":"26","author":"Fang","year":"2015","journal-title":"Environmetrics"},{"key":"2026061512340435000_vjaf138-B16","doi-asserted-by":"publisher","first-page":"2019","DOI":"10.1002\/etc.5610","article-title":"Introducing the no-significant-effect concentration","volume":"42","author":"Fisher","year":"2023","journal-title":"Environmental Toxicology and Chemistry"},{"key":"2026061512340435000_vjaf138-B17","doi-asserted-by":"publisher","first-page":"2141","DOI":"10.1002\/etc.3459","article-title":"Don\u2019t be fooled\u2014a no-observed-effect concentration is no substitute for a poor concentration-response experiment","volume":"35","author":"Fox","year":"2016","journal-title":"Environmental 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