Multilevel modeling of concentration-response data can improve risk assessment: a case study of copper effects on fish.

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.