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 data sets 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 modelling of the effects of copper on salmonids. Using studies compiled to support development of aquatic life guidelines and criteria in Canada and the US, we extracted raw concentration-response data from either the publications or through contact with study authors. Our final data set focused on survival as the endpoint, and included 20 experiments from 6 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 re-fit 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.