Multilevel Empirical Bayes Modeling for Improved Estimation of Toxicant Formulations to Suppress Parasitic Sea Lamprey in the Upper Great Lakes

• Published in: Biometrics Vol. 67; no. 3; pp. 1153 - 1162
• Main Authors: Hatfield, Laura A., Gutreuter, Steve, Boogaard, Michael A., Carlin, Bradley P.
• Format: Journal Article
• Language: English
• Published: Malden, USA Blackwell Publishing Inc 01.09.2011; Wiley-Blackwell; Blackwell Publishing Ltd
• Subjects: Alkalinity; analysis; Animals; Bayes Theorem; Bayesian analysis; Bayesian networks; BIOMETRIC PRACTICE; Biometrics; Biometry; Biometry - methods; Covariance matrices; Estimating techniques; Great Lakes; Hazardous Substances; Hazardous Substances - analysis; Hazardous Substances - pharmacology; hydrochemistry; Introduced Species; Introduced Species - statistics & numerical data; invasive species; Lakes; Larvae; Lethal concentration/dose; Markov chain Monte Carlo (MCMC); methods; Modeling; Models, Statistical; Multilevel models; Nonlinear model; North America; Parametric models; Parasites; pest control; Pesticides; Pesticides - analysis; Pesticides - toxicity; Petromyzon; Petromyzon marinus; Petromyzontidae; pharmacology; prediction; Quantal-response bioassay; seasonal variation; Seasons; Simulations; statistics; statistics & numerical data; toxic substances; toxicity; Toxicity Tests; North America; Great Lakes
• ISSN: 0006-341X; 1541-0420; 1541-0420
• DOI: 10.1111/j.1541-0420.2011.01566.x

Estimation of extreme quantal‐response statistics, such as the concentration required to kill 99.9% of test subjects (LC99.9), remains a challenge in the presence of multiple covariates and complex study designs. Accurate and precise estimates of the LC99.9 for mixtures of toxicants are critical to ongoing control of a parasitic invasive species, the sea lamprey, in the Laurentian Great Lakes of North America. The toxicity of those chemicals is affected by local and temporal variations in water chemistry, which must be incorporated into the modeling. We develop multilevel empirical Bayes models for data from multiple laboratory studies. Our approach yields more accurate and precise estimation of the LC99.9 compared to alternative models considered. This study demonstrates that properly incorporating hierarchical structure in laboratory data yields better estimates of LC99.9 stream treatment values that are critical to larvae control in the field. In addition, out‐of‐sample prediction of the results of in situ tests reveals the presence of a latent seasonal effect not manifest in the laboratory studies, suggesting avenues for future study and illustrating the importance of dual consideration of both experimental and observational data.