Bayesian approach to estimating reproductive inhibition potency in aquatic toxicity testing

Effectively and accurately assessing the toxicity of chemicals and their impact on the environment continues to be an important concern in ecotoxicology. Single experiments conducted by a particular laboratory commonly serve as the basis of toxicity risk assessment. These laboratories often have a long history of conducting experiments using particular protocols. In the present study, a Bayesian analysis for estimating potency based on a single experiment was formulated, which then served as the basis for incorporating the experimental information from historical controls. A Bayesian hierarchical model was developed to estimate the relative inhibition concentrations (RIp) of a toxicant and flexible ways of using historical control information were suggested. The methods were illustrated using a data set produced by the test for reproduction in Ceriodaphnia dubia in which the number of young produced over three broods was recorded. In addition, simulation studies were included to compare the Bayesian methods with previously proposed estimators of potency. The Bayesian methods gave more precise RIp estimates with smaller variation and nominal coverage probability offsetting a small negative bias in the point estimate. Incorporating historical control information in the Bayesian hierarchical model effectively uses the useful information from past similar experiments when estimating the RIp, and results in potency estimates that are more precise compared to frequentist methods.