Bayesian approach to potency estimation for aquatic toxicology experiments when a toxicant affects both fecundity and survival



Chemicals in aquatic systems may impact a variety of endpoints including mortality, growth, or reproduction. Clearly, growth or reproduction will only be observed in organisms that survive. Because it is common to observe mortality in studies focusing on the reproduction of organisms, especially in higher concentration conditions, the resulting observed numbers of young become a mixture of zeroes and positive counts. Zeroes are recorded for organisms that die before having any young and living organisms with no offspring. Positive counts are recorded for living organisms with offspring. Thus, responses reflect both fecundity and mortality of the organisms used in such tests. In the present study, the authors propose the estimation of the concentration associated with a specified level of reproductive inhibition (RIp) using a Bayesian zero-inflated Poisson (ZIP) regression model. This approach allows any prior information and expert knowledge about the model parameters to be incorporated into the regression coefficients or RIp estimation. Simulation studies are conducted to compare the Bayesian ZIP regression model and classical methods. The Bayesian estimator outperforms the frequentist alternative by producing more precise point estimates with smaller mean square differences between RIp estimates and true values, narrower interval estimates with better coverage probabilities. The authors also applied their proposed model to a study of Ceriodaphnia dubia exposed to a test toxicant. Environ. Toxicol. Chem. 2012; 31: 1920–1930. © 2012 SETAC