Comparing Methods for Determining Power Priors Based on Different Congruence Measures

Experiments are routinely conducted to evaluate the toxicity of water effluents or chemicals. In a Ceriodaphnia dubia reproduction test, organisms are exposed to varying concentration levels of the toxicant or other adverse treatment and the number of young produced after a given experiment period are recorded. To analyze the test outcomes, mean reproduction is modeled as a function of the concentration, and the estimated concentrations associated with specified levels of adverse effect often are used in risk management. While aquatic toxicity analyses often focus on outcomes from the current test, laboratories commonly have a history of conducting such tests using the same species, following a similar experimental protocol. So it seems reasonable to assume that the same underlying biological process generates the historical and current tests. In the present study, we propose using a calibrated power prior approach to incorporate historical control outcomes as prior input, and compare the behavior of the method when different congruence measures are used to determine the amount of historical input that will be incorporated. Simulation results show that three of the congruence measures can improve precision and reduce bias of the potency estimates.Supplementary material to this paper is provided online.