Incorporating Historical Data When Determining Sample Size Requirements for Aquatic Toxicity Experiments

In aquatic toxicity tests, responses of interest from organisms exposed to varying concentration levels of the toxicant or other adverse treatment are recorded. These responses are modeled as functions of the concentration and the concentration associated with specified levels of estimated adverse effect are used in risk management. While aquatic toxicity analyses often focus on outcomes from a single experiment, laboratories commonly have a history of conducting such experiments using the same species, following a similar experimental protocol. So it is often reasonable to believe that the same underlying biological process generates the historical and current experiments. This connection may facilitate the design of more efficient experiments. In the present study, we propose a simulation-based Bayesian sample size determination approach using historical control outcomes as prior input and illustrate it using a C. dubia reproduction experiment with count outcomes. Simulation results show that precision of the potency estimates is improved via incorporation of historical data. For a standard EPA required test of 60 total organisms, when a single historical control study is incorporated assuming moderate relevance, the mean length (AL) of the $$95\%$$ 95 % interval of $$\mathrm{RI}_{25}$$ RI 25 (the concentration associated with $$25\%$$ 25 % inhibition relative to control) is reduced by $$17\%$$ 17 % . So more precision is possible from the historical control data or a reduction of $$40\%$$ 40 % of the 60 organism would result in the same precision for a pre-specified AL criterion. The incorporation of multiple historical controls assuming moderate relevance would reduce AL by $$37\%$$ 37 % , translating into a reduction of $$70\%$$ 70 % of the current default sample size. Supplementary materials accompanying this paper appear online.