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 \(95\%\) interval of \(\mathrm{RI}_{25}\) (the concentration associated with \(25\%\) inhibition relative to control) is reduced by \(17\%\). So more precision is possible from the historical control data or a reduction of \(40\%\) 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 \(37\%\), translating into a reduction of \(70\%\) of the current default sample size.

Supplementary materials accompanying this paper appear online.

在水生毒性试验中，记录了暴露于不同浓度水平的毒物或其他不利处理的生物体的感兴趣反应。这些响应被建模为浓度的函数，并且与特定水平的估计不利影响相关的浓度用于风险管理。虽然水生毒性分析通常侧重于单个实验的结果，但实验室通常有使用相同物种进行此类实验的历史，遵循类似的实验方案。因此，相信相同的潜在生物学过程产生了历史和当前的实验通常是合理的。这种联系可能有助于设计更有效的实验。在目前的研究中，C. dubia繁殖实验与计数结果。模拟结果表明，通过结合历史数据可以提高效力估计的精度。对于标准 EPA 要求对 60 个总生物体进行测试，当假设中等相关性并入单个历史对照研究时，\ (\mathrm{RI}_{25 }\) （与对照相关的\(25\%\)抑制相关的浓度）减少了\(17\%\)。因此可以从历史控制数据中获得更高的精度或减少\(40\%\)对于预先指定的 AL 标准，60 种生物体中的 60 种生物体将产生相同的精度。假设中等相关性，并入多个历史控制将使 AL 减少\(37\%\)，转化为当前默认样本量的\(70\%\)减少。

本文随附的补充材料出现在网上。