Species reproduction is an important determinant of population dynamics. As such, this is an important parameter in environmental risk assessment. The closure principle computational approach test (CPCAT) was recently proposed as a method to derive a NOEC/LOEC for reproduction count data such as the number of juvenile Daphnia. The Poisson distribution used by CPCAT can be too restrictive as a model of the data-generating process. In practice, the generalized Poisson distribution could be more appropriate, as it allows for inequality of the population mean \(\mu\) and the population variance \(\sigma ^2\). It is of fundamental interest to explore the statistical power of CPCAT and the probability of determining a regulatory relevant effect correctly. Using a simulation, we varied between Poisson distribution (\(\mu =\sigma ^2\)) and generalized Poisson distribution allowing for over-dispersion (\(\mu <\sigma ^2\)) and under-dispersion (\(\mu >\sigma ^2\)). The results indicated that the probability of detecting the LOEC/NOEC correctly was \(\ge 0.8\) provided the effect was at least 20% above or below the mean level of the control group and mean reproduction of the control was at least 50 individuals while over-dispersion was missing. Specifically, under-dispersion increased, whereas over-dispersion reduced the statistical power of the CPCAT. Using the well-known Hampel identifier, we propose a simple and straight forward method to assess whether the data-generating process of real data could be over- or under-dispersed.

中文翻译：

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CPCAT作为克服NOEC / LOEC统计在生态毒理学方面的缺点的新颖工具：评估统计能力的模拟研究。

物种繁殖是种群动态的重要决定因素。因此，这是环境风险评估中的重要参数。最近提出了封闭原理计算方法测试（CPCAT）作为导出NOEC / LOEC的方法，以用于繁殖计数数据（例如幼水蚤的数量）。CPCAT使用的泊松分布作为数据生成过程的模型可能过于严格。实际上，广义泊松分布可能更合适，因为它允许总体均值\（\ mu \）和总体方差\（\ sigma ^ 2 \）不等式。探索CPCAT的统计能力以及正确确定监管相关效果的可能性具有根本意义。使用模拟，我们在泊松分布（\（\ mu = \ sigma ^ 2 \））和广义泊松分布之间进行了变化，从而允许过度分散（\（\ mu <\ sigma ^ 2 \））和欠分散（\ （\ mu> \ sigma ^ 2 \））。结果表明正确检测到LOEC / NOEC的概率为\（\ ge 0.8 \）前提是效果高于或低于对照组平均水平至少20％，并且对照组的平均繁殖量至少为50个个体，而没有过度分散。具体来说，分散不足会增加，而分散过度会降低CPCAT的统计能力。使用众所周知的Hampel标识符，我们提出了一种简单而直接的方法来评估实际数据的数据生成过程是过度分散还是分散。