The CPCAT as a novel tool to overcome the shortcomings of NOEC/LOEC statistics in ecotoxicology: a simulation study to evaluate the statistical power

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 μ and the population variance σ 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 ( μ = σ 2 ) and generalized Poisson distribution allowing for over-dispersion ( μ < σ 2 ) and under-dispersion ( μ > σ 2 ). The results indicated that the probability of detecting the LOEC/NOEC correctly was ≥ 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.