A Note on Comparing Several Poisson Means

Application of the Closure Principle Computational Approach Test to Assess Ecotoxicological Field Studies: Comparative Analysis Using Earthworm Field Test Abundance Data

Field studies to determine the effects of chemicals on earthworm communities are generally conducted according to International Organization for Standardization standard 11268-3 (and later comments). However, statistical test procedures suggested in the guideline are frequently criticized, mainly for 2 reasons: 1) Earthworm abundances are count data and often do not fulfill requirements for multiple t tests (normal distribution and homogeneity of variance), and 2) the resulting toxicity metrics of multiple testing procedures (no/lowest-observed-effect concentrations [NOEC/LOEC]) fail to adequately detect the actual level of effects. Recently, a new method to overcome these shortcomings was presented by the introduction of the closure principle computational approach test (CPCAT). We applied this statistical method to assess chemical effects on abundance in a large dataset of 26 earthworm field studies (with up to 3 test chemical application rates) and an additional extended study with 6 application rates. A comparative analysis was provided considering results of well-established multiple testing approaches (Dunnett's test) with particular consideration of the degree of overdispersion found in these data. It was shown that the CPCAT detects substantially more effects in earthworm field tests as statistically significant than standard t test approaches. This lowered the LOEC/NOEC for many chemical treatments to control comparisons. As a consequence, the statistically detected NOECs/LOECs were often set at lower percentage deviations between control and chemical treatment. This is the first time the performance of the CPCAT has been assessed within a comprehensive analysis of earthworm field study data. Environ Toxicol Chem 2021;40:1750-1760. © 2021 The Authors. Environmental Toxicology and Chemistry published by Wiley Periodicals LLC on behalf of SETAC.

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.