Statistical analysis of no observed effect concentrations or levels in eco-toxicological assays with overdispersed count endpoints

In (eco-)toxicological hazard characterization, the No Observed Adverse Effect Concentration or Level (NOAEC or NOAEL) approach is used and often required despite of its known limitations. For count data, statistical testing can be challenging, due to several confounding factors, such as zero inflation, low observation numbers, variance heterogeneity, over- or under-dispersion when applying the Poisson model or hierarchical experimental designs. As several tests are available for count data, we selected sixteen tests suitable for overdispersed counts and compared them in a simulation study. We assessed their performance considering data sets containing mixing distribution and over-dispersion with different observation numbers. It shows that there is no uniformly best approach because the assumed data conditions and assumptions are very different. However, the Dunnett-type procedure based on most likely transformation can be recommended, because of its size and power behavior, which is relatively better over most data conditions as compared to the available alternative test methods, and because it allows flexible modeling and effect sizes can be estimated by confidence intervals. Related R-code is provided for real data examples.