The species sensitivity distribution (SSD) model is firmly embedded in the regulatory arena as a method to derive the so-called ‘predicted no-effect concentration’ for a defined species assemblage exposed to a toxic stressor. The REACH technical guidance document (TGD) (ECHA, Guidance on Information Requirements and Chemical Safety Assessment), states that the log-normal SSD “is a pragmatic choice”, an assumption that has become commonplace in the ecotoxicological risk assessment community. The best way to fit a log-normal SSD for purposes of hazard assessment, on the other hand, is confusing. The sought-after quantity which intermediate (‘Level 2’ within the REACH TGD) risk assessments are based upon is the hazardous concentration to 5% of the defined species assemblage (the HC5). A standard approach is to estimate a median of the HC5 from the sampling distribution. This estimator has well understood statistical properties by construction. However, two alternative estimators - also based on a log-normal SSD - frequent the risk assessment literature. These estimators are constructed by least squares estimation of the ordered logarithmically transformed toxicity data modelled onto the corresponding plotting positions (cf. quantile plots). Standard hypothesis testing and diagnostics of the linear regression are inappropriate without further constraints (cf. generalized least squares). We consider evaluating which estimator, subject to the log-normality assumption, exhibits the best performance. The problem reduces to a fundamental problem of how to measure the performance of an estimator. This can be done by (1) ‘discrepancy’ between the estimator and ‘true’ value, or (2) ‘discrepancy’ between the true potentially affected fraction of species to the intended level. Evaluation of different ‘standard’ criteria (variance, bias, etc.) under the perspective of (1) indicates that the median estimator performs better for all reasonable samples sizes. For (2), the results concur on important scales of discrepancy. However, this performance is highly sensitive to the chosen criterion/scale and sample size. We conclude that the median estimator is preferable and that controversy could be overcome by a risk assessor reporting probabilistic distributions for risk managers in a Bayesian framework in addition to summary statistics; the median estimator is known to be a special case of this
