How to account for the uncertainty from standard toxicity tests in species sensitivity distributions: An example in non-target plants

This research proposes new perspectives accounting for the uncertainty on 50% effective rates (ER(50)) as interval input for species sensitivity distribution (SSD) analyses and evaluating how to include this uncertainty may influence the 5% Hazard Rate (HR(5)) estimation. We explored various endpoints (survival, emergence, shoot-dry-weight) for non-target plants from seven standard greenhouse studies that used different experimental approaches (vegetative vigour vs. seedling emergence) and applied seven herbicides at different growth stages. Firstly, for each endpoint of each study, a three-parameter log-logistic model was fitted to experimental toxicity test data for each species under a Bayesian framework to get a posterior probability distribution for ER(50). Then, in order to account for the uncertainty on the ER(50), we explored two censoring criteria to automatically censor ER(50) taking the ER(50) probability distribution and the range of tested rates into account. Secondly, based on dose-response fitting results and censoring criteria, we considered input ER(50) values for SSD analyses in three ways (only point estimates chosen as ER(50) medians, interval-censored ER(50) based on their 95% credible interval and censored ER(50) according to one of the two criteria), by fitting a log-normal distribution under a frequentist framework to get the three corresponding HR(5) estimates. We observed that SSD fitted reasonably well when there were at least six distinct intervals for the ER(50) values. By comparing the three SSD curves and the three HR(5) estimates, we shed new light on the fact that both propagating the uncertainty from the ER(50) estimates and including censored data into SSD analyses often leads to smaller point estimates of HR(5), which is more conservative in a risk assessment context. In addition, we recommend not to focus solely on the point estimate of the HR(5), but also to look at the precision of this estimate as depicted by its 95% confidence interval.