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

This research aims to account for the uncertainty on 50% effective rates (ER50) in species sensitivity distribution (SSD) analyses and to study how including this uncertainty may influence the 5% Hazard Rate (HR5) 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 ER50. Then in order to account for the uncertainty on the ER50, we explored two censoring criteria to censor ER50 taking the ER50 distribution and the range of tested rates into account. Based on dose-response fitting results and censoring criteria, we considered input ER50 values SSD analyses in three ways (only point estimates chosen as ER50 medians, interval-censored ER50 based on their 95% credible interval and censored ER50 according to one of the two criteria), by fitting a log-normal distribution under a frequentist framework to get the three corresponding HR5 estimates. We observed that SSD fitted reasonably well when there were at least six distinct ER50 values. By comparing the three SSD curves and the three HR5 estimates, we found that propagating the uncertainty from ER50 and including censored data into the SSD analysis often leads to smaller point estimates of HR5, which is more conservative in a risk assessment context. In addition, we recommend not to focus solely on the point estimate of the HR5, but also to look at the precision of this estimate as depicted by the 95% confidence interval.