Recommendations to address uncertainties in environmental risk assessment using toxicokinetics-toxicodynamics models

Providing reliable environmental quality standards (EQSs) is a challenging issue in environmental risk assessment (ERA). These EQSs are derived from toxicity endpoints estimated from dose-response models to identify and characterize the environmental hazard of chemical compounds such as those released by human activities. These toxicity endpoints include the classicalx% effect/lethal concentrations at a specific timet(EC/LC(x,t)) and the new multiplication factors applied to environmental exposure profiles leading tox% effect reduction at a specific timet(MF(x,t), or denotedLP(x,t) by the EFSA). However, classical dose-response models used to estimate toxicity endpoints have some weaknesses, such as their dependency on observation time points, which are likely to differ between species (e.g., experiment duration). Furthermore, real-world exposure profiles are rarely constant over time, which makes the use of classical dose-response models difficult and compromises the derivation ofMF(x,t). When dealing with survival or immobility toxicity test data, these issues can be overcome with the use of the general unified threshold model of survival (GUTS), a toxicokinetics-toxicodynamics (TKTD) model that provides an explicit framework to analyse both time- and concentration-dependent data sets as well as obtain a mechanistic derivation ofEC/LC(x,t) andMF(x,t) regardless of x and at any time t of interest. In addition, the assessment of a risk is inherently built upon probability distributions, such that the next critical step for ERA is to characterize the uncertainties of toxicity endpoints and, consequently, those of EQSs. With this perspective, we investigated the use of a Bayesian framework to obtain the uncertainties from the calibration process and to propagate them to model predictions, includingLC(x,t) andMF(x,t) derivations. We also explored the mathematical properties ofLC(x,t) andMF(x,t) as well as the impact of different experimental designs to provide some recommendations for a robust derivation of toxicity endpoints leading to reliable EQSs: avoid computingLC(x,t) andMF(x,t) for extremexvalues (0 or 100%), where uncertainty is maximal; computeMF(x,t) after a long period of time to take depuration time into account and test survival under few correlated and uncorrelated pulses of the contaminant in terms of depuration.