Recommendations to address uncertainties in environmental risk assessment using toxicokinetic-toxicodynamic 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 released by human activities. These toxicity endpoints include the classical x % effect/lethal concentrations at a specific time t ( EC / LC ( x , t )) and the new multiplication factors applied to environmental exposure profiles leading to x % effect reduction at a specific time t ( MF ( x , t ), or denoted LP ( 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 may prevent the derivation of MF ( 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 toxicokinetic-toxicodynamic (TKTD) model that provides an explicit framework to analyse both time- and concentration-dependent data sets as well as obtain a mechanistic derivation of EC / LC ( x , t ) and MF ( x , t ) regardless of x and at any time t of interest. In ERA, the assessment of a risk is inherently built upon probability distributions, such that the next critical step 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, including LC ( x , t ) and MF ( x , t ) derivations. We also explored the mathematical properties of LC ( x , t ) and MF ( 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 computing LC ( x , t ) and MF ( x , t ) for extreme x values (0 or 100%), where uncertainty is maximal; compute MF ( x , t ) after a long period of time to take depuration time into account and test survival under pulses with different periods of time between them.