Robust Likelihood‐Based Approach for Automated Optimization and Uncertainty Analysis of Toxicokinetic‐Toxicodynamic Models

Toxicokinetic-toxicodynamic (TKTD) models offer a mechanistic understanding of individual-level toxicity over time, and allow for meaningful extrapolations from laboratory tests to exposure conditions in the field. Thereby, they hold great potential for ecotoxicological studies, both in a regulatory context as well as for basic research. In contrast to mechanistic effect models at higher levels of biological organisation, TKTD models can be, and generally are, parameterised by fitting them to data (results from toxicity tests). Fitting models comes with a range of statistical and numerical challenges, which may hamper the application of TKTD models in a practical setting. Especially in the context of environmental risk assessment (ERA), there is a need for robust and user-friendly software tools to automatically extract the best-fitting model parameters, and quantify their uncertainty, from any data set. This paper presents a general outline for TKTD model analysis, rooted in likelihood-based ('frequentist') inference. The general outline is followed by a presentation of the specific algorithm that has been implemented into software for the robust and automated analysis of toxicity data for survival. However, the presented approach is more broadly applicable to low-dimensional problems. This article is protected by copyright. All rights reserved.

[1]  Roman Ashauer,et al.  Advantages of toxicokinetic and toxicodynamic modelling in aquatic ecotoxicology and risk assessment. , 2010, Journal of environmental monitoring : JEM.

[2]  Volker Grimm,et al.  How to use mechanistic effect models in environmental risk assessment of pesticides: Case studies and recommendations from the SETAC workshop MODELINK , 2016, Integrated environmental assessment and management.

[3]  Marie Laure Delignette-Muller,et al.  Robust Fit of Toxicokinetic-Toxicodynamic Models Using Prior Knowledge Contained in the Design of Survival Toxicity Tests. , 2017, Environmental science & technology.

[4]  Jens Timmer,et al.  Joining forces of Bayesian and frequentist methodology: a study for inference in the presence of non-identifiability , 2012, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[5]  Tjalling Jager,et al.  Revisiting simplified DEBtox models for analysing ecotoxicity data , 2020 .

[6]  Jens Timmer,et al.  Likelihood based observability analysis and confidence intervals for predictions of dynamic models , 2011, BMC Systems Biology.

[7]  Volker Grimm,et al.  Mechanistic effect modeling for ecological risk assessment: Where to go from here? , 2013, Integrated environmental assessment and management.

[8]  Luis A. Escobar,et al.  Teaching about Approximate Confidence Regions Based on Maximum Likelihood Estimation , 1995 .

[9]  Sebastiaan A L M Kooijman,et al.  Making Sense of Ecotoxicological Test Results: Towards Application of Process-based Models , 2006, Ecotoxicology.

[10]  Gonçalo M. Marques,et al.  The AmP project: Comparing species on the basis of dynamic energy budget parameters , 2018, PLoS Comput. Biol..

[11]  C. Russom,et al.  Predicting modes of toxic action from chemical structure: Acute toxicity in the fathead minnow (Pimephales promelas) , 1997 .

[12]  Ursula Klingmüller,et al.  Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood , 2009, Bioinform..

[13]  Peter A. J. Hilbers,et al.  An integrated strategy for prediction uncertainty analysis , 2012, Bioinform..

[14]  Roman Ashauer,et al.  Toxicokinetic and toxicodynamic modeling explains carry-over toxicity from exposure to diazinon by slow organism recovery. , 2010, Environmental science & technology.

[15]  Roman Ashauer,et al.  How to Evaluate the Quality of Toxicokinetic—Toxicodynamic Models in the Context of Environmental Risk Assessment , 2018, Integrated environmental assessment and management.

[16]  Roman Ashauer,et al.  General unified threshold model of survival--a toxicokinetic-toxicodynamic framework for ecotoxicology. , 2011, Environmental science & technology.

[17]  Roman Ashauer,et al.  A METHOD TO PREDICT AND UNDERSTAND FISH SURVIVAL UNDER DYNAMIC CHEMICAL STRESS USING STANDARD ECOTOXICITY DATA , 2013, Environmental toxicology and chemistry.

[18]  Jens Timmer,et al.  Profile likelihood in systems biology , 2013, The FEBS journal.

[19]  Philippe Veber,et al.  Fit Reduced GUTS Models Online: From Theory to Practice. , 2018, Integrated environmental assessment and management.