Dose-response analysis of toxicological and pharmacological mixtures with the model deviation ratio method: problems and solutions.

Risk assessment for mixtures of chemicals requires to investigate the magnitude of their potential adverse effects on living organisms. This is usually done by assessing how experimental toxicological mixture data depart from the model of Loewe additivity. Several recent scientific studies propose to perform this task using an ad hoc method known as Model Deviation Ratio (MDR) method. Moreover, the first official European regulatory document for the study of combined exposures explicitly recommends the use of the MDR method (EFSA Scientific Committee et al. Guidance on harmonised methodologies for human health, animal health and ecological risk assessment of combined exposure to multiple chemicals. EFSA Journal, 2019). We show here that the MDR method is not rooted in statistical principles and can lead to erroneous claims. We show however that the distribution of the MDR can be evaluated by simulations and show how this allows us to devise and carry out a bona fide statistical test. The proposed method accounts for uncertainty in the estimation of ED/EC50 and does not require a minimum sample size. The computer code developped in this study is made available as an R package called MDR.

[1]  J. Belden,et al.  How Well Can We Predict the Toxicity of Pesticide Mixtures to Aquatic Life? , 2007 .

[2]  J. Belden,et al.  Joint toxicity of chlorpyrifos and esfenvalerate to fathead minnows and midge larvae , 2006, Environmental toxicology and chemistry.

[3]  S. Murray,et al.  Joint acute toxicity of esfenvalerate and diazinon to larval fathead minnows (Pimephales promelas) , 2003, Environmental toxicology and chemistry.

[4]  J. Ioannidis.  Why Most Published Research Findings Are False , 2019, CHANCE.

[5]  Julien Etienne,et al.  EU Insights Chemical mixtures awareness, understanding and risk perceptions , 2019, EFSA Supporting Publications.

[6]  Erik Lebret,et al.  Current EU research activities on combined exposure to multiple chemicals☆ , 2018, Environment international.

[7]  Christopher D. Chambers,et al.  Redefine statistical significance , 2017, Nature Human Behaviour.

[8]  J. Streibig,et al.  A review of independent action compared to concentration addition as reference models for mixtures of compounds with different molecular target sites , 2008 .

[9]  M. Lydy,et al.  Synergistic toxicity of atrazine and organophosphate insecticides contravenes the response addition mixture model , 1997 .

[10]  M. Liguoro,et al.  The sensitivity of Daphnia magna and Daphnia curvirostris to 10 veterinary antibacterials and to some of their binary mixtures , 2014 .

[11]  J. Belden,et al.  Impact of atrazine on organophosphate insecticide toxicity , 2000 .

[12]  C. I. Bliss.  THE TOXICITY OF POISONS APPLIED JOINTLY1 , 1939 .

[13]  A. Coors,et al.  Predicting the aquatic toxicity of commercial pesticide mixtures , 2011 .

[14]  Alicia Paini,et al.  Regulatory assessment and risk management of chemical mixtures: challenges and ways forward , 2019, Critical reviews in toxicology.

[15]  N. Cedergreen.  Quantifying Synergy: A Systematic Review of Mixture Toxicity Studies within Environmental Toxicology , 2014, PloS one.

[16]  S. H. Bennekou,et al.  Guidance on harmonised methodologies for human health, animal health and ecological risk assessment of combined exposure to multiple chemicals , 2019, EFSA journal. European Food Safety Authority.

[17]  J. Jensen.  Sur les fonctions convexes et les inégalités entre les valeurs moyennes , 1906 .

[18]  J. Mbabazi,et al.  Principles and Methods for the Risk Assessment of Chemicals in Food , 2011 .

[19]  T. Backhaus,et al.  Predictability of the toxicity of multiple chemical mixtures to Vibrio fischeri: Mixtures composed of similarly acting chemicals , 2000 .

[20]  M. Möder,et al.  Mixture toxicity of wood preservative products in the fish embryo toxicity test , 2012, Environmental toxicology and chemistry.