Dose–response analysis of toxicological and pharmacological mixtures with the model deviation ratio method: Problems and solutions

Abstract

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.