Significance testing of synergistic/antagonistic, dose level‐dependent, or dose ratio‐dependent effects in mixture dose‐response analysis

Abstract

In ecotoxicology, the state of the art for effect assessment of chemical mixtures is through multiple dose-response analysis of single compounds and their combinations. Investigating whether such data deviate from the reference models of concentration addition and/or independent action to identify overall synergism or antagonism is becoming routine. However, recent data show that more complex deviation patterns, such as dose ratio-dependent deviation and dose level-dependent deviation, need to be addressed. For concentration addition, methods to detect such deviation patterns exist, but they are stand-alone methods developed separately in literature, and conclusions derived from these analyses are therefore difficult to compare. For independent action, hardly any methods to detect such deviations from this reference model exist. This paper describes how these well-established mixture toxicity principles have been incorporated in a coherent data analysis procedure enabling detection and quantification of dose level-and dose ratio-specific synergism or antagonism from both the concentration addition and the independent action models. Significance testing of which deviation pattern describes the data best is carried out through maximum likelihood analysis. This analysis procedure is demonstrated through various data sets, and its applicability and limitations in mixture research are discussed.

Identifying Toxic Impacts of Metals Potentially Released during Deep-Sea Mining—A Synthesis of the Challenges to Quantifying Risk

“…As evidence of this complexity, laboratory studies of the toxicity of copper and cadmium mixtures in the decapod crustacean Palaemon varians were assessed by testing deviation from independent addition reference model (IA) predictions (see Jonker et al, 2005;Pan et al, 2015). Brown et al (2017a) assessed 96-h lethal toxicity in a mixture of copper and cadmium based on the predicted LC 29 of both metals (derived from the modeled mortality responses to individual metals in each temperature/pressure treatment), and compared with mortality in a control treatment and in individual LC 29 exposures to copper and cadmium.…”

Challenges in risk assessment of multiple mycotoxins in food

“…synergism at low doses and antagonism at higher doses) or on the ratio of doses between the compounds in the mixture (e.g. the extent of the synergism or the antagonism depends on the relative contribution of each compound in the mixture) (Jonker et al, 2004(Jonker et al, , 2005. Because MoA of chemicals in mixtures is often unknown or incompletely understood, a frequent option has been the application of both models of CA and IA for actual effect prediction, rather than making a theoretically based choice.…”

“…The CI indicates not only the type of interaction (additivity, synergism or antagonism) but also the magnitude of the interaction found. In addition, the conceptual models of CA and IA incorporating also a set of deviation functions within a nested framework (Jonker et al, 2004(Jonker et al, , 2005 have been effectively applied to the analysis of cytotoxic effects of mycotoxins mixtures (Tavares et al, 2013; Table 1). …”

Ecotoxicity of binary mixtures of Microcystis aeruginosa and insecticides to Daphnia pulex

“…Furthermore, the central composite design (Fig. S1) has been identified as one of the 139 better designs to evaluate mixture toxicity with the currently available models (Jonker et al, 2005). Each 140 designpoint was replicated three times, i.e.…”

“…The deviation function G is defined identically for both reference models and is as follows (Jonker et al, 2005): 208…”