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

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.