An overall risk probability-based method for quantification of synergistic and antagonistic effects in health risk assessment for mixtures: theoretical concepts

In the assessment of health risks of environmental pollutants, the method of dose addition and the method of independent action are used to assess mixture effects when no synergistic and/or antagonistic effects are present. Currently, no method exists to quantify synergistic and/or antagonistic effects for mixtures. The purpose of this paper is to develop the theoretical concepts of an overall risk probability (ORP)-based method to quantify the synergistic and antagonistic effects in health risk assessment for mixtures. The ORP for health effects of environmental chemicals was determined from the cumulative probabilities of exposure and effects. This method was used to calculate the ORP for independent mixtures and for mixtures with synergistic and antagonistic effects. For the independent mixtures, a mixture ORP can be calculated from the product of the ORPs of individual components. For systems of interacting mixtures, a synergistic coefficient and an antagonistic coefficient were defined respectively to quantify the ORPs of each individual component in the mixture. The component ORPs with synergistic and/or antagonistic effects were then used to calculate the total ORP for the mixture. An ORP-based method was developed to quantify synergistic and antagonistic effects in health risk assessment for mixtures. This represents a first method to generally quantify mixture effects of interacting toxicants.