Statistical analysis of interactive cytotoxicity in human epidermal keratinocytes following exposure to a mixture of four metals

Exposure to mixtures of chemicals is an important and relevant environmental issue. Of particular interest is the detection and characterization of departure of biological effects from additivity. Methodology based on the assumption of additivity is used in fitting single-chemicaldata. Interactionsare determined and characterized by making comparisons between the observed and predicted responses at mixtures along a fixed ratio ray of the component substances. Two simultaneous tests are developed for testing for any departure from additivity. Multiple comparisons procedures are used to compare observed responses to that predicted under additivity. A simultaneous confidence band on the predicted responses along the mixture ray is also developed. The methods are illustrated with cytotoxicity data that arise when human epidermal keratinocytes are exposed to a mixture of arsenic, chromium, cadmium, and lead. Synergistic, antagonistic, and additive cytotoxicities were observed at different dose levels of the four-metal mixture.