US EPA

The excess cancer risk that might result from exposure to a mixture of chemical carcinogens usually is estimated with data from experiments conducted on individual chemicals. An upper bound on the total excess risk is estimated commonly by summing individual upper bound risk estimates. The degree to which this approach might overstate the true risk associated with the mixture has not been evaluated previously. This paper reports the results of a Monte Carlo simulation study on the degree of reduction in conservatism that might be achived using alternative methods for calculating mixture upper bounds. An unexpected finding is that for chemicals that exhibit strongly linear dose-response relationships, the summing of multistage-model-based upper bounds on excess risk can be anti-conservative, that is, it can provide less than the nominal 100(1-x)% coverage.

Kodell, R. L., H. Ahn, J. J. Chen, J. A. Springer, C. N. Barton, AND R. Hertzberg. Upper Bound Risk Estimates For Mixtures Of Carcinogens. Toxicology v.105(2-3):199-208, (1995).