A simple upper limit for the sum of the risks of the components in a mixture

Natural or manufactured products may contain mixtures of carcinogens and the human environment certainly contains mixtures of carcinogens. Various authors have shown that the total risk of a mixture can be approximated by the sum of the risks of the individual components under a variety of conditions at low doses. Under these conditions, summing the individual estimated upper bound risks, as currently often done, is too conservative because it is unlikely that all risks for a mixture are at their maximum levels simultaneously. In the absence of synergism, a simple procedure is proposed for estimating a more appropriate upper bound of the additive risks for a mixture of carcinogens. These simple limits also apply to noncancer endpoints when the risks of the components are approximately additive.