A published method by Mantel and Bryan for calculating “safe” doses of carcinogens is updated by incorporating several improvements. These improvements include more effective procedures for taking into account any spontaneous tumor rate and for combining data at several dose levels. An added feature is that it permits the combining of data from several experiments by postulating that it is only the spontaneous rate that differs between experiments. The improved method is illustrated with data from five hypothetical experiments, using a risk level of 10-8, a conservative slope of one probit or normal deviate per tenfold dose increase, and a nominal assurance level of 99%. The hypothetical experiments were geared to bring out particular points as, for example, the applicability of the model in the absence of control data. A large variety of issues involved in the determination of “safe” doses are discussed, including questions of experiment design and extrapolation between species. A statistical appendix is provided, laying the framework for the calculating procedure and detailing complications therein.

The “safe” dose approach helps resolve certain dilemmas in questions relating to food additives. A “no-detectablelevel” prescription for chemical residues may be dangerous to the public where detection techniques are insufficiently sensitive, but it can become far too restrictive as exquisitely sensitive detection techniques are developed. Only levels in excess of the “safe” dose would require detection. Calculated values for the “safe” dose could be updated and increased as more clear evidence of safety becomes available.

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Work partly supported by USPHS Research Grant CA-15686 from he National Cancer Institute.

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