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Previous applications of carcinogenic risk assessment using mathematical models of carcinogenesis have focused largely on the case where the level of exposure remains constant over time. In many situations, however, the dose of the carcinogen varies with time. In this paper, we discuss both the classical Armitage–Doll multistage model and the Moolgavkar–Venzon–Knudson two–stage birth–death–mutation model with time‐dependent dosing regimens. Bounds on the degree of underestimation of risk that can occur through the use of a simple time‐weighted average dose are derived by means of comparison with an equivalent constant dose corresponding to the actual risk under the time‐dependent dosing regimen.

Applications of methods for carcinogenic risk assessment often focus on estimating lifetime cancer risk. With intermittent or time‐dependent exposures, lifetime risk is often approximated on the basis of a lifetime average daily dose (LADD). In this article, we show that there exists a lifetime equivalent constant dose (LECD)which leads to the same lifetime risk as the actual time‐dependent exposure pattern. The ratio C= LECD/LADD then provides a measure of accuracy of risk estimates based on the LADD, as well as a basis for correcting such estimates. Theoretical results derived under the classical multistage model and the two‐stage birth‐death‐mutation model suggest that the maximum value of C, which represents the factor by which the LADD may lead to underestimates of risk, will often lie in the range of 2‐ to 5‐fold. The practical application of these results is illustrated in the case of astronauts subjected to relatively short‐term exposure to volatile organics in a closed space station environment, and in the case of the ingestion of pesticide residues in food where consumption patterns vary with age.