Comparison of dose-effect relationships of carcinogens following low-dose chronic exposure and high-dose single injection: an analysis by the median-effect principle.

Experimental dose-effect relationships of carcinogens following either acute (single dose) or chronic (time to tumor) exposure appears to conform with the median-effect principle (Chou, J. Theor. Biol. 59, 253-276, 1976) of the mass-action law: f(a)/ (1 - f(a)) = (D/D(m))m, where D is dose or cumulative dose, D(m) is the D required for the median-effect, m is the Hill-type coefficient, and f(a) is the fraction that is affected by D. The parameters m and D(m) are the basic characteristics for each carcinogen at specified experimental conditions. A plot of y = log [(f(a))-(-1)-1]-1 vs x =(D) gives the slope, m, and the intercept, log D(m), at y = 0. Using previously reported data, it is shown that dose-effect relationships of carcinogens obtained from various experimental designs (e.g., mode of exposure, route of administration, age at beginning of exposure to carcinogen, type of tumor produced, and strain and sex of animal used) can be normalized and compared directly on the same gauge and thus their consistency with the mass-law principle can be clearly demonstrated. The analysis suggests that chemical carcinogens, like non-carcinogenic chemicals, exert their effects according to the principle of the mass-action law. It also suggests that the interaction of the ultimate carcinogens and the probable targets is a multi-event or a slow-transition process (i.e., m > 1). The analytical procedure described by f(a) = [1 + (D(m)/D)(m)]-1 provides a simplified general method for assessment of low-dose risk of carcinogens.