To conduct better health risk assessments, this study introduced two risk-based principles and a series of line-lognormal-intersection theorems that helped derive the safe ranges of the cancer slope factors (CSFs) for 708 carcinogenic chemicals. The extrapolated linear dose-response relationships presented in this study can ensure safety with respect to both static and dose-based instantaneous risks compared to the lognormal dose-response model. The theorems proved that the maximum static and dose-based hazard risk ratios of a lognormal curve and a linear model are independent of a chemical's toxicity (the effect dose that corresponds to a 50% response, or ED50), where the selected linear extrapolation (m value) and the individual variability (sigma) of the responses to carcinogenic chemicals are two determining factors. The theorems also indicated that individual variability determines the range of m if the acceptable risk ratios were regulated. When s was 1.36 (i.e., the 50th percentile of the individual variability's lognormal distribution), the safe range of m was derived as [11.22, 21.46] (i.e., from ED11.22 to ED21.46); if the 95th percentile of the s lognormal distribution was used, the safe range of m was [1.13, 4.57] (i.e., from ED1.13 to ED4.57). This study also showed that for a relatively homogenous population (i.e., s is relatively small) that has similar characteristics, the linear dose-response extrapolation method might not be completely effective due to the shape shift of the lognormal curve that draws the static risk of the extrapolated linear model away from the lognormal model. (C) 2020 Elsevier Ltd. All rights reserved.
