Risk-based principles and incompleteness theorems for linear dose-response extrapolation for carcinogenic chemicals

Area of Science:

• Environmental Health
• Toxicology
• Risk Assessment

Background:

• Health risk assessments rely on accurate dose-response models for carcinogenic chemicals.
• Existing models may not fully capture the complexities of individual variability in response to chemical exposure.
• Cancer slope factors (CSFs) are critical for quantifying cancer risk.

Purpose of the Study:

• To introduce novel risk-based principles and line-lognormal-intersection theorems for deriving safe CSF ranges.
• To compare the safety assurances of linear dose-response extrapolation versus the lognormal model.
• To analyze the influence of individual variability on safe extrapolation parameters.

Main Methods:

• Development of two risk-based principles and a series of line-lognormal-intersection theorems.
• Derivation of safe ranges for cancer slope factors (CSFs) for 708 chemicals.
• Analysis of static and dose-based instantaneous risks under linear and lognormal models.

Main Results:

• Theorems demonstrate that maximum static and dose-based hazard risk ratios are independent of chemical toxicity (ED50).
• Linear extrapolation (m value) and individual variability (σ) are key determinants of risk ratios.
• Safe ranges for m were derived based on different percentiles of individual variability (σ=1.36 and 95th percentile).

Conclusions:

• The introduced theorems provide a robust framework for establishing safe CSF ranges.
• Linear dose-response extrapolation offers safety assurances for both static and dose-based risks.
• Linear extrapolation may be less effective in homogenous populations due to lognormal curve shape shifts.