A Unified Probabilistic Framework for Dose-Response Assessment of Human Health Effects

Abstract

Background: When chemical health hazards have been identified, probabilistic dose-response assessment ("hazard characterization") quantifies uncertainty and/or variability in toxicity as a function of human exposure. Existing probabilistic approaches differ for different types of endpoints or modes-of-action, lacking a unifying framework.

Objectives: We developed a unified framework for probabilistic dose-response assessment.

Methods: We established a framework based on four principles: a) individual and population dose responses are distinct; b) dose-response relationships for all (including quantal) endpoints can be recast as relating to an underlying continuous measure of response at the individual level; c) for effects relevant to humans, "effect metrics" can be specified to define "toxicologically equivalent" sizes for this underlying individual response; and d) dose-response assessment requires making adjustments and accounting for uncertainty and variability. We then derived a step-by-step probabilistic approach for dose-response assessment of animal toxicology data similar to how nonprobabilistic reference doses are derived, illustrating the approach with example non-cancer and cancer datasets.

Results: Probabilistically derived exposure limits are based on estimating a "target human dose" (HDMI), which requires risk management-informed choices for the magnitude (M) of individual effect being protected against, the remaining incidence (I) of individuals with effects ≥ M in the population, and the percent confidence. In the example datasets, probabilistically derived 90% confidence intervals for HDMI values span a 40- to 60-fold range, where I = 1% of the population experiences ≥ M = 1%-10% effect sizes.

Conclusions: Although some implementation challenges remain, this unified probabilistic framework can provide substantially more complete and transparent characterization of chemical hazards and support better-informed risk management decisions.

Figure 1

Deterministic quantal endpoints: quantal responses reflecting incidences of a continuous response above/below a fixed cut point. The various dose–response lines in the upper panel reflect the (hypothetical) dose responses of individual animals.

Figure 2

Stochastic quantal endpoints: quantal responses reflecting individual probability of effect. The dashed lines in the upper and lower panel are the same, representing the (hypothetical) dose response of the median animal. In the upper panel, the solid lines represent (hypothetical) individual dose–response curves. In the lower panel, the solid line reflects the expected value of the observed quantal response from the population of individual responses, which is less steep than the dose response of the median animal.

Figure 3

Implementation of the unified probabilistic framework to derive the uncertainty distribution for HD_M*^I* and a corresponding probabilistic RfD. In step 1, BMD analysis is used to derive the uncertainty distribution for AD_M*. In step 2, this distribution is combined with uncertainties in dosimetric adjustment, animal-to-human toxicokinetics and toxicodynamics, and other study-specific limitations, to derive the uncertainty distribution for HD_M*. In step 3, the distribution is further combined with the uncertainty in the human variability factor corresponding to the selected incidence I* in the population to derive the uncertainty distribution for HD_M*^I*. The lower 95% (one-sided) confidence limit on HD_M*^I* can be chosen as the “probabilistic RfD” corresponding to the selected values of M* and I*. See “Methods” and Table 2 for additional details. This approach is illustrated with two example datasets, with results shown in Table 4 and Figures 4 and 5.

Figure 4

Results of analysis of example continuous dataset [rat body weight (BW) changes] as a function of dose (milligrams per kilogram BW per day). (A) Representative benchmark dose (BMD) modeling results using the Hill model with M* = 5% change. (B) Median estimate and 5th and 95th percentile estimates for the incidence (I) of effects of size > M* (i.e., 5% change in BW) as a function of population exposure [dose; i.e, I_≥M*(Dose)]. For reference, also shown are the probabilistic RfDs corresponding to a 1% incidence of effects of size > M* at 95% (one-sided) confidence (black square), the 90% (two-sided) CI for the benchmark dose (vertical gray shaded area), and a deterministic RfD equal to the BMDL/100 (vertical blue line).

Figure 5

Results of analysis of example quantal dataset (forestomach tumors in mice) as a function of dose (milligrams per kilogram BW per day). (A) Representative benchmark dose (BMD) modeling results using the Weibull model. Multiple BMD estimates are shown, with the ED₅₀ corresponding to M* = tumor, and the BMD₁₀ and BMD₀₁ corresponding to M* = 10% and 1% extra risk, respectively. (B–D) Median estimate and 5th and 95th percentile estimates ) for the incidence (I) of effects of size > M* as a function of population exposure [dose; i.e, I_≥M*(Dose)]. In (B), mouse forestomach tumors are treated as a deterministic quantal endpoint, whereas in (C,D), tumors are treated as a stochastic quantal endpoint [in (C), M* = 10% extra risk; in (D), M* = 1% extra risk)]. For reference, also shown in each panel are the probabilistic RfDs corresponding to a 1% incidence of effects of size > M* at 95% (one-sided) confidence (black square) and the 90% (two-sided) confidence interval (CI) for the benchmark dose (vertical gray shaded area).

Figure 6

Comparison of estimated human population tumor incidences as a function of exposure [dose (milligrams per kilogram BW per day)] when treating tumors as a deterministic or a stochastic endpoint. Shown are the 90% (two-sided) CIs for human population tumor incidence calculated from the probabilistic approach, depending on whether tumors in the example dataset are treated as deterministic or stochastic quantal endpoints. For reference, also shown is the population tumor incidence derived using the default U.S. EPA method of linear extrapolation from a point of departure equal to the animal BMDL₁₀ allometrically scaled by multiplying by (BW_animal/BW_human)^0.25 (blue line).