Table 2.

Summary of unified probabilistic framework.

Step and goal	New input(s) for each step	Output(s) for each step
1. Critical ED in animal. Estimate the uncertainty distribution for ADM*, the animal dose associated with the critical effect size M*.	Animal dose–response data Toxicologically equivalent effect metric (M) Critical effect size (M*) Appropriate BMD analysis	ADM* = uncertainty distribution for BMD based on analysis of animal dose–response data.
2. Equipotent dose in median human. Infer the uncertainty distribution for HDM* = HD(0.5≥M*), the human dose at which 50% of the human population has effects greater than or equal to the critical effect size M*.	ADM* from step 1 DAF, distribution for the dosimetric adjustment factor due to differences in body size between animal and human AHU, distribution for the “animal-to-human uncertainties” due to unknown chemical- and/or species-specific toxicokinetic or toxicodynamic differences OU, the distributions for “other uncertainties” due to study- and/or endpoint-specific conditions that differ from the target conditions	HDM* = ADM* × DAF/ (AHU × OU) = uncertainty distribution derived by multiplying ADM* by uncertain factors.
3. Equipotent dose in sensitive human (for an exposure limit). Infer HDM*I* = HD(I*≥M*), the dose at which a target incidence I*≥M* yields effects of size ≥ M*. Select a particular value HD* from the uncertainty distribution based on level of confidence.	HD(0.5≥M*) from step 2, serving as the uncertainty distribution for the median of the human variability distribution A log-normal human variability distribution, and a separate uncertainty distribution for its variance σH2a A target incidence I*, from which a human variability factor HVI* for the ratio between the “sensitive” and median individual is calculated [= exp(zI* σH) for a log-normal distribution, where zI is the normal z-score for the I* quantile]	HDM*I* = HDM* × HVI* = uncertainty distribution for the I* percentile of a human variability distribution with median equal to HDM* and standard deviation on log scale of σH.
aWe use a log-normal distribution for the uncertainty in the variance, but other distributions could in principle be used.