Figure 5.

(A) Hierarchical population statistical model for PBPK model uncertainty and variability. Square nodes represent fixed or observed quantities, circle nodes represent uncertain or unobserved quantities, and the inverted triangle represents PBPK model outputs; solid arrows indicate a stochastic relationship represented by a conditional distribution [e.g., A→B means B ~ P(B|A)], whereas dashed arrows indicate a functional relationship [e.g., B = f(A)]. The population consists of studies i, each of which contains experiments or strains j, with exposure parameters E_ij, and data y_ij collected at times t_ij. The PBPK model produces outputs f_ij. The difference between data and predictions is assumed to have a distribution with variance σ², which is assigned a prior distribution (Pr). The PBPK model uses non–strain-specific parameters θ_i, measured covariates φ_i, and strain-specific parameters ψj. The parameters are each drawn from population distributions with mean M_{θ or ψ} and variance V_{θ or ψ}, each of which are in turn assigned prior distributions. (B) Comparison of data (data points with ± 1 SD error bars) and PBPK model predictions (solid lines represent interquartile range, gray area represents 95% CI) for two representative mouse inbred strains (data from Bradford et al. 2011). Dotted lines indicate the limits of detection.