Mark Transtrum 1
1 Cross Stream Bioanalytics (Salt Lake City, USA)
Objectives
Overparameterized mechanistic models are common in pharmacometrics, particularly in physiologically based pharmacokinetic (PBPK) modeling. While such models may achieve acceptable goodness-of-fit, redundant or weakly identifiable parameter directions can influence predictive uncertainty in subtle ways. We investigated whether overparameterization can induce entropic over-confidence, defined here as the suppression of predictive population variance arising from redundant parameter directions that concentrate accepted parameter mass along identifiable ridges. Specifically, we examined whether predictive uncertainty for organ-level area under the curve (AUC) can depend on model representation even when competing models provide statistically indistinguishable fits to observed data.
Methods
A mechanistic alpha-particle radiopharmaceutical PBPK model (29 parameters) was compared to a reduced model (16 parameters) derived using the Manifold Boundary Approximation Method (MBAM). MBAM uses information geometry to identify parameter directions that are unidentifiable or predictively insignificant and systematically projects the model toward boundary limits along those directions while preserving selected data and downstream predictions.
For multiple datasets (30 compartment–time observations each), full and reduced models were fit using multi-start optimization. Acceptable fits were defined using a chi-square–calibrated threshold to ensure comparable fit adequacy within each model. Local Fisher Information Matrix (FIM) spectra were computed to characterize practical identifiability and to guide perturbations of optimization initialization.
Bootstrap resampling was combined with multi-start optimization and chi-square–based likelihood thresholding to generate ensembles of acceptable parameter sets. From these ensembles, population-level parameter distributions were estimated via empirical Bayes procedures and propagated through the forward model to obtain predictive distributions for log-transformed organ AUC. This empirical Bayes approach differs from full Bayesian posterior sampling in that prior distributions are estimated from the data rather than specified a priori. Predictive uncertainty was summarized using standard deviations and percentile intervals.
Results
Across datasets where reduced and full models achieved statistically indistinguishable goodness-of-fit, predictive uncertainty for organ AUC differed substantially between representations in selected cases. In a representative dataset, mean weighted sum of squares (WSS) values were comparable between full and reduced models (0.72 vs 0.61), with similar variability across accepted ensembles. Despite comparable fit distributions, the reduced model produced markedly broader predictive distributions for log AUC across multiple organs. For example, the standard deviation of log AUC for marrow Ac225 was 0.17 under the full model versus 1.45 under the reduced model (approximately 8-fold increase). Similar inflation was observed across liver, kidney, spleen, and tumor log AUC endpoints, with reduced-to-full standard deviation ratios ranging from approximately 6 to 15. These differences persisted across increasing perturbation scales.
In other datasets with comparable fit quality, predictive variances were similar between model representations. Local FIM analysis indicated that datasets exhibiting representation-dependent behavior contained parameter directions weakly identifiable from data yet strongly influential for AUC variability.
Conclusions
These findings demonstrate representation-dependent differences in predictive uncertainty in PBPK population inference: predictive population variance for decision-relevant endpoints can depend strongly on model representation, even when competing models provide statistically indistinguishable fits to observed data. In selected datasets, information-geometric reduction via MBAM revealed substantially broader AUC uncertainty than the overparameterized model under the same ensemble construction, consistent with entropic over-confidence induced by redundant parameter directions.
Predictive equivalence at the level of point estimates does not guarantee equivalence of predictive variance. Even when two models span the same predictive manifold, they need not induce the same uncertainty over those predictions. Explicit assessment of identifiability and representational entropy may therefore be critical when quantifying uncertainty for dose selection or risk assessment in overparameterized PBPK models.
References:
Transtrum, Mark K., and Peng Qiu. “Model reduction by manifold boundaries.” Physical review letters 113.9 (2014): 098701.
Quinn, Katherine N., et al. “Information geometry for multiparameter models: New perspectives on the origin of simplicity.” Reports on Progress in Physics 86.3 (2023): 035901.
Sher, Anna, et al. “A quantitative systems pharmacology perspective on the importance of parameter identifiability.” Bulletin of Mathematical Biology 84.3 (2022): 39.
Reference: PAGE 34 (2026) Abstr 11883 [www.page-meeting.org/?abstract=11883]
Poster: Methodology - Model Evaluation