A Copula-Based Framework for Modeling Dependency Structures in PBPK Virtual Populations: A Chinese Adult Case Study

Physiologically based pharmacokinetic (PBPK) models require virtual populations that preserve dependencies between organ physiological parameters and demographic covariates. We developed a copula-based framework to model organ-demographic dependencies and benchmarked it against PK-Sim using Chinese adults.

Demographic data for Chinese adults aged 18-65 years from public databases and literature-derived organ/tissue weights were used. Marginal distributions were estimated using kernel density estimation, and dependencies were modeled with vine copulas. Virtual individuals were generated by conditional sampling and inverse marginal transformation, conserving whole-body mass by scaling muscle and adipose tissue weights. A range-matched PK-Sim population served as the comparator.

The analysis included 45,154 demographic records and 11 organs/tissues. Fitted copula models reproduced the observed marginal distributions and dependencies. In the generated virtual population, P5-P95 intervals of organ/tissue weights encompassed Chinese reference means. Compared with PK-Sim, 83.6% of organ/tissue-pair comparisons exhibited higher Kendall's τ values, whereas PK-Sim generally produced weak or near-zero correlations. Organ-demographic relationships were more consistent with published data for most organs, although discrepancies remained for the pancreas and muscle.

Explicit modeling of dependency structures, in addition to marginal distributions, generated PBPK virtual populations with more physiologically plausible relationships among organ parameters and demographic covariates.