Objective Conventional pharmacodynamic (PD) modeling workflows require manual model selection, repeated equation rewriting, and empirical parameter adjustment, resulting in limited automation, high cross-scenario migration costs, and insufficient reproducibility. This study aims to develop PD Union, a unified, automated, and interpretable framework for mechanistic PD modeling.

Methods PD Union is built upon a unified continuous dynamical skeleton that organizes absorption and systemic exposure module, the receptor module, the drug input module, the first delay module, the primary pharmacodynamic function module, the primary pharmacodynamic state module, the downstream pharmacodynamic state module, the second delay module, the feedback module, the circadian modulation module, the biophase module, the direct effect module, the disease state module, the second PD axis first delay module, the second PD axis primary pharmacodynamic function module, the second PD axis primary pharmacodynamic state module, the second PD axis downstream pharmacodynamic state module, the second PD axis second delay module, and the second PD axis feedback module. A machine learning-based structure identification module is incorporated to recognize drug input modes and mechanism labels from population PK/PD time series, followed by constrained population parameter optimization, forming an integrated pipeline of structure identification, candidate generation, and parameter fitting.

Results Validation was conducted at two levels. In standardized synthetic benchmarking across 14 representative single-endpoint scenarios, the structure identification model achieved an output mode accuracy(NRMSE) of 0.7600 and macro-average F1 of 0.6307; parameter fitting yielded an NRMSE mean of 0.146 and median of 0.117. In the unified reconstruction validation based on 15 population pharmacokinetics/pharmacodynamics (PK/PD) literature data, the mean NRMSE of PDUnion model for PD was 0.261, and the median was 0.228. Among the 15 studies, 14 performed better than the models provided in the original literature.

Conclusions PD Union demonstrates that interpretable mechanistic modularization combined with machine learning-assisted structure identification is feasible for automated PD modeling. The framework provides an executable methodological foundation for unified, reproducible, and extensible mechanistic PD modeling, with potential applicability to multi-endpoint and complex disease-state modeling scenarios.

The authors have declared no competing interest.

This study did not receive any funding

I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained.

Yes

The details of the IRB/oversight body that provided approval or exemption for the research described are given below:

The article utilized publicly available data from 15 real documents or reconstructed data based on them. The corresponding articles are all publicly accessible. Below are their sources： (1)DOI: 10.1002/cpt.70173 (2)DOI: 10.1093/jpp/rgaf123 (3)DOI: 10.1097/FTD.0000000000001310 (4)DOI: 10.1111/cts.70404 (5)DOI: 10.1111/pan.70050 (6)DOI: 10.2147/DDDT.S533428 (7)DOI: 10.1111/jdi.70034 (8)DOI: 10.1002/bcp.70477 (9)DOI: 10.1002/psp4.70181 (10)DOI: 10.1111/cts.70388 (11)DOI: 10.1002/psp4.70209 (12)DOI: 10.1002/psp4.70210 (13)DOI: 10.1007/s11095-026-04028-0 (14)DOI: 10.1007/s40262-025-01595-0 (15)DOI: 10.1007/s40262-025-01598-x

I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals.

Yes

I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).

Yes

I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable.

Yes

All data produced in the present study are available upon reasonable request to the authors.