Federated Estimation of Population Pharmacokinetic Models with Exact Equivalence to Pooled-Data Analysis

Population pharmacokinetic (PopPK) analysis relies on nonlinear mixed-effects modeling of pooled data; however, sharing subject-level data across sites is often restricted. This study develops a federated framework that exactly recovers the global objective function corresponding to centralized pooled-data analysis, thereby yielding identical parameter estimates without sharing subject-level data.

Each site computes its local contributions to the global objective function and corresponding gradients. A central server aggregates these quantities to reconstruct the global objective function and gradient at each parameter value. Performance was evaluated using simulations of a one-compartment oral model under two multi-site scenarios: heterogeneous sparse sampling and between-site heterogeneity in covariate distribution. Federated estimation was compared with centralized pooled-data estimation, independent site-specific estimation, and weighted combination of site-specific estimates and variances. Parameter uncertainty was assessed using bootstrap resampling.

Across scenarios, federated estimation yielded parameter estimates and bootstrap confidence intervals that closely matched with those from centralized pooled-data estimation for fixed effects, between-subject variability, and residual error. In contrast, independent site-specific estimation showed deviations under certain conditions, and weighted pooling of site-specific estimates did not reproduce centralized variance estimates.

The proposed federated framework enables mathematically equivalent PopPK estimation without sharing subject-level data.