Stochastic Differential Equations (SDEs) in NONMEM for Probing Population Pharmacokinetic Model Misspecification: Diagnostic Utility, Practical Considerations, and Future Directions

Population pharmacokinetic (popPK) models are commonly developed using ordinary differential equations (ODEs) to describe deterministic concentration-time profiles, with unexplained variability typically attributed to interindividual variability or residual error. When model misspecification is present, system-level deviations may be absorbed into these conventional variability terms, making the source and magnitude of model inadequacy difficult to assess quantitatively. Stochastic differential equations (SDEs) provide an alternative framework by introducing an explicit system-noise component into the structural model, allowing model-data mismatch to be evaluated more directly. However, historical implementation of SDE-based models in NONMEM has been technically challenging. The availability of the Fortran plug-in subroutine SDE.f90 substantially lowers this barrier and enables more practical implementation of SDE-based models in NONMEM. In this work, SDE-based nonlinear mixed-effects models were evaluated as a quantitative diagnostic framework for probing popPK model misspecification. The SDE.f90 implementation was first verified using simulated one-compartment intravenous bolus datasets with stochastic process noise. Additional simulation-estimation scenarios were then conducted under intentionally misspecified structural or stochastic assumptions, including time-varying elimination, compartmental misspecification, and residual error misspecification. Across these scenarios, the estimated system-noise parameter was generally sensitive to misspecification, with larger values usually associated with greater structural or stochastic mismatch. SDE-based modeling also helped partially separate system-level variability from residual variability and, in selected settings, supported localization of misspecification to specific model components, thereby helping guide model refinement. Overall, SDE-based popPK modeling is a useful addition to the pharmacometric diagnostic toolbox, with system-noise estimates best interpreted together with structural model evaluation, residual diagnostics, parameter behavior, and pharmacologic plausibility.