Amplified Bioanalytical Uncertainty Propagation Impact on Population Pharmacokinetic Modeling

Objectives: During bioanalysis, samples are typically diluted to a validated calibration range after dilution integrity studies [ 1]. However, dilution and back-calculation will introduce random and constant multiplicative errors, which can accumulate and propagate, potentially leading to a significantly large error in the final result [ 2]. Therefore, diluting observations differently can break the independent and identically distributed (iid) property of residuals assumed in pharmacokinetic (PK) modeling [ 3]. This work aims to study the impact of propagated error from multiple dilutions on population PK parameter estimation. Methods: First, bioanalytical data of oxycodone, mitragynine, and NEU7032 were used to demonstrate that assay errors closely follow a combined additive plus proportional error model. A total of 9,000 simulations were conducted, exploring combinations of five factors (number of subjects, dose, additive error, proportional error, and maximum dilution factor), with 10 replicates per combination. Dose levels, parameters, and time points were inspired by zanubrutinib studies and deemed appropriate across all combinations using D-optimal design [ 4]. Simulations were performed using rxode2 to simulate a typical 2-compartment model with a total of 12 parameters, 5 fixed (θ), 5 random inter-individual variability (ω), and 2 residual (σ) parameters. Fitting was performed using both SAEM/Monolix and FOCEI/NONMEM, capturing parameter estimates, uncertainties, and objective function values. Realistic constraints were imposed on the simulation. First, to mimic regulatory compliance, LLOQ was constrained to a 20% coefficient of variation [ 1], where the standard deviation was assumed to be a combined error model. Additionally, dilution was demoted or skipped on some observations to avoid additional BLOQ introduction. To assess overall accuracy, we calculated the mean absolute percentage error difference (diffMAPE) between parameters in the undiluted case and corresponding diluted cases. To identify the most significant factors on the parameter inaccuracy, we calculated SHAP (SHapley Additive exPlanations) values using XGBoost (eXtreme Gradient Boosting) regression models, where the outcomes were PK parameter estimates and the predictors were simulation factors and other PK-derived features. Results: The bioanalytical error structure was well represented by a combined additive (σadd) and proportional (σprop) error model. As expected, the objective function value increased as dilution increased. We also observed an identifiability issue, where σadd is not always inflated while σprop will be inflated instead. Inaccuracies on fixed and random effects of peripheral compartment parameters (V2 and Q) were significant (up to 80% diffMAPE). Base SHAP values implied that most inaccuracies occurred on σadd, σprop, ωV2, and θV2. The top global SHAP values were for dilution factor, additive error, and ratio of observations BLOQ. Conclusions: We advocate for both pharmacometrics and bioanalytical scientists to be aware of potential error propagation from bioanalytical methods, as this has been demonstrated to lead to inaccurate PK parameter estimates and could impact downstream decision-making.