Moustafa M. A. Ibrahim 1, Jasmine H. Hughes 2, Ron J. Keizer 2, Martin Bergstrand 3
1 Department of Pharmacy, Uppsala University (Uppsala, Sweden), 2 InsightRX (San Francisco, USA), 3 Pharmetheus (Uppsala, Sweden)
Background
The visual predictive check (VPC) and the prediction-corrected VPC (pcVPC) are standard diagnostic tools used to evaluate the suitability of pharmacometric models [1]. However, real-world data (RWD) often reflects adaptive clinical decision-making, where treatments such as dosing intervals or sampling schedules are dynamically modified in response to patient drug concentrations or treatment response. Similar adaptive designs are sometimes also featured in randomized clinical trials. In scenarios where dosing intervals and/or sampling times are adapted, traditional VPCs and pcVPCs can display apparent deviations between observations and model predictions—falsely indicating a model misspecification even when the underlying model is perfectly unbiased [2].
Objectives
To evaluate the utility of the reference corrected VPC (rcVPC) methodology to address the diagnostic challenges posed by adaptive study designs and RWD.
Methods
The rcVPC methodology normalizes both observed and simulated dependent variables to a user-defined reference dataset (e.g., a fixed dosing regimen) to evaluate the structural and stochastic components of the model [3]. The applicability of rcVPC was tested for RWD inspired simulated case-studies where VPC and pcVPC had previously demonstrated shortcomings [2]. This included a simulated adaptive dosing scenario (Case 1), comprising 200 patients receiving a one-compartment intravenous drug. While the dose amount was fixed at 4000 U, the dosing intervals (ranging between 4 and 48 hours) were dynamically adapted to target a trough concentration of 12.5 U/L. Separately, for the same cases also positive control scenarios were run, with misspecified models (scenario 1: population CL +20%). The model’s predictive performance was graphically evaluated using standard VPC, pcVPC, and rcVPC. For the rcVPC, observations and predictions were normalized to a reference dataset assuming a fixed 12-hour dosing interval (Q12h) regimen for all subjects.
Results
When evaluated with a traditional VPC, the adaptive dosing interval scenario falsely indicated an overestimation of variability in drug concentrations. This occurred because patient observations converged on the target concentration, while the simulated data did not retain the correlation between initial trough concentrations and subsequent dosing. The application of the pcVPC failed to resolve this discrepancy, continuing to demonstrate a substantial separation between observed and predicted percentiles that misleadingly indicated misspecification. Conversely, the rcVPC approach successfully corrected for the adaptive design by normalizing the data to the fixed Q12h reference regimen and inherently applying a variability correction. For the investigated case studies rcVPC plots appropriately indicated if the applied model featured a model misspecification or not.
Discussion and Conclusion
The results of this study indicate that rcVPC methodology can provide important advantages in the presence of adaptive dosing intervals and sampling times. This can be especially relevant in application to RWD. In combination with other novel VPC methodology [4] this will offer an improved toolbox for efficient, reliable and interpretable model evaluation for complex datasets.
References:
[1] Bergstrand M, Hooker AC, Wallin JE, Karlsson MO. Prediction-corrected visual predictive checks for diagnosing nonlinear mixed-effects models. AAPS J. 2011 Jun;13(2):143-51.
[2] Hughes JHH, Bergstrand M, Keizer RJ. The visual predictive check and real-world data. CPT (In press)
[3] Ibrahim MMA, Jonsson EN, Bergstrand M. The Reference-Corrected Visual Predictive Check: A More Intuitive Diagnostic for Non-Linear Mixed Effects Models. AAPS J. 2025 Apr 29;27(4):86.
[4] Keizer RJ, Bergstrand M, Hughes JHH. Visual Predictive Checks for Real-World Data using Propensity-Sore-Matching. PAGE 2026.
Reference: PAGE 34 (2026) Abstr 11858 [www.page-meeting.org/?abstract=11858]
Poster: Methodology - Model Evaluation