Aanisah Hanuun 1, Anouk Muller 2, Tim Preijers 1
1 Department of Hospital Pharmacy, Erasmus University Medical Center Rotterdam (Rotterdam, Netherlands), 2 Department of Medical Microbiology and Infectious Diseases, Erasmus University Medical Center Rotterdam (Rotterdam, Netherlands)
Objectives
In clinical practice, many treatments are given as combination therapies. However, population pharmacokinetic (popPK) analysis typically evaluates each drug independently, potentially ignoring shared variability and correlations between the pharmacokinetic (PK) parameters[1]. This limitation may lead to biased predictions, such as for the calculation of the probability of target attainment (PTA). Synchronous combined popPK modelling, in which two parent drugs are analysed simultaneously, offers a potential solution by capturing shared sources of variability and estimating correlations in PK parameters. While synchronous popPK approaches are well established for parent-metabolite pairs, they rely on mechanistic linkages and cannot be directly generalised to independent parent-parent drug combinations. Although several studies have applied synchronous modelling to co-administered drugs, the approach remains heterogeneous and lacking in standardisation. Consequently, no standardised framework currently exists to guide synchronous modelling of parent-parent popPK analysis, leaving a methodological gap in model-informed drug development. The aim of this study was to establish a generalisable framework that can serve as a standard approach for joint parent–parent popPK analysis. To achieve this, two independently developed popPK models for co-administered drugs were integrated into a joint modelling framework and multiple joint modelling approaches were explored. Each approach was evaluated, and the best-performing joint model was selected and compared against the separate models in terms of predictive performance. The selected joint model was then applied to assess whether synchronous and independent modelling approaches yield different PTA outcomes.
Methods
Previously developed popPK models for cefepime and zidebactam, based on phase 1 and phase 3 clinical studies in adults receiving intravenous monotherapy or combination therapy, were independently re-estimated and verified in NONMEM using data from individuals who received both drugs (n=524). Intravenous doses ranged from 500–2000 mg for cefepime and 500–1000 mg for zidebactam, administered as one-hour infusions every 8 hours. The verified models were then merged into a single control stream while maintaining drug-specific structural components. Seven joint modelling strategies of increasing complexity were systematically evaluated: (i) a shared renal clearance covariate at the population level; (ii) correlated inter-individual variability (IIV) via off-diagonal OMEGA elements[2]; (iii) proportional clearance linking, where zidebactam clearance was defined as a proportional function of individual cefepime clearance[3]; (iv) PK clearance coupling with an estimable coupling strength parameter; (v) shared ETAs constraining variability terms to be identical across drugs[3]; and (vi-vii) combinations integrating proportional clearance linking or coupling with shared ETAs. Models were compared using the drop in objective function value (dOFV) between nested models, AIC/BIC, condition number, parameter precision, shrinkage, goodness-of-fit (GOF) plots, and visual predictive checks (VPCs). Predictive performance was assessed using the relative root mean square error (rRMSE) and mean absolute percentage error (MAPE), comparing the separate versus the final joint models. To assess differences in PTA, Monte Carlo simulations (n=1000) were performed in individuals with augmented renal clearance (MDRD 130 and 150 mL/min/1.73m²) receiving cefepime 2000 mg and zidebactam 1000 mg every 8 hours, aiming for a PK/PD target of 39.2% fT>1/8xMIC and 30.9% fT>1/128xMIC, respectively, across MIC values of 64, 128, and 256 mg/L for Acinetobacter baumannii.
Results
Both base models were successfully verified and merged into one, with stable parameter estimates and satisfactory GOF and VPC diagnostics, confirming adequate model reproducibility prior to joint modelling. Among the seven joint approaches evaluated, the shared renal clearance covariate yielded only an insignificant improvement in OFV, while correlated ETAs resulted in unstable model runs. The remaining approaches showed significant improvements, with the combination of proportional clearance linking and shared ETAs identified as the best-performing joint model based on the lowest AIC/BIC and condition number, with adequate GOF plots and VPC, physiologically plausible parameter estimates, and acceptable precision and shrinkage. In the final joint model, all parameter estimates demonstrated adequate precision, with RSE below 50% for structural parameters and below 30% for IIV parameters, and shrinkage remained acceptable across all parameters. The typical clearance of zidebactam in the separate model (6.21 L/h) was re-parameterised to a proportional linking parameter of 1.06, indicating that individual zidebactam clearance was approximately equal to individual cefepime clearance and that zidebactam clearance was now driven by cefepime clearance through the proportional linking parameter rather than estimated independently. IIV on zidebactam clearance decreased markedly from approximately 35.9% coefficient of variation (CV) to 5.5% CV, indicating that nearly all individual variability in zidebactam clearance is explained by the transmitted variability from cefepime clearance through the proportional link. Prediction performance metrics were comparable between separate and joint models, with rRMSE improving by 4.6% for cefepime and 12.6% for zidebactam. MAPE showed minimal differences of less than 1% for both drugs, indicating that synchronous modelling did not compromise predictive accuracy. The PTA analysis demonstrated that the joint model predominantly predicted lower PTA values than the separate model. However, at MIC 64 mg/L, both models achieved a >95% PTA for the simulated regimen. For cefepime at MDRD 130 mL/min/1.73m², PTA decreased by 0.8% and 5.8% at MICs of 64 and 128 mg/L, respectively, with a 0.1% increase at 256 mg/L. At MDRD 150 mL/min/1.73m², the PTA decreased with 1.3%, 5.0%, and 1.0% across the same MICs, respectively. Across all conditions in both models, zidebactam achieved 100% PTA.
Conclusion
Proportional clearance linking combined with shared ETAs was identified as the most suitable framework for synchronous popPK analysis of cefepime and zidebactam, providing the best balance between model fit and parsimony. The joint model maintained comparable predictive accuracy to separate models, while the PTA analysis demonstrated that independent modelling predominantly overestimated the PTA. These findings highlight the importance of accounting for shared PK variability in co-administered drugs and provide a practical framework applicable to other combination therapies.
References:
[1] Khalid K, Rox K. All roads lead to Rome: enhancing the probability of target attainment with different pharmacokinetic/pharmacodynamic modelling approaches. Antibiotics (Basel). 2023;12(4):690.
[2] Xie R, Rogers H, Chow JW, Soto E, Raber SR. Population pharmacokinetic/ pharmacodynamic modeling to optimize aztreonam-avibactam dose regimens for adult patients. Antimicrob Agents Chemother. 2025;69(8):e01950-24.
[3] Wallenburg E, ter Heine R, Schouten JA, Raaijmakers J, ten Oever J, Kolwijck E, et al. An integral pharmacokinetic analysis of piperacillin and tazobactam in plasma and urine in critically ill patients. Clin Pharmacokinet. 2022;61(6):907–918.
Reference: PAGE 34 (2026) Abstr 12094 [www.page-meeting.org/?abstract=12094]
Poster: Drug/Disease Modelling - Other Topics