Influence of interoccasion variability on parameter estimates of a population pharmacokinetic model under various sparse study designs
Emily Behrens (1), Sebastian G. Wicha (1)
(1) Dept. of Clinical Pharmacy, Institute of Pharmacy, University of Hamburg, Germany
Objectives:
Sampling schemes to inform pharmacokinetic (PK) modelling in phase II clinical studies are sparse. Typically, sampling is performed in a single dosing interval, which conceptionally hampers the quantification of interoccasion variability (IOV) of a PK parameter. The aim of the simulation study was to evaluate the impact of IOV on the accuracy and precision of parameter estimates of a population PK model under different sampling schemes.
Methods:
The simulation study was conducted using an adapted one compartment model describing the population PK of linezolid in multidrug-resistant tuberculosis patients [1]. All data was simulated and analysed using NONMEM (version 7.5.0), operated using the PsN (version 5.0.0) stochastic simulation and estimation tool (SSE) [2].
A daily dose of 600 mg was simulated for 150 patients. Two different types of models were used for simulations of PK data in one to three observed dosing occasions (OCC):
- models with IIVs of 32% on CL, V, KA and IOV of 25% (IOV25) or 75% (IOV75) included on each PK parameter (CL, V or KA) at a time and
- a model with IIVs of 32% on CL, V, KA without IOV.
The sampling schemes
- [a] 2, 3, 4, 5 h and
- [b] 0, 2, 3, 4, 5 h after dose were evaluated.
For parameter estimation five candidate models were used: the same model as used for simulation, a model with IIVs on CL, V, KA without IOV, and models with IIVs on Cl, V, KA and an IOV on other PK parameters than those used in the simulation model.
Bias and imprecision, expressed as relative root mean squared error (rRMSE) and relative bias (rbias) of the population parameters, were used as evaluation criteria. Moreover, the difference in objective function value was analysed regarding the type I error rate to falsely include a variability parameter that was not simulated or power (at alpha=0.05) to detect a simulated (‘true’) IOV in a given scenario.
Results:
Power/Type I error:
Overall, the power to detect IOV increased with inclusion of more observed OCCs due to more observed datapoints and thereby better-informed models. Moreover, SSEs performed with IOV75 led to higher power outcome than those with IOV25.
For scenario (1), where IOV25 on CL and IIVs were simulated simultaneously, for sampling in one OCC, the power was 0.6% or 77.8% to detect an IOV, for sampling scheme (a) or (b), respectively. In addition, when IOV25 was implemented on V for sampling scheme (a) or (b), the power was 5.8%/58.4% demonstrating an increase in the power to detect an IOV caused by one additional sample at time 0 h. In comparison to scenario (1) with IOV on CL or V, an IOV on KA was most difficult to estimate and less likely to be detected even in two OCCs in sampling scheme (a) or (b), e.g. 67.2%/51.4% (IOV25) also showing, that sampling scheme (b) did not result in higher power to detect the IOV on KA.
For scenario (2), where solely IIV was simulated, for sampling scheme (b) in one OCC, the type I error rate to falsely include an IOV for the alternative models with IOV25 on Cl was 18.4%. Only in presence of two and three OCCs the type I error rates declined noticeably, e.g. 0.8% for two OCCs with IOV25 on CL. Compared to that, lower type I error rates of ≤0.2% were observed in sampling scheme (a) for one OCC.
rBias/rRMSE:
The imprecision in estimating the IOV decreased when a second or third OCC was observed, e.g. in scenario (1) with IOV75 on CL for sampling scheme (a) the drop in rRMSE from one OCC to two OCCs was 32%. Neglecting a simulated IOV in the estimation step led to higher rbias values on residual error, e.g. rbias increased on IOV25 on V in three OCCs in sampling scheme (b) from 1.4 to 39.8%.
Conclusions:
This study has shown that in some scenarios -based on power calculations- it is unlikely to detect an IOV that is truly present. The inclusion of a 0 h after dose sample, while technically allowing to parameterise an IOV (although with high imprecision), leads to higher type I error rate and thus a higher risk of falsely detecting the presence of IOV. Small differences between the evaluated sampling schemes can lead to increased power to identify IOV but increase the type I error rate at the same time. Sampling schemes including a 0 h sample in combination with sampling in at least two observed OCCs improved the ability to correctly parameterize and estimate the IOV with good accuracy and precision. Further models will be evaluated to assess the detectability of IOV in e.g. a two-compartment model.
References:
[1] A. K. Tietjen, N. Kroemer, D. Cattaneo, S. Baldelli, and S. G. Wicha, ‘Population pharmacokinetics and target attainment analysis of linezolid in multidrug-resistant tuberculosis patients’, Br. J. Clin. Pharmacol., vol. 88, no. 4, pp. 1835–1844, Apr. 2022, doi: 10.1111/bcp.15102.
[2] L. Lindbom, P. Pihlgren, and N. Jonsson, ‘PsN-Toolkit—A collection of computer intensive statistical methods for non-linear mixed effect modeling using NONMEM’, Comput. Methods Programs Biomed., vol. 79, no. 3, pp. 241–257, Sep. 2005, doi: 10.1016/j.cmpb.2005.04.005. Acknowledgement:
This project has received funding from the Innovative Medicines Initiative 2 Joint Undertaking (JU) under grant agreement No 101007873. The JU receives support from the European Union’s Horizon 2020 research and innovation programme and EFPIA, Deutsches Zentrum für Infektionsforschung e. V. (DZIF), and Ludwig-Maximilians-Universität München (LMU). EFPIA/AP contribute to 50% of funding, whereas the contribution of DZIF and the LMU University Hospital Munich has been granted by the German Federal Ministry of Education and Research.