Evangelos Karakitsios (1), Aris Dokoumetzidis (1)
(1) School of Pharmacy, University of Athens, Greece
Objectives: To develop a methodology, following [3], to estimate the population pharmacokinetic (PopPK) parameters along with the related Inter-Group Variabilities (IGVs) from multiple reported aggregate concentration-time datasets, in particular mean plasma concentrations and their standard deviations (SDs) versus time, of different dosage-groups. The method was applied to published data of gevokizumab [2] for which a minimal physiological pharmacokinetic model (mPBPK) has been proposed [1].
Methods: Initially a simulation study was carried out and the method was applied to simulated aggregate data of only one dosage-group. The plasma concentrations from a Monte Carlo (MC) simulation of a number of patients were generated in R from the distributions of the mPBPK model parameters including inter-individual variability (IIV) for some of them. Then, for each time point the mean plasma concentration and its SD were obtained. The same procedure was also followed in the Bayesian platform of Stan in order to obtain the respective predicted aggregate data except for a much greater number of patients was used in the MC simulation. Latin Hypercube sampling was used for this MC step to improve speed. More particularly, the model was parametrized in terms of the two vascular reflection coefficients σ1 and σ2 for tight and leaky tissues, respectively, drug plasma clearance CL, as well as the IIV terms: ωCL and ωV, for the SD of the lognormal distributions of plasma clearance and volume of human body respectively. Also, two separate exponential residual error terms were assumed, one for the means and one for the SDs. The Bayesian priors used for the model’s parameters were as less informative as possible. The predicted data were lastly fitted in Stan to the simulated data. Indicative VPCs were plotted and to further evaluate the performance of the method simulations and estimations were carried out calculating the bias and precision of the estimates, from 200 simulated datasets.
Afterwards, the same concept was applied to five literature gevokizumab datasets [2] in order to estimate the drug’s PopPK parameters. The clinical aggregate data were captured using Digitizer software and the Bayesian framework described above was combined with hierarchical modeling utilizing a mixed effects approach. IGV was considered for the three PK parameters of each group (CL, σ1, σ2), following log-Student’s t-distribution, because of the small size of the dosage-groups, estimating the respective mean group and IGV terms. Also, separate IIV terms were assumed for each group without a distributional assumption for IGV, in a semi-hierarchical approach. The model on the platform of Stan was run with 4 chains with 2000 samples each and used 2000 warm-up iterations. The goodness of fit was assessed using diagnostic plots. All simulations were performed with R and the PopPK parameters were estimated in RStan.
Results: In the simulation study of 200 datasets, the percent relative bias in the population parameters σ1, σ2, CL, ωCL and ωV was 0.057, -0.083, -0.016, 0.72 and 5.64 respectively, while the respective percent relative root mean squared error was 1.23, 1.63, 0.53, 5.34 and 8.65. Also, the estimates of the PopPK parameters of gevokizumab took the following values in the final model: mean inter-group values σ1=0.9504, σ2=0.7674, CL=0.0064L/hr, CVs of IIV for each group, ωCL[1]=0.1813, ωCL[2]= 0.1138, ωCL[3]= 0.0798, ωCL[4]=0.0374, ωCL[5]=0.2002, ωV[1]= 0.1676, ωV[2]= 0.3213, ωV[3]= 0.0733, ωV[4]=0.0960 and ωV[5]= 0.1000, respectively. The estimates of the IGVs were: CL_sd=0.1254, σ1_sd=0.0338 and σ2_sd=0.1810. Moreover, for each parameter, the MCMC diagnostic parameters were: bulk Effective Sample Size (ESS) and tail-ESS > 100 for each chain, Rhat < 1.01 and all the Monte Carlo standard errors were less than 0.0029.
Conclusions: The results of the simulation study suggest that the method is capable of estimating all the parameters with satisfactory bias and precision and also the VPCs show that the model describes well the simulated data, although the parameters have been estimated only from the aggregation of these data. Furthermore, the convergence of gevokizumab’s final model was good. Conclusively, this method could be used when multiple aggregate concentration-time datasets from different sources need to be combined in a meta-analysis approach in order to estimate the PopPK parameters of a drug.
References:
[1] Cao Y, Balthasar JP, Jusko WJ. Second-generation minimal physiologically-based pharmacokinetic model for monoclonal antibodies. J Pharmacokinet Pharmacodyn. 2013;40:597–607.
[2] Cavelti-Weder C, Babians-Brunner A, Keller C, Stahel MA, Kurz-Levin M, Zayed H, Solinger AM, Mandrup-Poulsen T, Dinarello CA, Donath MY. Effects of gevokizumab on glycemia and inflammatory markers in type 2 diabetes. Diabetes Care. 2012;35:1654–1662.
[3] Karakitsios E., Dokoumetzidis A. A methodology to estimate population pharmacokinetic parameters from aggregate concentration-time data and its application to gevokizumab. PAGE 28 (2019) Abstr 8895 [www.page-meeting.org/?abstract=8895].
Reference: PAGE () Abstr 9441 [www.page-meeting.org/?abstract=9441]
Poster: Methodology - Estimation Methods