A methodology to estimate population pharmacokinetic parameters from aggregate concentration-time data and its application to gevokizumab.
Evangelos Karakitsios (1), Aris Dokoumetzidis (1)
(1) School of Pharmacy, University of Athens, Greece
Objectives: The aim of the present study was to develop and assess the performance of a methodology to estimate the population pharmacokinetic (PK) parameters along with the Inter-Individual Variabilities (IIVs) from reported aggregate concentration-time data, in particular mean plasma concentrations and their standard deviations (SDs) versus time, such as those often found in published graphs. This method was applied to published data of gevokizumab, a novel monoclonal anti-interleukin-1β antibody in order to estimate population pharmacokinetic (PopPK) parameters of a minimal physiological pharmacokinetic model (mPBPK).
Methods: A function was constructed in R based on an mPBPK model [1] that predicts (output) the mean concentrations and their standard deviations (SD) from a Monte Carlo (MC) simulation of a number of patients generated from the distributions of the mPBPK model parameters including IIV for some of them (input). The model was parametrized in terms of the vascular reflection coefficients σ1 and σ2 for tight and leaky tissues, respectively, drug plasma clearance CL, and the IIV terms ωCL and ωV, for the SD of the lognormal distributions of plasma clearance and volume of human body respectively. This function was fitted to data of mean concentration and SD in order to estimate the model parameters and their corresponding IIV using Maximum likelihood method with a quasi-Newton optimiser. Latin Hypercube sampling was used for the MC step to improve speed. Also, two separate exponential residual error terms were assumed, one for the means and one for the SDs. To evaluate the performance of the method simulations and estimations were carried out calculating the bias and precision of the estimates, from 1000 simulated datasets. Furthermore representative VPCs from the simulated datasets were plotted. Ultimately, scanned data from literature of gevokizumab [2] were used to estimate the population parameters of an mPBPK model of the drug and the goodness of fit was assessed using diagnostic plots. The entire analysis was performed using R software (Rstudio).
Results: The per cent relative bias in the population parameters σ1, σ2, CL, ωCL and ωV was -0.11, 0.15, -0.14, -6.6 and 5.8 respectively. The respective per cent relative root mean squared error was 1.3, 1.8, 0.6, 8.1 and 9.0. The results show that the method is capable of estimating all the parameters with satisfactory bias and precision. Also, internal validation of VPC resulted that the model is robust and describes well the data including the observed variability. The estimates of the pharmacokinetic parameters of gevokizumab took the following values (SE in parentheses) in the final model: σ1=0.973 (3.37%), σ2=0.750 (3.10%), CLp=0.00652 L/hr (0.0168%), ωCL=0.0974 (1.36%), ωV=0.102 (1.08%) and residual error parameters were sigma1=0.112 and sigma2=0.461.
Conclusions: We present a methodology to estimate population pharmacokinetic parameters using only patients’ mean plasma concentrations and their SDs vs time. The methodology describes adequately simulated data, indicating that the loss of information from averaging can be recovered. This method could be applied to any PK model in order to estimate PopPK parameters when only a published graph with aggregate PK profile and SDs is available.
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.
