Drug–drug interaction predictions with PBPK models and optimal multiresponse sampling time designs: application to midazolam and a phase I compound. Part 2: clinical trial results

Purpose To compare results of population PK analyses obtained with a full empirical design (FD) and an optimal sparse design (MD) in a Drug–Drug Interaction (DDI) study aiming to evaluate the potential CYP3A4 inhibitory effect of a drug in development, SX, on a reference substrate, midazolam (MDZ). Secondary aim was to evaluate the interaction of SX on MDZ in the in vivo study. Methods To compare designs, real data were analysed by population PK modelling technique using either FD or MD with NONMEM FOCEI for SX and with NONMEM FOCEI and MONOLIX SAEM for MDZ. When applicable a Wald test was performed to compare model parameter estimates, such as apparent clearance (CL/F), across designs. To conclude on the potential interaction of SX on MDZ PK, a Student paired test was applied to compare the individual PK parameters (i.e. log(AUC) and log(C_max)) obtained either by a non-compartmental approach (NCA) using FD or from empirical Bayes estimates (EBE) obtained after fitting the model separately on each treatment group using either FD or MD. Results For SX, whatever the design, CL/F was well estimated and no statistical differences were found between CL/F estimated values obtained with FD (CL/F = 8.2 l/h) and MD (CL/F = 8.2 l/h). For MDZ, only MONOLIX was able to estimate CL/F and to provide its standard error of estimation with MD. With MONOLIX, whatever the design and the administration setting, MDZ CL/F was well estimated and there were no statistical differences between CL/F estimated values obtained with FD (72 l/h and 40 l/h for MDZ alone and for MDZ with SX, respectively) and MD (77 l/h and 45 l/h for MDZ alone and for MDZ with SX, respectively). Whatever the approach, NCA or population PK modelling, and for the latter approach, whatever the design, MD or FD, comparison tests showed that there was a statistical difference (P < 0.0001) between individual MDZ log(AUC) obtained after MDZ administration alone and co-administered with SX. Regarding C_max, there was a statistical difference (P < 0.05) between individual MDZ log(C_max) obtained under the 2 administration settings in all cases, except with the sparse design with MONOLIX. However, the effect on C_max was small. Finally, SX was shown to be a moderate CYP3A4 inhibitor, which at therapeutic doses increased MDZ exposure by a factor of 2 in average and almost did not affect the C_max. Conclusion The optimal sparse design enabled the estimation of CL/F of a CYP3A4 substrate and inhibitor when co-administered together and to show the interaction leading to the same conclusion as the full empirical design.     

Performance Comparison of Various Maximum Likelihood Nonlinear Mixed-Effects Estimation Methods for Dose–Response Models

Estimation methods for nonlinear mixed-effects modelling have considerably improved over the last decades. Nowadays, several algorithms implemented in different software are used. The present study aimed at comparing their performance for dose-response models. Eight scenarios were considered using a sigmoid E(max) model, with varying sigmoidicity and residual error models. One hundred simulated datasets for each scenario were generated. One hundred individuals with observations at four doses constituted the rich design and at two doses, the sparse design. Nine parametric approaches for maximum likelihood estimation were studied: first-order conditional estimation (FOCE) in NONMEM and R, LAPLACE in NONMEM and SAS, adaptive Gaussian quadrature (AGQ) in SAS, and stochastic approximation expectation maximization (SAEM) in NONMEM and MONOLIX (both SAEM approaches with default and modified settings). All approaches started first from initial estimates set to the true values and second, using altered values. Results were examined through relative root mean squared error (RRMSE) of the estimates. With true initial conditions, full completion rate was obtained with all approaches except FOCE in R. Runtimes were shortest with FOCE and LAPLACE and longest with AGQ. Under the rich design, all approaches performed well except FOCE in R. When starting from altered initial conditions, AGQ, and then FOCE in NONMEM, LAPLACE in SAS, and SAEM in NONMEM and MONOLIX with tuned settings, consistently displayed lower RRMSE than the other approaches. For standard dose-response models analyzed through mixed-effects models, differences were identified in the performance of estimation methods available in current software, giving material to modellers to identify suitable approaches based on an accuracy-versus-runtime trade-off.     

Implementation and Evaluation of the SAEM Algorithm for Longitudinal Ordered Categorical Data with an Illustration in Pharmacokinetics–Pharmacodynamics

Analysis of longitudinal ordered categorical efficacy or safety data in clinical trials using mixed models is increasingly performed. However, algorithms available for maximum likelihood estimation using an approximation of the likelihood integral, including LAPLACE approach, may give rise to biased parameter estimates. The SAEM algorithm is an efficient and powerful tool in the analysis of continuous/count mixed models. The aim of this study was to implement and investigate the performance of the SAEM algorithm for longitudinal categorical data. The SAEM algorithm is extended for parameter estimation in ordered categorical mixed models together with an estimation of the Fisher information matrix and the likelihood. We used Monte Carlo simulations using previously published scenarios evaluated with NONMEM. Accuracy and precision in parameter estimation and standard error estimates were assessed in terms of relative bias and root mean square error. This algorithm was illustrated on the simultaneous analysis of pharmacokinetic and discretized efficacy data obtained after a single dose of warfarin in healthy volunteers. The new SAEM algorithm is implemented in MONOLIX 3.1 for discrete mixed models. The analyses show that for parameter estimation, the relative bias is low for both fixed effects and variance components in all models studied. Estimated and empirical standard errors are similar. The warfarin example illustrates how simple and rapid it is to analyze simultaneously continuous and discrete data with MONOLIX 3.1. The SAEM algorithm is extended for analysis of longitudinal categorical data. It provides accurate estimates parameters and standard errors. The estimation is fast and stable.     

A survey of population analysis methods and software for complex pharmacokinetic and pharmacodynamic models with examples

An overview is provided of the present population analysis methods and an assessment of which software packages are most appropriate for various PK/PD modeling problems. Four PK/PD example problems were solved using the programs NONMEM VI beta version, PDx-MCPEM, S-ADAPT, MONOLIX, and WinBUGS, informally assessed for reasonable accuracy and stability in analyzing these problems. Also, for each program we describe their general interface, ease of use, and abilities. We conclude with discussing which algorithms and software are most suitable for which types of PK/PD problems. NONMEM FO method is accurate and fast with 2-compartment models, if intra-individual and interindividual variances are small. The NONMEM FOCE method is slower than FO, but gives accurate population values regardless of size of intra- and interindividual errors. However, if data are very sparse, the NONMEM FOCE method can lead to inaccurate values, while the Laplace method can provide more accurate results. The exact EM methods (performed using S-ADAPT, PDx-MCPEM, and MONOLIX) have greater stability in analyzing complex PK/PD models, and can provide accurate results with sparse or rich data. MCPEM methods perform more slowly than NONMEM FOCE for simple models, but perform more quickly and stably than NONMEM FOCE for complex models. WinBUGS provides accurate assessments of the population parameters, standard errors and 95% confidence intervals for all examples. Like the MCPEM methods, WinBUGS's efficiency increases relative to NONMEM when solving the complex PK/PD models.     

Evaluation of Uncertainty Parameters Estimated by Different Population PK Software and Methods

The uncertainty associated with parameter estimations is essential for population model building, evaluation, and simulation. Summarized by the standard error (SE), its estimation is sometimes questionable. Herein, we evaluate SEs provided by different non linear mixed-effect estimation methods associated with their estimation performances. Methods based on maximum likelihood (FO and FOCE in NONMEM^TM, nlme in Splus^TM, and SAEM in MONOLIX) and Bayesian theory (WinBUGS) were evaluated on datasets obtained by simulations of a one-compartment PK model using 9 different designs. Bootstrap techniques were applied to FO, FOCE, and nlme. We compared SE estimations, parameter estimations, convergence, and computation time. Regarding SE estimations, methods provided concordant results for fixed effects. On random effects, SAEM and WinBUGS, tended respectively to under or over-estimate them. With sparse data, FO provided biased estimations of SE and discordant results between bootstrapped and original datasets. Regarding parameter estimations, FO showed a systematic bias on fixed and random effects. WinBUGS provided biased estimations, but only with sparse data. SAEM and WinBUGS converged systematically while FOCE failed in half of the cases. Applying bootstrap with FOCE yielded CPU times too large for routine application and bootstrap with nlme resulted in frequent crashes. In conclusion, FO provided bias on parameter estimations and on SE estimations of random effects. Methods like FOCE provided unbiased results but convergence was the biggest issue. Bootstrap did not improve SEs for FOCE methods, except when confidence interval of random effects is needed. WinBUGS gave consistent results but required long computation times. SAEM was in-between, showing few under-estimated SE but unbiased parameter estimations.     

Simultaneous vs. Sequential Analysis for Population PK/PD Data II: Robustness of Methods

A model can be fit to joint PK/PD data (concentration and effect) either simultaneously or sequentially. The results of a companion paper suggested that when the data-analytic and true models agree, a particular sequential approach is computationally faster than the simultaneous one, yet produces hardly less precise PD parameter estimates, and for suitable designs, about as accurate PD standard error estimates. In this paper, we compare the performance of various methods for the case that the data-analytic model is misspecified. We illustrate these methods by applying them to a set of real data. Using NONMEM, population PK/PD observations were simulated under various study designs according to a one- or two-compartment PK model and direct Emax or sigmoid Emax model. A one-compartment PK model and Emax PD model were fit to the simulated observations by simultaneous and sequential methods. Predictive performance (interpolation and extrapolation) of PD and the type-I error rate of a likelihood ratio test are compared. The real data set consists of PK and (more frequent) PD observations after administration of the muscle relaxant vecuronium. When only the PK data-analytic model is misspecified, the simultaneous method has greater precision than the sequential methods. However a sequential method that uses a non-parametric PK model performs better than both other methods when PK model misspecification is severe. When the PD data-analytic model is misspecified, sequential and simultaneous methods perform similarly. The analysis of the real data shows that the PK fitted with the simultaneous method can be quite sensitive to PD model misspecification, yielding a possible diagnostic for this type of misspecification.     

Estimation of Population Pharmacokinetic Parameters of Saquinavir in HIV Patients with the MONOLIX Software

In nonlinear mixed-effects models, estimation methods based on a linearization of the likelihood are widely used although they have several methodological drawbacks. Kuhn and Lavielle (Comput. Statist. Data Anal. 49:1020–1038 (2005)) developed an estimation method which combines the SAEM (Stochastic Approximation EM) algorithm, with a MCMC (Markov Chain Monte Carlo) procedure for maximum likelihood estimation in nonlinear mixed-effects models without linearization. This method is implemented in the Matlab software MONOLIX which is available at http://www.math.u-psud.fr/~lavielle/monolix/logiciels. In this paper we apply MONOLIX to the analysis of the pharmacokinetics of saquinavir, a protease inhibitor, from concentrations measured after single dose administration in 100 HIV patients, some with advance disease. We also illustrate how to use MONOLIX to build the covariate model using the Bayesian Information Criterion. Saquinavir oral clearance (CL/F) was estimated to be 1.26 L/h and to increase with body mass index, the inter-patient variability for CL/F being 120%. Several methodological developments are ongoing to extend SAEM which is a very promising estimation method for population pharmacockinetic/pharmacodynamic analyses.     

Simultaneous vs. Sequential Analysis for Population PK/PD Data I: Best-Case Performance

Dose [-concentration]-effect relationships can be obtained by fitting a predictive pharmacokinetic (PK)-pharmacodynamic (PD) model to both concentration and effect observations. Either a model can befit simultaneously to all the data ("simultaneous" method), or first a model can befit to the PK data and then a model can be fit to the PD data, conditioning in some way on the PK data or on the estimates of the PK parameters ("sequential" method). Using simulated data, we compare the performance of the simultaneous method with that of three sequential method variants with respect to computation time, estimation precision, and inference. Using NONMEM, under various study designs, observations of one type of PK and one type of PD response from different numbers of individuals were simulated according to a one-compartment PK model and direct Emax PD model, with parameters drawn from an appropriate population distribution. The same PK and PD models were fit to these observations using simultaneous and sequential methods. Performance measures include computation time,fraction of cases for which estimates are successfully obtained, precision of PD parameter estimates, precision of PD parameter standard error estimates, and type-I error rates of a likelihood ratio test. With the sequential method, computation time is less, and estimates are more likely to be obtained. Using the First Order Conditional Estimation (FOCE) method, a sequential approach that conditions on both population PK parameter estimates and PK data, estimates PD parameters and their standard errors about as well as the "gold standard" simultaneous method, and saves about 40% computation time. Type-I error rates of likelihood ratio test for both simultaneous and sequential approaches are close to the nominal rates.     

Comparison of Nonmem 7.2 estimation methods and parallel processing efficiency on a target-mediated drug disposition model

The paper compares performance of Nonmem estimation methods--first order conditional estimation with interaction (FOCEI), iterative two stage (ITS), Monte Carlo importance sampling (IMP), importance sampling assisted by mode a posteriori (IMPMAP), stochastic approximation expectation-maximization (SAEM), and Markov chain Monte Carlo Bayesian (BAYES), on the simulated examples of a monoclonal antibody with target-mediated drug disposition (TMDD), demonstrates how optimization of the estimation options improves performance, and compares standard errors of Nonmem parameter estimates with those predicted by PFIM 3.2 optimal design software. In the examples of the one- and two-target quasi-steady-state TMDD models with rich sampling, the parameter estimates and standard errors of the new Nonmem 7.2.0 ITS, IMP, IMPMAP, SAEM and BAYES estimation methods were similar to the FOCEI method, although larger deviation from the true parameter values (those used to simulate the data) was observed using the BAYES method for poorly identifiable parameters. Standard errors of the parameter estimates were in general agreement with the PFIM 3.2 predictions. The ITS, IMP, and IMPMAP methods with the convergence tester were the fastest methods, reducing the computation time by about ten times relative to the FOCEI method. Use of lower computational precision requirements for the FOCEI method reduced the estimation time by 3-5 times without compromising the quality of the parameter estimates, and equaled or exceeded the speed of the SAEM and BAYES methods. Use of parallel computations with 4-12 processors running on the same computer improved the speed proportionally to the number of processors with the efficiency (for 12 processor run) in the range of 85-95% for all methods except BAYES, which had parallelization efficiency of about 70%.     

Pharmacokinetic/Pharmacodynamic Modellingof GnRH Antagonist Degarelix: A Comparisonof the Non-linear Mixed-Effects Programs NONMEM and NLME

In this paper, the two non-linear mixed-effects programs NONMEM and NLME were compared for their use in population pharmacokinetic/pharmacodynamic (PK/PD) modelling. We have described the first-order conditional estimation (FOCE) method as implemented in NONMEM and the alternating algorithm in NLME proposed by Lindstrom and Bates. The two programs were tested using clinical PK/PD data of a new gonadotropin-releasing hormone (GnRH) antagonist degarelix currently being developed for prostate cancer treatment. The pharmacokinetics of intravenous administered degarelix was analysed using a three compartment model while the pharmacodynamics was analysed using a turnover model with a pool compartment. The results indicated that the two algorithms produce consistent parameter estimates. The bias and precision of the two algorithms were further investigated using a parametric bootstrap procedure which showed that NONMEM produced more accurate results than NLME together with the nlmeODE package for this specific study.     

Evaluation of Estimation Methods and Power of Tests of Discrete Covariates in Repeated Time-to-Event Parametric Models: Application to Gaucher Patients Treated by Imiglucerase

Analysis of repeated time-to-event data is increasingly performed in pharmacometrics using parametric frailty models. The aims of this simulation study were (1) to assess estimation performance of Stochastic Approximation Expectation Maximization (SAEM) algorithm in MONOLIX, Adaptive Gaussian Quadrature (AGQ), and Laplace algorithm in PROC NLMIXED of SAS and (2) to evaluate properties of test of a dichotomous covariate on occurrence of events. The simulation setting is inspired from an analysis of occurrence of bone events after the initiation of treatment by imiglucerase in patients with Gaucher Disease (GD). We simulated repeated events with an exponential model and various dropout rates: no, low, or high. Several values of baseline hazard model, variability, number of subject, and effect of covariate were studied. For each scenario, 100 datasets were simulated for estimation performance and 500 for test performance. We evaluated estimation performance through relative bias and relative root mean square error (RRMSE). We studied properties of Wald and likelihood ratio test (LRT). We used these methods to analyze occurrence of bone events in patients with GD after starting an enzyme replacement therapy. SAEM with three chains and AGQ algorithms provided good estimates of parameters much better than SAEM with one chain and Laplace which often provided poor estimates. Despite a small number of repeated events, SAEM with three chains and AGQ gave small biases and RRMSE. Type I errors were closed to 5%, and power varied as expected for SAEM with three chains and AGQ. Probability of having at least one event under treatment was 19.1%.     

Population Cell Life Span Models for Effects of Drugs Following Indirect Mechanisms of Action

Pharmacokinetic/pharmacodynamic (PK/PD) models for hematological drug effects exist that assume that cells are produced by a zero- or first-order process, survive for a specific duration (cell lifespan), and then are lost. Due to the fact that delay differential equations (DDE) are needed for cell lifespan models, their software implementation is not straightforward. Our objective is to demonstrate methods to implement three different cell lifespan models for dealing with hematological drug effects and to evaluate the performance of NONMEM to estimate the model parameters. For the basic lifespan indirect response (LIDR) model, cells are produced by a zero-order process and removed due to senescence. The modified LIDR model adds a precursor pool. The LIDR model of cytotoxicity assumes a three-pool indirect model to account for the cell proliferation with capacity-limited cytotoxicity followed by maturation, and removal from the circulation. A numerical method (method of steps) implementing DDE in NONMEM was introduced. Simulation followed by estimation was used to evaluate NONMEM performance and the impact of the minimization algorithm (first-order method vs. first-order conditional estimation method) and the model for residual variability on the estimates of the population parameters. The FOCE method combined with log-transformation of data was found to be superior. This report provides methodology that will assist in application of population methods for assessing hematological responses to various types of drugs     

A novel global search algorithm for nonlinear mixed-effects models using particle swarm optimization

NONMEM is one of the most popular approaches to a population pharmacokinetics/pharmacodynamics (PK/PD) analysis in fitting nonlinear mixed-effects models. As a local optimization algorithm, NONMEM usually requires an initial value close enough to the global optimum. This paper proposes a novel global search algorithm called P-NONMEM. It combines the global search strategy by particle swarm optimization (PSO) and the local estimation strategy of NONMEM. In the proposed algorithm, initial values (particles) are generated randomly by PSO, and NONMEM is implemented for each particle to find a local optimum for fixed effects and variance parameters. P-NONMEM guarantees the global optimization for fixed effects and variance parameters. Under certain regularity conditions, it also leads to global optimization for random effects. Because P-NONMEM doesn’t run PSO search for random effect estimation, it avoids tremendous computational burden. In the simulation studies, we have shown that P-NONMEM has much improved convergence performance than NONMEM. Even when the initial values were far away from the global optima, P-NONMEM converged nicely for all fixed effects, random effects, and variance components.     

Simultaneous versus sequential pharmacokinetic-pharmacodynamic population analysis using an iterative two-stage Bayesian technique

A method for simultaneous pharmacokinetic-pharmacodynamic (PK-PD) population analysis using an Iterative Two-Stage Bayesian (ITSB) algorithm was developed. The method was evaluated using clinical data and Monte Carlo simulations.Data from a clinical study with rocuronium in nine anesthetized patients and data generated by Monte Carlo simulation using a similar study design were analysed by sequential PK-PD analysis, PD analysis with nonparametric PK data and simultaneous PK-PD analysis. Both PK and PD data sets were 'rich' with respect to the number of measurements per individual. The accuracy and precision of the estimated population parameters were evaluated by comparing their mean error (ME) and root mean squared error (RMSE), respectively. The influence of PD model misspecification on the results was also investigated.The simultaneous PK-PD analysis resulted in slightly more precise population parameter estimates than the sequential PK-PD analysis and the nonparametric PK method. In the presence of PD model misspecification, however, simultaneous analysis resulted in poor PK parameter estimates, while sequential PK-PD analysis performed well.In conclusion, ITSB is a valuable technique for PK-PD population analysis of rich data sets. The sequential PK-PD method is better suited for the analysis of rich data than the simultaneous analysis.     

Development of a Complex Parent-Metabolite Joint Population Pharmacokinetic Model

This study aimed to develop a joint population pharmacokinetic model for an antipsychotic agent in development (S33138) and its active metabolite (S35424) produced by reversible metabolism. Because such a model leads to identifiability problems and numerical difficulties, the model building was performed using the FOCE-I and the Stochastic Approximation Expectation Maximization (SAEM) estimation algorithms in NONMEM and MONOLIX, respectively. Four different structural models were compared based on Bayesian information criteria. Models were first written as ordinary differential equations systems and then in closed form (CF) to facilitate further analyses. The impact of polymorphisms on genes coding for the CYP2C19 and CYP2D6 enzymes, respectively involved in the parent drug and the metabolite elimination were investigated using permutation Wald test. The parent drug and metabolite plasma concentrations of 101 patients were analyzed on two occasions after 4 and 8 weeks of treatment at 1, 3, 6, and 24 h following daily oral administration. All configurations led to a two compartment model with back-transformation of the metabolite into the parent drug and a first-pass effect. The elimination clearance of the metabolite through other processes than back-transformation was decreased by 35% [9-53%] in CYP2D6 poor metabolizer. Permutation tests were performed to ensure the robustness of the analysis, using SAEM and CF. In conclusion, we developed a complex joint pharmacokinetic model adequately predicting the impact of CYP2D6 polymorphisms on the parent drug and its metabolite concentrations through the back-transformation mechanism.     

Predictive performance of a semiparametric method to estimate population pharmacokinetic parameters using NONMEM

Routine clinical pharmacokinetic (PK) data collected from patients receiving inulin were analyzed to estimate population PK parameters; 560 plasma concentration determinations for inulin were obtained from 90 patients. The data were analyzed using NONMEM. The population PK parameters were estimated using a Constrained Longitudinal Splines (CLS) semiparametric approach and a first-order conditional method (FOCE). The mean posterior individual clearance values were 7.73 L/hr using both parametric and semiparametric methods. This estimation was compared with clearances estimated using standard nonlinear weighted least squares approach (reference value, 7.64 L/hr). The bias was not statistically different from zero and the precision of the estimates was 0.415 L/hr using parametric method and 0.984 L/hr using semiparametric method. To evaluate the predictive performances of the population parameters, 17 new subjects were used. First, the individual inulin clearance values were estimated from drug concentration-time curve using a nonlinear weighted least-squares method then they were estimated using the NONMEM POSTHOC method obtained using parametric and CLS methods as well as an alternative method based on a Monte Carlo simulation approach. The population parameters combined with two individual inulin plasma concentrations (0.25 and 2 hr) led to an estimation of individual clearances without bias and with a good precision. This paper not only evaluates the relative performance of the parametric and the CLS methods for sparse data but also introduces a new method for individual estimation.     

Pharmacokinetic-pharmacodynamic modelling in the early development phase of anti-psychotics: a comparison of the effects of clozapine, S 16924 and S 18327 in the EEG model in rats

1. The use of pharmacokinetic/pharmacodynamic (PK/PD) analysis in early compound development was investigated in the rat for two developmental anti-psychotic compounds with clozapine as a positive control. 2. Three plasma samples were collected from each of eight animals according to a pre-defined sampling matrix allowing a total of 12 time points for PK analysis. Quantitative electroencephalography (QEEG), particularly the theta and beta frequencies, was used as a measurement of pharmacological effect. 3. PK/KD modelling of the sparse PK data available relative to a rich set of PD data was achieved using a population approach in NONMEM (IV). Individual PK parameter estimates were incorporated into a PK/PD model. 4. Qualitative EEG changes in rat and human were similar for clozapine, but different for the two developmental compounds, suggesting that changes in these PD parameters may not be specifically related to the anti-psychotic activity. 5. Although no definitive data are available concerning the signal specificity of EEG frequency bands with respect to dopaminergic or serotonergic receptor activity, qualitative and quantitative differences seen in EEG parameters are likely to result from the multiple receptor occupancy for these compounds. 6. The results confirm the value of population PK/PD modelling in conjunction with sparse sampling to enable determination of concentration effect relationships in the pre-clinical development programme of CNS-active drugs.     

Predictive Performance of a Semiparametric Method to Estimate Population Pharmacokinetic Parameters Using NONMEM

Routine clinical pharmacokinetic (PK) data collected from patients receiving inulin were analyzed to estimate population PK parameters; 560 plasma concentration determinations for inulin were obtained from 90 patients. The data were analyzed using NONMEM. The population PK parameters were estimated using a Constrained Longitudinal Splines (CLS) semiparametric approach and a first-order conditional method (FOCE). The mean posterior individual clearance values were 7.73 L/hr using both parametric and semiparametric methods. This estimation was compared with clearances estimated using standard nonlinear weighted least squares approach (reference value, 7.64 L/hr). The bias was not statistically different from zero and the precision of the estimates was 0.415 L/hr using parametric method and 0.984 L/hr using semiparametric method. To evaluate the predictive performances of the population parameters, 17 new subjects were used. First, the individual inulin clearance values were estimated from drug concentration–time curve using a nonlinear weighted least-squares method then they were estimated using the NONMEM POSTHOC method obtained using parametric and CLS methods as well as an alternative method based on a Monte Carlo simulation approach. The population parameters combined with two individual inulin plasma concentrations (0.25 and 2 hr) led to an estimation of individual clearances without bias and with a good precision. This paper not only evaluates the relative performance of the parametric and the CLS methods for sparse data but also introduces a new method for individual estimation.     

Comparing the performance of FOCE and different expectation-maximization methods in handling complex population physiologically-based pharmacokinetic models

For the purpose of population pharmacometric modeling, a variety of mathematic algorithms are implemented in major modeling software packages to facilitate the maximum likelihood modeling, such as FO, FOCE, Laplace, ITS and EM. These methods are all designed to estimate the set of parameters that maximize the joint likelihood of observations in a given problem. While FOCE is still currently the most widely used method in population modeling, EM methods are getting more popular as the current-generation methods of choice because of their robustness with more complex models and sparse data structures. There are several versions of EM method implementation that are available in public modeling software packages. Although there have been several studies and reviews comparing the performance of different methods in handling relatively simple models, there has not been a dedicated study to compare different versions of EM algorithms in solving complex PBPK models. This study took everolimus as a model drug and simulated PK data based on published results. Three most popular EM methods (SAEM, IMP and QRPEM) and FOCE (as a benchmark reference) were evaluated for their estimation accuracy and converging speed when solving models of increased complexity. Both sparse and rich sampling data structure were tested. We concluded that FOCE was superior to EM methods for simple structured models. For more complex models and/ or sparse data, EM methods are much more robust. While the estimation accuracy was very close across EM methods, the general ranking of speed (fastest to slowest) was: QRPEM, IMP and SAEM. IMP gave the most realistic estimation of parameter standard errors, while under- and over- estimation of standard errors were observed in SAEM and QRPEM methods.     

Population pharmacokinetics and bayesian estimator of cyclosporine in pediatric renal transplant patients

Cyclosporine A (CsA) is an immunosuppressive drug widely used in pediatric renal graft recipients. Its large interindividual pharmacokinetic variability and narrow therapeutic index render therapeutic drug monitoring necessary. However, information about CsA pharmacokinetics is scarce and no population pharmacokinetic (popPK) studies in these populations have been reported so far. to the objectives of this study were 1) to develop a PKpop model and identify the individual factors influencing the variability of CsA pharmacokinetics in pediatric kidney recipients; and 2) to build a Bayesian estimator allowing the estimation of the main PK parameters and exposure indices to CsA on the basis of a limited sampling strategy (LSS). The popPK analysis was performed using the NONMEM program. A total of 256 PK profiles of CsA collected in 98 pediatric renal transplant patients (mean age 9.7 +/- 4.5 years old) within the first year posttransplantation were studied. A 2-compartment model with first-order elimination, and Erlang distribution to describe the absorption phase, fitted the data adequately. For Bayesian estimation, the best LSS was determined based on its performance in estimating area under the concentration-time curve (AUC0-12h) and validated in an independent group of 20 patients. The popPK analysis identified body weight and posttransplant delay as individual factors influencing the apparent central volume of distribution and the apparent clearance, respectively. Bayesian estimation allowed accurate prediction of AUC0-12h using predose, C1h, and C3h blood samples with a mean bias between observed and estimated AUC of 0.5% +/- 11% and good precision (root mean square error = 10.9%). This article reports the first popPK study of CsA in pediatric renal transplant patients. It confirms the reliability and feasibility of CsA AUC estimation in this population. The body weight and the posttransplantation delay were identified to influence PK interindividual variability of CsA and were included in the Bayesian estimator developed, which could be helpful in further clinical trials.