Comparison of calculation results of five population pharmacokinetic analysis tools / 中国临床药理学与治疗学

AIM: To compare the results calculated by population pharmacokinetic analysis tools Phoenix NLME, Monolix, R nlmixr package and CPhaMAS cloud platform with the gold standard sofeware NONMEM. METHODS: Fifty sparse sampling data sets based on a one-compartment model and fifty dense sampling data sets based on a two-compartment model were simulated, and the above five analysis tools were used to calculate the population typical value, individual variability and individual pharmacokinetic parameters. RESULTS: The population typical value and individual variability calculated by CPhaMAS and Phoenix NLME had the highest matching degree with NONMEM, followed by nlmixr. Monolix had the lowest matching degree, but Monolix and nlmixr might be more robust. The correspondence between clearance and distribution volume was better than the absorption rate constant. Except the absorption rate constant calculated by Monolix and intercompartmental clearance calculated by nlmixr, the correlation coefficients of individual pharmacokinetic parameters calculated by all analytical tools were greater than 0.99. CONCLUSION: The results calculated by the above four population pharmacokinetic analysis tools are highly correlated with that of NONMEM.

Meropenem population pharmacokinetic model for the Chinese elderly established by model-based META analysis / 中国临床药理学与治疗学

AIM: To build a meropenem population pharmacokinetic model for Chinese elderly through model-based meta-analysis. METHODS: Informations including dosing regimen, sampling times, concentrations, sample size, age, gender, body weight (BW) and creatinine clearance were extracted after the literature were retrieved. The model was built by NONMEM. Stepwise covariate modeling strategy was used for covariates analysis. RESULTS: A two-compartment model was applied to describe meropenem pharmacokinetics. After stepwise covariate modeling, covariates that remained significant in the final model were creatinine clearance (CLcr) on CL and the BW on V

Characterization of circadian blood pressure patterns using non-linear mixed effects modeling

Characterizing the time course of baseline or pre-drug blood pressure is important in acquiring unbiased estimates of antihypertensive drug effect. In this study, we recruited 23 healthy male volunteers and measured systolic (SBP) and diastolic blood pressure (DBP) over 24 hours on an hourly basis. Using a non-linear mixed effects model, circadian rhythm observed in blood pressure measurements was described by incorporating two cosine functions with periods 24 and 12 hours. A mixture model was applied to identify subgroups exhibiting qualitatively different circadian rhythms. Our results suggested that 78% of the study population, defined as ‘dippers’, demonstrated a typical circadian profile with a morning rise and a nocturnal dip. The remaining 22% of the subjects defined as ‘non-dippers’, however, were not adequately described using the typical profile and demonstrated an elevation of blood pressure during night-time. Covariate search identified weight as being positively correlated with mesor of SBP. Visual predictive checks using 1,000 simulated datasets were performed for model validation. Observations were in agreement with predicted values in ‘dippers’, but deviated slightly in ‘non-dippers’. Our work is expected to serve as a useful reference in assessing systematic intra-day blood pressure fluctuations and antihypertensive effects as well as assessing drug safety of incrementally modified drugs.

Performance of a mixture model by the degree of a missing categorical covariate when estimating clearance in NONMEM

The accuracy and predictability of mixture models in NONMEM® may change depending on the relative size of inter-individual differences and the size of the differences in the parameters between subpopulations. This study explored the accuracy of mixture models when dealing with missing a categorical covariate under various situations that may occur in reality. We generated simulation data under various scenarios where genotypes representing extensive metabolizers (EM) and poor metabolizers (PM) of drug-metabolizing enzymes affect the clearance of a drug by different degrees, and the inter-individual variations in clearance are different for each scenario. From each simulated datum, a specific proportion of the covariate (genotype information) was randomly removed. Based on these simulation data, the proportion of each individual subpopulation and the clearance were estimated using a mixture model. Overall, the clearance estimate was more accurate when the difference in clearance between subpopulations was large, and the inter-individual variations were small. In some scenarios that showed higher ETA or epsilon shrinkage, the clearance estimates were significantly biased. The mixture model made better predictions for individuals in the EM subpopulation than for individuals in the PM subpopulation. However, the estimated values were not significantly affected by the tested ratio, if the sample size was secured to some extent. The current simulation study suggests that when the coefficient of variation of inter-individual variations of clearance exceeds 40%, the mixture model should be used carefully, and it should be taken into account that shrinkage can bias the results.

Prediction of the human in vivo antiplatelet effect of S- and R-indobufen using population pharmacodynamic modeling and simulation based on in vitro platelet aggregation test

Indobufen (Ibustrin®), a reversible inhibitor of platelet aggregation, exists in two enantiomeric forms in 1:1 ratio. Here, we characterized the anti-platelet effect of S- and R-indobufen using response surface modeling using NONMEM® and predicted the therapeutic doses exerting the maximal efficacy of each enantioselective S- and R-indobufen formulation. S- and R-indobufen were added individually or together to 24 plasma samples from drug-naïve healthy subjects, generating 892 samples containing randomly selected concentrations of the drugs of 0–128 mg/L. Collagen-induced platelet aggregation in platelet-rich plasma was determined using a Chrono-log Lumi-Aggregometer. Inhibitory sigmoid I(max) model adequately described the anti-platelet effect. The S-form was more potent, whereas the R-form showed less inter-individual variation. No significant interaction was observed between the two enantiomers. The anti-platelet effect of multiple treatments with 200 mg indobufen twice daily doses was predicted in the simulation study, and the effect of S- or R-indobufen alone at various doses was predicted to define optimal dosing regimen for each enantiomer. Simulation study predicted that 200 mg twice daily administration of S-indobufen alone will produce more treatment effect than S-and R-mixture formulation. S-indobufen produced treatment effect at lower concentration than R-indobufen. However, inter-individual variation of the pharmacodynamic response was smaller in R-indobufen. The present study suggests the optimal doses of R-and S-enantioselective indobufen formulations in terms of treatment efficacy for patients with thromboembolic problems. The proposed methodology in this study can be applied to the develop novel enantio-selective drugs more efficiently.

Population pharmacokinetic analysis of metformin administered as fixed-dose combination in Korean healthy adults

Metformin, an oral antihyperglycemic agent, is widely used as the first-line pharmacotherapy for type 2 diabetes mellitus (T2DM). It has been in use for several decades as numerous different formulations. However, despite its use, population pharmacokinetic (PK) modeling of metformin is not well developed. The aim of the present study was to evaluate the effect of formulation on PK parameters by developing a population PK model of metformin in Koreans and using this model to assess bioequivalence. We used a comparative PK study of a single agent and a fixed-dose combination of metformin in 36 healthy volunteers. The population PK model of metformin was developed using NONMEM (version 7.3). Visual predictive checks and bootstrap methods were performed to determine the adequacy of the model. The plasma concentration-time profile was best described by a two-compartment, first-order elimination model with first-order absorption followed by zeroorder absorption with lag time. From the covariate analysis, formulation had significant effect (p < 0.01) on relative bioavailability (F = 0.94) and first-order absorption constant (Ka = 0.83), but the difference was within the range of bioequivalence criteria. No other covariate was shown to have significant effect on PK parameters. The PK profile of the disposition phase was consistent with the published literature. However, in the present study, the multiple peaks found during the absorption phase implied the possible diversity of absorption PK profile depending on formulation or population. Unlike traditional bioequivalence analysis, the population PK model reflects formulation differences on specific parameters and reflected simulation can be performed.

Comparison of various estimation methods for the parameters of Michaelis-Menten equation based on in vitro elimination kinetic simulation data

The Michaelis-Menten equation is one of the best-known models describing the enzyme kinetics of in vitro drug elimination experiments, and takes a form of equation relating reaction rate (V) to the substrate concentration ([S]) via the maximum reaction rate (Vmax) and the Michaelis constant (Km). The current study was conducted to compare the accuracy and precision of the parameter estimates in the Michaelis-Menten equation from various estimation methods using simulated data. One thousand replicates of simulated [S] over serial time data were generated using the results of a previous study, incorporating additive or combined error models as a source of random variables in the Monte-Carlo simulation using R. From each replicate of simulated data, Vmax and Km were estimated by five different methods, including traditional linearization methods and nonlinear ones without linearization using NONMEM. The relative accuracy and precision of the estimated parameters were compared by the median values and their 90% confidence intervals. Overall, Vmax and Km estimation by nonlinear methods (NM) provided the most accurate and precise results from the tested 5 estimation methods. The superiority of parameter estimation by NM was even more evident in the simulated data incorporating the combined error model. The current simulation study suggests that NMs using a program such as NONMEM provide more reliable and accurate parameter estimates of the Michaelis-Menten equation than traditional linearization methods in in vitro drug elimination kinetic experiments.

Influence of Oxygen to Population Pharmacokinetics/Pharmacodynamics of Alcohol in Healthy Volunteers

OBJECTIVE: To develop a population pharmacokinetics (PK)/pharmacodynamics (PD) model for alcohol in healthy volunteers and to elucidate individual characteristics to affects alcohol's PK or PD including dissolved oxygen. METHODS: Following multiple intakes of total 540 mL alcohol (19.42 v/v%) to healthy volunteer, blood alcohol concentration was measured using a Breathe alcohol analyser (Lion SD-400 Alcolmeter®). A sequential population PK/PD modeling was performed using NONMEM (ver 7.3). RESULTS: Eighteen healthy volunteer were included in the study. PK model of alcohol was well explained by one-compartment model with first-order absorption and Michaelis-Menten elimination kinetics. K(a), V/F, V(max), K(m) is 8.1 hr⁻¹, 73.7 L, 9.65 g/hr, 0.041 g/L, respectively. Covariate analysis revealed that gender significantly influenced V(max) (Male vs Female, 9.65 g/hr vs 7.38 g/hr). PD model of temporary systolic blood pressure decreasing effect of alcohol was explained by biophase model with inhibitory E(max) model. K(e0), I(max), E(0), IC(50) were 0.23 hr⁻¹, 44.9 mmHg, 138 mmHg, 0.693 g/L, respectively. CONCLUSION: Model evaluation results suggested that this PK/PD model was robust and has good precision.

Pharmacometric models simulation using NONMEM, Berkeley Madonna and R

In this tutorial, we introduce a differential equation simulation model for use in pharmacometrics involving NONMEM, Berkeley Madonna, and R. We report components of the simulation code and similarities/differences between software, rather than how to use each software. Depending on the purpose of the simulation, an appropriate tool can be selected for effective communication.

Forensic science meets clinical pharmacology: pharmacokinetic model based estimation of alcohol concentration of a defendant as requested by a local prosecutor's office

Drunk driving is a serious social problem. We estimated the blood alcohol concentration of a defendant on the request of local prosecutor's office in Korea. Based on the defendant's history, and a previously constructed pharmacokinetic model for alcohol, we estimated the possible alcohol concentration over time during his driving using a Bayesian method implemented in NONMEM®. To ensure generalizability and to take the parameter uncertainty of the alcohol pharmacokinetic models into account, a non-parametric bootstrap with 1,000 replicates was applied to the Bayesian estimations. The current analysis enabled the prediction of the defendant's possible blood alcohol concentrations over time with a 95% prediction interval. The results showed a high probability that the alcohol concentration was ≥ 0.05% during driving. The current estimation of the alcohol concentration during driving by the Bayesian method could be used as scientific evidence during court trials.

Decreased potency of fimasartan in liver cirrhosis was quantified using mixed-effects analysis

Fimasartan is a nonpeptide angiotensin II receptor blocker. In a previous study that compared the pharmacokinetics (PK) of fimasartan between patients with hepatic impairment (cirrhosis) and healthy subjects, the exposure to fimasartan was found to be higher in patients, but the decrease of blood pressure (BP) was not clinically significant in those with moderate hepatic impairment. The aims of this study were to develop a population PK-pharmacodynamic (PD) model of fimasartan and to evaluate the effect of hepatic function on BP reduction by fimasartan using previously published data. A 2-compartment linear model with mixed zero-order absorption followed by first-order absorption with a lag time adequately described fimasartan PK, and the effect of fimasartan on BP changes was well explained by the inhibitory sigmoid function in the turnover PK-PD model overlaid with a model of circadian rhythm (NONMEM version 7.2). According to our PD model, the lower BP responses in hepatic impairment were the result of the increased fimasartan EC₅₀ in patients, rather than from a saturation of effect. This is congruent with the reported pathophysiological change of increased plasma ACE and renin activity in hepatic cirrhosis.

Population pharmacokinetics of intravenous infusing busulfan in patients undergoing hematopoietic stem cell transplantation / 中国药学杂志

OBJECTIVE: To establish a population pharmacokinetic model of intravenous infusing busulfan in HSCT patients, and to explore physiological and pathological factors which may influence the pharmacokinetic parameters. METHODS: We have collected clinical history information of 35 patients undergoing HSCT surgery and taking busulfan intravenous infusion for treatment. These information such as physiological and pathological factors and busulfan concentration data were used to perform the population pharmacokinetic analysis by applying the method of nonlinear mixed effects modeling(NONMEM). RESULTS: A statistical model of busulfan is established, including variables such as body weight, sex, serum creatinine clearance. The success of 973 out of 1 000 times resampling trials (by bootstrap) shows that the newly parameters value are very close to the estimate value calculated from the final model by NONMEM, which demonstrates the established population pharmacokinetic model of busulfanis stable, effective and predictable. CONCLUSION: The population pharmacokinetic model is established, which is capable of depicting the pharmacokinetic characteristics of busulfan. It is found that patients' weight, gender and creatinine clearance influence pharmacokinetic parameters, which can be useful and valuable for the clinical individualized dosing regimens.

Mixed?effects analysis of increased rosuvastatin absorption by coadministered telmisartan

The Cmax and AUC of rosuvastatin increase when it is coadministered with telmisartan. The aim of this study was to explore which of the pharmacokinetic (PK) parameters of rosuvastatin are changed by telmisartan to cause such an interaction. We used data from drug–drug interaction (DDI) studies of 74 healthy volunteers performed in three different institutions. Rosuvastatin population PK models with or without telmisartan were developed using NONMEM (version 7.3). The plasma concentration–time profile of rosuvastatin was best described by a two-compartment, first-order elimination model with simultaneous Erlang and zero-order absorption when given rosuvastatin alone. When telmisartan was coadministered, the zero-order absorption fraction of rosuvastatin had to be omitted from the model because the absorption was dramatically accelerated. Notwithstanding the accelerated absorption, the relative bioavailability (BA) parameter estimate in the model demonstrated that the telmisartan-induced increase in BA was only about 20% and the clearance was not influenced by telmisartan at all in the final PK model. Thus, our model implies that telmisartan may influence the absorption process of rosuvastatin rather than its metabolic elimination. This may be used as a clue for further physiologically based PK (PBPK) approaches to investigate the mechanism of rosuvastatin–telmisartan DDI.

R-based reproduction of the estimation process hidden behind NONMEM® Part 2: First-order conditional estimation

The first-order conditional estimation (FOCE) method is more complex than the first-order (FO) approximation method because it estimates the empirical Bayes estimate (EBE) for each iteration. By contrast, it is a further approximation of the Laplacian (LAPL) method, which uses second-order expansion terms. FOCE without INTERACTION can only be used for an additive error model, while FOCE with INTERACTION (FOCEI) can be used for any error model. The formula for FOCE without INTERACTION can be derived directly from the extension of the FO method, while the FOCE with INTERACTION method is a slight simplification of the LAPL method. Detailed formulas and R scripts are presented here for the reproduction of objective function values by NONMEM.

Tips for the choice of initial estimates in NONMEM

The importance of precise information and knowledge on the initial estimates (IEs) in modeling has not been paid its due attention so far. By focusing on the IE, this tutorial may serve as a practical guide for beginners in pharmacometrics. A 'good' set of IEs rather than arbitrary values is required because the IEs where NONMEM kicks off its estimation may influence the subsequent objective function minimization. To provide NONMEM with acceptable IEs, modelers should understand the exact meaning of THETA, OMEGA and SIGMA based on physiology. In practice, problems related to the value of the IE are more likely to occur for THETAs rather than the random-effect terms. Because it is almost impossible for a modeler to give a precise IE for OMEGAs at the beginning, it may be a good practice to start at relatively small IEs for them. NONMEM may fail to converge when too small IEs are provided for residual error parameters; thus, it is recommended to give sufficiently large values for them. The understandings on the roles, meanings and implications of IEs even help modelers in troubleshooting situations which frequently occur over the whole modeling process.

Population pharmacokinetics of imatinib mesylate in healthy Korean subjects

Imatinib (Gleevec™; Novartis Pharmaceuticals) is an orally administered protein-tyrosine kinase inhibitor. The goal of this study was to investigate the population pharmacokinetics (PK) of imatinib (as imatinib mesylate) in healthy male Koreans. A total of 1,773 plasma samples from 112 healthy male volunteers enrolled in three phase I clinical studies were used. Among the subjects, 76 received 400 mg and 36 received 100 mg as single oral doses. Peripheral blood sampling for PK analysis was done at 0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 6, 8, 12, 24, 48, 60 and 72 (at 400 mg group) h after dosing. The firstorder conditional estimation with interaction method of NONMEM® (ver. 7.3) was used to build the population PK model. A two-compartment model with Weibull absorption and elimination gave the best fit to the data. The estimates of clearance (CL/F), volume of central compartment (Vc/F), intercompartmental clearance (Q/F), peripheral volume (Vp/F) and their interindividual variabily (%CV) were 13.6 L/h (23.4%), 153 L (29.2%), 8.64 L/h (35.9%) and 64 L (67%), respectively.

Population pharmacokinetics and inter-laboratory variability of sildenafil and its metabolite after oral administration in Korean healthy male volunteers

This study was to clarify population pharmacokinetics (PK) of sildenafil and its metabolite, N-desmethyl sildenafil (NDS) in Korean healthy male population using a pooled data from multiple clinical trials in consideration of inter-institution and inter-laboratory difference. A population PK analysis was performed with data of 243 healthy volunteers from five single-center (4 centers) comparative PK trials. The dataset included 7,376 sildenafil and NDS concentration (3,688 for each analyte) observed during 24 hours after the single dose of original sildenafil (either 50 mg or 100 mg of Viagra®). The plasma concentration was assayed in two laboratories. Various model structure was tested and the final model was evaluated using visual predictive checks. Demographic and clinical variables were assessed as potential covariates for PK parameters. A one-compartment first-order elimination model with proportional error was selected for the dispositional characteristics of sildenafil, and two-compartment model was chosen for NDS. Three transit compartments with Erlang-type absorption for fast absorption pathway and one compartment for slow absorption pathway constructed overall absorption model. The first-pass effect was rejected since it does not improve the model. The difference of NDS level by the bioanalysis laboratory was selected as the only covariate. Even though a direct comparison was difficult, the general trend in PK of sildenafil and NDS for Korean healthy male was considered similar to that of the other populations reported previously. It is recommended that the laboratory effect should be explored and evaluated when dataset is built using results from several laboratories.

Population pharmacokinetic analysis of the multiple peaks phenomenon in sumatriptan

The objective of this study was to develop a population pharmacokinetic (PK) model for sumatriptan, which frequently shows an atypical absorption profile with multiple peaks. Sumatriptan, a selective agonist for the vascular serotonin (5-HT1) receptor that causes vasoconstriction of the cerebral arteries, is used for the acute treatment of migraine attack with or without aura. Despite its relatively high between-subject variability, few reports have addressed PK modeling of sumatriptan. Plasma data obtained after a single 50-mg oral dose of sumatriptan in 26 healthy Korean male subjects were used. Blood samples were collected 0 (predose), 0.25, 0.5, 0.75, 1, 1.5, 2, 2.5, 3, 4, 6, 8, 10, and 12 h after dosing. Plasma sumatriptan concentrations were analyzed using UPLC/MS/MS. Population PK analysis was performed using plasma concentration data for sumatriptan with NONMEM (ver. 7.2). A total of 364 concentrations of sumatriptan were captured by a one-compartment model with first-order elimination, and a combined transit compartment model and first-order absorption with lag time was successful in describing the PK with multiple peaks in the absorption phase of sumatriptan. The creatinine clearance as a covariate significantly (P < 0.01) influenced the absorption fraction (f ). The final model was validated through a visual predictive check and bootstrapping with no serious model misspecification.

R-based reproduction of the estimation process hidden behind NONMEM(R) Part 1: first-order approximation method

NONMEM(R) is the most-widely used nonlinear mixed effects modelling tool introduced into population PK/PD analysis. Even though thousands of pharmaceutical scientists utilize NONMEM(R) routinely for their data analysis, the various estimation methods implemented in NONMEM(R) remain a mystery for most users due to the complex statistical and mathematical derivations underlying the algorithm used in NONMEM(R). In this tutorial, we demonstrated how to directly obtain the objective function value and post hoc eta for the first order approximation method by the use of R. We hope that this tutorial helps pharmacometricians understand the underlying estimation process of nonlinear mixed effects modelling.