NONMEM Estimates Research Articles

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%.

Digoxin population pharmacokinetics from routine clinical data: role of patient characteristics for estimating dosing regimens.

Routine clinical pharmacokinetic data collected from patients receiving digoxin have been analysed to evaluate the role of patient characteristics for estimating dosing regimens. The data were analysed using NONMEM, a computer program designed for population pharmacokinetic analysis that allows pooling of data. The pharmacokinetic model of digoxin was described using a one-compartment steady-state model. The effect of a variety of developmental and demographic factors on clearance was investigated. NONMEM estimates indicate that digoxin clearance was influenced by the demographic variables of age, total body weight, serum creatinine and sex. The interindividual variability in digoxin clearance was modelled with additive error with an estimated standard deviation of 46.15 L day-1 and the intraindividual variability, or residual error was 0.209 ng mL-1. The dosing method based on clearance values obtained by NONMEM analysis allowed the prediction of the steady-state concentration as a function of maintenance dose with acceptable error for therapeutic drug monitoring.

Detection of Carbamazepine-induced Changes in Valproic Acid Relative Clearance in Man by Simple Pharmacokinetic Screening

Selecting the optimum dose of valproic acid is difficult because the pharmacokinetics are complicated by inter-patient variability and by effects arising as a result of co-administration with other antiepileptic drugs. The multiple peak approach has been used to evaluate the effect of age, total body weight, dose, gender and comedication (carbamazepine-induced change) on population estimates of valproic acid relative clearance. Routine clinical pharmacokinetic data (n = 479) were collected from 207 epilepsy patients on combination therapy. The data were analysed by a simple steady-state pharmacokinetic model with the use of NONMEM, a computer program designed for population pharmacokinetic analysis that enables pooling of data. NONMEM estimates suggested that the rate of valproic acid clearance in patients receiving concomitant administration of valproic acid and carbamazepine decreased non-linearly with increasing total body weight in the maturation process, and increased non-linearly with increasing valproic acid dose. The clearance in females was 5.7% less than in males. NONMEM estimates also suggested that the rate of valproic acid clearance increased non-linearly with increasing carbamazepine dose. Concomitant administration of valproic acid and carbamazepine with other antiepileptic drugs resulted in an increase in valproic acid clearance of 10%. The final regression model of valproic acid relative clearance was CL = 6.06TBW-0.168 x DOSE0.414 x CBZDOSE0.093 x 0.943GEN x 1.10CO, where CL is the clearance (mL kg-1 h-1), TBW is the total body weight (kg), DOSE is the dose of valproic acid, CBZDOSE is the dose of carbamazepine, GEN = 0 for males and 1 for females and CO = 0 for concomitant administration of valproic acid and carbamazepine and 1 for concomitant administration of valproic acid and carbamazepine with other antiepileptic drugs. This technique can be used to estimate the pharmacokinetic parameters of a population from sparse data collected during routine clinical care and to determine the extent to which patient characteristics influence drug pharmacokinetics.

Phenobarbitone population pharmacokinetics from routine clinical data: role of patient characteristics for estimating dosing regimens.

Routine clinical pharmacokinetic data collected from patients receiving phenobarbitone have been analysed to evaluate the role of patient characteristics for estimating dosing regimens. The data were analysed using NONMEM, a computer program designed for population pharmacokinetic analysis that allows pooling of data. The pharmacokinetic model of phenobarbitone was described using a one-compartment steady-state model. The effect of a variety of developmental and demographic factors on clearance was investigated. NONMEM estimates indicated a nonlinear function of total body weight as the optimum adjustment of phenobarbitone clearance. Concomitant administration of phenobarbitone and other antiepileptic drugs showed a decrease of phenobarbitone clearance in young children. The dosing method based on clearance values obtained by NONMEM analysis allowed the prediction of the steady-state concentration as a function of maintenance dose with acceptable error for therapeutic drug monitoring.

A feasibility study of the multiple-peak approach for pharmacokinetic screening: population-based investigation of valproic acid relative clearance using routine clinical pharmacokinetic data.

The multiple-peak approach was used to evaluate the effect of age, body mass, dose and gender on the population estimates of valproic acid relative clearance. Routine clinical pharmacokinetic data (n = 474) was collected from 250 patients receiving valproic acid and no other drug. The data was analysed according to a simple steady-state pharmacokinetic model using NONMEM, a computer program designed for population pharmacokinetic analysis allowing pooling of data. The final regression model for relative clearance (CL, mL kg-1 h-1) was: CL = 18.9 x body weight(-0.276) x daily dose(0.142) x gender where gender = 1 for males, 0.877 for females. NONMEM estimates suggested that the rate of valproic acid clearance decreased nonlinearly with increasing body weight in the maturation process, and increased nonlinearly with increasing valproic acid dose (mg kg-1 day-1). The clearance in females was about 11% less than in males. These estimates were similar to those detected from previous studies.

Effect of radiation on the penetration of irinotecan in rat cerebrospinal fluid

Anticancer agents are useful for treating brain tumors, but sub therapeutic concentrations due to decreased blood-brain barrier (BBB) penetration limit their effectiveness. This study evaluated the effect of cranial radiation on the pharmacokinetics of irinotecan in plasma and cerebrospinal fluid (CSF). Rats (n = 48) were treated with irinotecan (10 mg/kg), and then administered 10 or 20 Gy or sham irradiation as control after drug. The pharmacokinetics for irinotecan, SN-38, and APC were measured in plasma and CSF over 6 h. Up to 7 plasma samples per animal were collected, and one CSF sample was collected per animal (serial sacrifice design). Population pharmacokinetic analysis was performed with NONMEM, and radiation tested as a covariate for the fraction of irinotecan (f(CSF)) entering the CSF. The estimate of f(CSF) (% and RSE) was 0.165 (73.5) for the control group and 0.265 (66.5) for radiation-treated groups, respectively (P < 0.05). Predictive check plots showed that the model adequately described the overall trend and variability in the observed data. The median values of bootstrap parameters were similar to the NONMEM estimates based on the original data set. These results indicate that cranially administered radiation can increase the penetration of anticancer agents such as irinotecan into the CSF. Studies that evaluate radiation-fractionation, radiation-time course effect relationships, blood-brain barrier and blood-tumor barrier effects for irinotecan and other anticancer agents are warranted.

Derivation of various NONMEM estimation methods

Derivation of various NONMEM estimation methods

Derivation of various NONMEM estimation methods

Various estimation methods and the lack of a systematic derivation of the core objective function implemented in NONMEM for nonlinear mixed effect modeling has caused consistent confusion and inquiry among scientists who routinely use NONMEM for data analysis. This paper provides a detailed derivation of the objective functions for the most commonly used estimation methods in NONMEM, such as the Laplacian method, the first-order conditional estimation method (FOCE) with or without interaction, and the first-order method (FO). In addition, models with homogenous or heterogeneous residual error were used to demonstrate the relationship between the objective functions derived from two different types of approximation, namely Laplacian approximation of log-likelihood and linearized model approximation. The relationship between these estimation methods and those implemented in SAS and Splus is discussed.

Mixed-effects modelling of the interspecies pharmacokinetic scaling of pegylated human erythropoietin

The aim of this study was to develop a population pharmacokinetic model for interspecies allometric scaling of pegylated r-HuEPO (PEG-EPO) pharmacokinetics to man. A total of 927 serum concentrations from 193 rats, 6 rabbits, 34 monkeys, and 9 dogs obtained after a single dose of PEG-EPO, administered by the i.v. (dose range: 12.5–550 μg/kg) and s.c. (dose range: 12.5–500 μg/kg) routes, were pooled in this analysis. An open two-compartment model with first-order absorption and lag time (Tlag) and linear elimination from the central compartment was fitted to the data using the NONMEM V software. Body weight (WT) was used as a scaling factor and the effect of brain weight (BW), sex, and pregnancy status on the pharmacokinetic parameters was investigated. The final model was evaluated by means of a non-parametric bootstrap analysis and used to predict the PEG-EPO pharmacokinetic parameters in healthy male subjects. The systemic clearance (CL) in males was estimated to be 4.08WT1.030 × BW−0.345 ml/h. In females, the CL was 90.7% of the CL in males. The volumes of the central (Vc) and the peripheral (Vp) compartment were characterized as 57.8WT0.959 ml, and 48.1WT1.150 ml, respectively. Intercompartmental flow was estimated at 2.32WT0.930 ml/h. Absorption rate constant (Ka) was estimated at 0.0538WT−0.149. The absolute s.c. bioavailability F was calculated at 52.5, 80.2, and 49.4% in rat, monkey, and dog, respectively. The interindividual variability in the population pharmacokinetic parameters was fairly low (<35%). Non-parametric bootstrap confirmed the accuracy of the NONMEM estimates. The mean model predicted pharmacokinetic parameters in healthy male subjects of 70 kg were estimated at: CL: 26.2 ml/h; Vc: 3.6 l; Q: 286 l/h; Vp: 6.9 l, and Ka: 0.031 h −1. The population pharmacokinetic model developed was appropriate to describe the time course of PEG-EPO serum concentrations and their variability in different species. The model predicted pharmacokinetics of PEG-EPO in humans suggest a less frequent dosing regimen relative to erythropoietin and darbepoetin, potentially leading to a simplification of anemia management.

Does sex affect theophylline Emax? A mixture model method

Background The use of sex as a covariate to explain systematic differences in peak expiratory flow rate (PEFR) after treatment with theophylline has been studied using the likelihood ratio test (LRT) with NONMEM. Results were equivocal and depended on the NONMEM estimation method. Method A mixture model was used with NONMEM to estimate the probability that a model with an effect of sex on Emax (PEFR) was preferred over the same model without sex. The mixture model was also used to test an allometric function of body weight as a covariate on Emax. The evidence for a model including sex on Emax (Pr(sex)) was computed from the average of 1000 non-parametric bootstrap estimates of the mixing parameter. The odds favouring a model can be calculated from Pr(sex)/(1−Pr(sex)). The odds against the model is the inverse of this relationship. Results The odds favouring sex without weight were 4.7 while the odds against sex when allometric weight scaling was added into the model were 8.3. Conclusions Sex does not affect the Emax for theophylline. Any influence of sex can be explained by weight. Mixtures of models offer an alternative to the LRT for choosing among models. Clinical Pharmacology & Therapeutics (2005) 77, P93–P93; doi: 10.1016/j.clpt.2004.12.247

Non-linear mixed-effects pharmacokinetic/pharmacodynamic modelling in NLME using differential equations.

The standard software for non-linear mixed-effect analysis of pharmacokinetic/pharmacodynamic (PK/PD) data is NONMEM while the non-linear mixed-effects package NLME is an alternative as long as the models are fairly simple. We present the nlmeODE package which combines the ordinary differential equation (ODE) solver package odesolve and the non-linear mixed effects package NLME thereby enabling the analysis of complicated systems of ODEs by non-linear mixed-effects modelling. The pharmacokinetics of the anti-asthmatic drug theophylline is used to illustrate the applicability of the nlmeODE package for population PK/PD analysis using the available data analysis tools in R for model inspection and validation. The nlmeODE package is numerically stable and provides accurate parameter estimates which are consistent with NONMEM estimates.

Estimation of pharmacokinetic parameters from non-compartmental variables using Microsoft Excel®

This study was conducted to develop a method, termed 'back analysis (BA)', for converting non-compartmental variables to compartment model dependent pharmacokinetic parameters for both one- and two-compartment models. A Microsoft Excel spreadsheet was implemented with the use of Solver and visual basic functions. The performance of the BA method in estimating pharmacokinetic parameter values was evaluated by comparing the parameter values obtained to a standard modelling software program, NONMEM, using simulated data. The results show that the BA method was reasonably precise and provided low bias in estimating fixed and random effect parameters for both one- and two-compartment models. The pharmacokinetic parameters estimated from the BA method were similar to those of NONMEM estimation.

Population-Based Investigation of Carbamazepine Relative Clearance Using Routine Clinical Pharmacokinetic Data in Japan

A multiple peak approach was used to evaluate the effect of age, total bodyweight, dose, gender and co-medication on the population estimates of carbamazepine relative clearance. Routine clinical pharmacokinetic data (n = 689) were collected from 317 patients receiving carbamazepine. The data were analysed according to a simple steady-state pharmacokinetic model with the use of NONMEM, a computer program designed for population pharmacokinetic analysis that allows pooling of data. NONMEM estimates indicated that the rate of carbamazepine clearance decreased nonlinearly with increasing total body weight in the maturation process, and increased nonlinearly with increasing daily dose (mg/kg) of carbamazepine. Concomitant administration of carbamazepine and other antiepileptic drugs showed an increase in carbamazepine clearance. These estimates were similar to those detected in previous studies.

POPULATION PHARMACOKINETICS OF DIGOXIN IN DUCHENNE MUSCULAR DYSTROPHY (DMD) PATIENTS

Routine clinical pharmacokinetic data collected from Duchenne muscular dystrophy (DMD) patients receiving digoxin have been analyzed to evaluate the role of patients' characteristics for estimating dosing regimens. The data were analyzed using NONMEM, a computer program designed for population pharmacokinetic analysis that allows pooling of data. The pharmacokinetic model of digoxin was described using a one-compartment steady-state model. The effect of factors on digoxin clearance was investigated. NONMEM estimates indicate that digoxin clearance was influenced by the variables of body weight and combination with diuretics. The interindividual variability in digoxin clearance was modeled with proportional error with an estimated coefficient of variation of 25%, and the intraindividual variability in digoxin concentration was modeled with equal error with an estimated standard deviation of 0.0828 ng ml(minus sign1). In order to determine whether the population parameters obtained in this study were accurate, we administered digoxin according to individual dosage regimens in four DMD patients, using these values obtained by the Bayesian method. As a result, we found that mean prediction error, which indicates the deviation of prediction accuracy for digoxin concentration in plasma, was small, as were mean absolute prediction error and root mean squared error, showing the accuracy of this prediction method. The dosing method based on clearance values obtained by NONMEM analysis allowed the prediction of the steady-state concentration as a function of maintenance dose with acceptable error for therapeutic drug monitoring.

Minimal Modelling of Glucose Kinetics by Nonmem Estimation

Minimal Modelling of Glucose Kinetics by Nonmem Estimation

Lithium Population Pharmacokinetics from Routine Clinical Data

Routine clinical pharmacokinetic data (n = 303) collected from 90 patients receiving lithium have been analyzed to evaluate the role of patient characteristics for estimating dosing regimens. The data were analyzed using NONMEM, a computer program designed for population pharmacokinetic analysis that allows pooling of data. The pharmacokinetic model of lithium was described using a one-compartment steady-state model. The effect of a variety of developmental and demographic factors on clearance was investigated. NONMEM estimates indicated that lithium clearance was influenced by the demographic variables of age, total body weight, and serum creatinine. The interindividual variability in lithium clearance was modeled with proportional error with an estimated coefficient of variation of 25.1%. The intraindividual variability, or residual error, was 14.3%. The dosing method based on clearance values obtained by NONMEM analysis allowed the prediction of the minimum steady-state lithium concentration as a function of maintenance dose with acceptable error for therapeutic drug monitoring.

Experience with NONMEM: analysis of routine phenytoin clinical pharmacokinetic data.

NONMEM, a program package the produces the extended least squares estimates of population parameters for a nonlinear mixed-effect model, has been applied to two data sets from patients routinely receiving phenytoin. A general model for the data is proposed. The models used in previous, standard-method analyses of each data set are compared to the general model using NONMEM. The comparison involves two questions: The first asks whether the parameters estimated previously agree with NONMEM estimates when the original model is used. We find that for fixed-effect parameters they generally do, while for interindividual random-effect parameters the previous methods' estimates appear upward biased relative to NONMEM. Second, the original model per se is compared to the general model by comparing the best fit to each. The general model is clearly superior. NONMEM's ability to distinguish among models, and to precisely estimate their parameters from sparse individual data, is illustrated and verified.

Evaluation of methods for estimating population pharmacokinetic parameters. III. Monoexponential model: routine clinical pharmacokinetic data.

Individual pharmacokinetic parameters quantify the pharmacokinetics of an individual, while population pharmacokinetic parameters quantify population mean kinetics, interindividual kinetic variability, and residual variability, including intraindividual variability and measurement error. Individual pharmacokinetics are estimated by fitting a pharmacokinetic model to individual data. Population pharmacokinetic parameters have traditionally been estimated by doing this separately for each individual, and then combining the individual parameter estimates, the Standard Two Stage (STS) approach. Another approach, NONMEM, appropriately pools data across individuals and is therefore less dependent on individual parameter estimates. This study provides further evidence of NONMEM's validity and usefulness by comparing both approaches on simulated routine-type pharmacokinetic data arising from a monoexponential model. The estimates of population parameters (notably those describing interindividual variability) provided by the STS method are poorer than those provided by NONMEM, especially when there is considerable residual error. Further, NONMEM's estimates of population parameters do not require that the data be restricted to special types of routine data such as those obtained only at steady state, or only at peak or trough, nor do the estimates improve with such data. NONMEM's estimates do improve, however, when a data set is enhanced by the addition of single-observation-per-individual type data. Thus, population parameters can be estimated efficiently from data that simulate real clinical pharmacokinetic conditions.

Evaluation of methods for estimating population pharmacokinetic parameters. II. Biexponential model and experimental pharmacokinetic data.

Individual pharmacokinetic parameters quantify the pharmacokinetics of an individual, while population pharmacokinetic parameters quantify population mean-kinetics, interindividual variability, and residual variability, including intraindividual variability and measurement error. Individual pharmacokinetics are estimated by fitting individual data to a pharmacokinetic model. Population pharmacokinetic parameters have been estimated either by fitting all individuals' data together as though there were no individual kinetic difference, the naive pooled data (NPD) approach, or by fitting each individuals' data separately and then combining the individual parameter estimates, the two stage (TS) approach. A third approach, NONMEM, takes a middle course between these. This study provides further evidence of NONMEM's validity by comparing, using simulation, the three approaches on three types of data sets corresponding to three typical types of pharmacokinetic studies. The estimates of population parameters provided by the NPD method are poorer than those provided by either of the other methods. The estimates provided by the TS method are adequate for mean values and for residual variability, but not for interindividual kinetic variability. NONMEM's estimates are as good as those of the TS method for mean parameters and for residual variability, and considerably better for interindividual variability. The latter estimates are still not acceptable in an absolute sense. This is probably due, not to an intrinsic fault of the method (as it is in the case of the TS approach), but to an insufficient number of individuals being studied.