E. Niclas Jonsson

PsN-Toolkit-A collection of computer intensive statistical methods for non-linear mixed effect modeling using NONMEM

PsN-Toolkit is a collection of statistical tools for pharmacometric data analysis using the non-linear mixed effect modeling software NONMEM. The toolkit is object oriented and written in the programming language Perl using the programming library Perl-speaks-NONMEM (PsN). Five methods: the Bootstrap, the Jackknife, Log-likelihood Profiling, Case-deletion Diagnostics and Stepwise Covariate Model building are included as separate classes and may be used in user-written Perl scripts or through stand-alone command line applications. The tools are designed with the ability to cooperate and with an emphasis on common structures for workflow and result handling. Parallel execution of independent tool sections is supported on shared memory multiprocessor (SMP) computers, Mosix/openMosix clusters and distributed computing environments following the NorduGrid standard. In conclusion, PsN-Toolkit makes it easier to use the Bootstrap, the Jackknife, Log-likelihood Profiling, Case-deletion Diagnostics and Stepwise Covariate Model building in pharmacometric data analysis.

Perl-speaks-NONMEM (PsN)—a Perl module for NONMEM related programming

The NONMEM program is the most widely used nonlinear regression software in population pharmacokinetic/pharmacodynamic (PK/PD) analyses. In this article we describe a programming library, Perl-speaks-NONMEM (PsN), intended for programmers that aim at using the computational capability of NONMEM in external applications. The library is object oriented and written in the programming language Perl. The classes of the library are built around NONMEMs data, model and output files. The specification of the NONMEM model is easily set or changed through the model and data file classes while the output from a model fit is accessed through the output file class. The classes have methods that help the programmer perform common repetitive tasks, e.g. summarising the output from a NONMEM run, setting the initial estimates of a model based on a previous run or truncating values over a certain threshold in the data file. PsN creates a basis for the development of high-level software using NONMEM as the regression tool.

Assessment of Actual Significance Levels for Covariate Effects in NONMEM

The objectives of this study were to assess the difference between actual and nominal significance levels, as judged by the likelihood ratio test, for hypothesis tests regarding covariate effects using NONMEM, and to study what factors influence these levels. Also, a strategy for obtaining closer agreement between nominal and actual significance levels was investigated. Pharmacokinetic (PK) data without covariate relationships were simulated from a one compartment iv bolus model for 50 individuals. Models with and without covariate relationships were then fitted to the data, and differences in the objective function values were calculated. Alterations were made to the simulation settings; the structural and error models, the number of individuals, the number of samples per individual and the covariate distribution. Different estimation methods in NONMEM were also tried. In addition, a strategy for estimating the actual significance levels for a specific data set, model and parameter was investigated using covariate randomization and a real data set. Under most conditions when the first-order (FO) method was used, the actual significance level for including a covariate relationship in a model was higher than the nominal significance level. Among factors with high impact were frequency of sampling and residual error magnitude. The use of the first-order conditional estimation method with interaction (FOCE-INTER) resulted in close agreement between actual and nominal significance levels. The results from the covariate randomization procedure of the real data set were in agreement with the results from the simulation study. With the FO method the actual significance levels were higher than the nominal, independent of the covariate type, but depending on the parameter influenced. When using FOCE-INTER the actual and nominal levels were similar. The most important factors influencing the actual significance levels for the FO method are the approximation of the influence of the random effects in a nonlinear model, a heteroscedastic error structure in which an existing interaction between interindividual and residual variability is not accounted for in the model, and a lognormal distribution of the residual error which is approximated by a symmetric distribution. Estimation with FOCE–INTER and the covariate randomization procedure provide means to achieve agreement between nominal and actual significance levels.

Comparison of stepwise covariate model building strategies in population pharmacokinetic-pharmacodynamic analysis

The aim of this study was to compare 2 stepwise covariate model-building strategies, frequently used in the analysis of pharmacokinetic-pharmacodynamic (PK-PD) data using nonlinear mixed-effects models, with respect to included covariates and predictive performance. In addition, the effects of stepwise regression on the estimated covariate coefficients wise regression on the estimated covariate coefficients were assessed. Using simulated and real PK data, covariate models were built applying (1) stepwise generalized additive models (GAM) for identifying potential covariates, followed by backward elimination in the computer program NONMEM, and (2) stepwise forward inclusion and backward elimination in NONMEM. Different versions of these procedures were tried (eg, treating different study occasions as separate individuals in the GAM, or fixing a part of the parameters when the NONMEM procedure was used). The final covariate models were compared, including their ability to predict a separate data set or their performance in cross-validation. The bias in the estimated coefficients (selection bias) was assessed. The model-building procedures performed similarly in the data sets explored. No major differences in the resulting covariate models were seen, and the predictive performances overlapped. Therefore, the choice of model-building procedure in these examples could be based on other aspects such as analyst-and computer-time efficiency. There was a tendency to selection bias in the estimates, although this was small relative to the overall variability in the estimates. The predictive performances of the stepwise models were also reasonably good. Thus, selection bias seems to be a minor problem in this typical PK covariate analysis.

Comparison of some practical sampling strategies for population pharmacokinetic studies

Using population analysis, sparsely sampled Phase 3 clinical data can be utilized to determine the pharmacokinetic characteristics of the target population. Data arising from such studies are likely to be constrained to certain sampling windows, i.e., the visiting hours at the study clinic. When the sampling window is narrow compared to the half-life of the drug, the advantage of taking more than one sample is not obvious. Study designs with one or two samples per visit have been compared with respect to (i) precision and bias of the population parameter estimates, (ii) the ability to identify the underlying pharmacokinetic model, and (iii) the estimation of individual parameter values. The first point was assessed using simulated data while the latter two were studied using a real data set. Results show: (i) Parameter estimates are more biased and imprecise when only one sample is taken compared to when two samples are obtained, this is true irrespective of the time span between the two samples. (ii) Ability to identify a more complex model is increased if two samples are taken. Specifically, the variability between occasions can be quantified. (iii) Two-sample designs are generally better with respect to prediction of individual parameter values. Even minor changes to commonly employed study designs, in this case the addition of one sample at each study occasion, can improve quality and quantity of the information obtained.

BRAIN DISTRIBUTION OF CETIRIZINE ENANTIOMERS: COMPARISON OF THREE DIFFERENT TISSUE-TO-PLASMA PARTITION COEFFICIENTS: Kp, Kp,u, AND Kp,uu

The objective of this study was to compare the blood-brain barrier (BBB) transport and brain distribution of levo- (R-CZE) and dextrocetirizine (S-CZE). Microdialysis probes, calibrated using retrodialysis by drug, were placed into the frontal cortex and right jugular vein of eight guinea pigs. Racemic CZE (2.7 mg/kg) was administered as a 60-min i.v. infusion. Unbound and total concentrations of the enantiomers were measured in blood and brain with liquid chromatography-tandem mass spectrometry. The brain distribution of the CZE enantiomers were compared using the parameters Kp, Kp,u, Kp,uu, and Vu,br. Kp compares total brain concentration to total plasma concentration, Kp,u compensates for binding in plasma, whereas Kp,uu also compensates for binding within the brain tissue and directly quantifies the transport across the BBB. Vu,br describes binding within the brain. The stereoselective brain distribution indicated by the Kp of 0.22 and 0.04 for S- and R-CZE, respectively, was caused by different binding to plasma proteins. The transport of the CZE enantiomers across the BBB was not stereoselective, since the Kp,uu was 0.17 and 0.14 (N.S.) for S- and R-CZE, respectively. The Kp,uu values show that the enantiomers are effluxed to a large extent across the BBB. The Vu,br of approximately 2.5 ml/g brain was also similar for both the enantiomers, and the value indicates high binding to brain tissue. Thus, when determining stereoselectivity in brain distribution, it is important to study all factors governing this distribution, binding in blood and brain, and the BBB equilibrium.

Morphine Blood-Brain Barrier Transport Is Influenced by Probenecid Co-Administration

AbstractPurpose. The objective of this study was to investigate the possible influence of probenecid on morphine transport across the blood-brain barrier (BBB) in rats. Methods. Microdialysis probes, calibrated using retrodialysis by drug, were placed into the striatum and jugular vein of seven Sprague-Dawley rats. Morphine was administered as a 4-h exponential infusion. The experiment was repeated the next day with the addition of probenecid, administered as a bolus dose (20 mg/kg) followed by a constant infusion (20 mg/kg/h). Models for BBB transport were built using the computer program NONMEM. Results. The steady-state ratio of 0.29 ± 0.07 of unbound morphine concentration in brain to that in blood indicates that morphine is actively effluxed at the BBB. Probenecid co-administration increased the ratio to 0.39 ± 0.04 (p < 0.05). Models in which probenecid influenced the brain efflux clearance rather than the influx clearance, well described the data. The half-life in brain increased from 58 ± 9 min to 115 ± 25 min when probenecid was co-administered. Systemic clearance of morphine also decreased upon probenecid co-administration, and M3G formation was decreased. Conclusion. This study indicates that morphine is a substrate for the probenecid-sensitive transporters at the BBB. Co-administration of probenecid decreased the brain efflux clearance of morphine.

A pharmacokinetic-pharmacodynamic model for the quantitative prediction of dofetilide clinical QT prolongation from human ether-a-go-go-related gene current inhibition data.

QT prolongation is an important biomarker of the arrhythmia torsades de pointes and appears to be related mainly to blockade of delayed inward cardiac rectifier potassium currents. The aim of this study was to quantify the relationship between in vitro human ether‐a‐go‐go‐related gene (hERG) potassium channel blockade and the magnitude of QT prolongation in humans for the class III antiarrhythmic dofetilide.

Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations.

PurposeThe objective of the present analysis was to explore the use of stochastic differential equations (SDEs) in population pharmacokinetic/pharmacodynamic (PK/PD) modeling.MethodsThe intra-individual variability in nonlinear mixed-effects models based on SDEs is decomposed into two types of noise: a measurement and a system noise term. The measurement noise represents uncorrelated error due to, for example, assay error while the system noise accounts for structural misspecifications, approximations of the dynamical model, and true random physiological fluctuations. Since the system noise accounts for model misspecifications, the SDEs provide a diagnostic tool for model appropriateness. The focus of the article is on the implementation of the Extended Kalman Filter (EKF) in NONMEM® for parameter estimation in SDE models.ResultsVarious applications of SDEs in population PK/PD modeling are illustrated through a systematic model development example using clinical PK data of the gonadotropin releasing hormone (GnRH) antagonist degarelix. The dynamic noise estimates were used to track variations in model parameters and systematically build an absorption model for subcutaneously administered degarelix.ConclusionsThe EKF-based algorithm was successfully implemented in NONMEM for parameter estimation in population PK/PD models described by systems of SDEs. The example indicated that it was possible to pinpoint structural model deficiencies, and that valuable information may be obtained by tracking unexplained variations in parameters.

Assessment of Type I Error Rates for the Statistical Sub-model in NONMEM

The aim of this study was to assess the type I error rate when applying the likelihood ratio (LR) test, for components of the statistical sub-model in NONMEM. Data were simulated from a pharmacokinetic one compartment intravenous bolus model. Two models were fitted to the data, the simulation model and a model containing one additional parameter, and the difference in objective function values between models was calculated. The additional parameter was either (i) a covariate effect on the interindividual variability in CL or V, (ii) a covariate effect on the residual error variability, (iii) a covariance term between CL and V, or (iv) interindividual variability in V. Factors in the simulation conditions (number of individuals and samples per individual, interindividual and residual error magnitude, residual error model) were varied systematically to assess their potential influence on the type I error rate. Different estimation methods within NONMEM were tried. When the first-order conditional estimation method with interaction (FOCE INTER) was used the estimated type I error rates for inclusion of a covariate effect (i) on the interindividual variability, or (ii) on the residual error variability, were in agreement with the type I error rate expected under the assumption that the model approximations made by the estimation method are negligible. When the residual error variability was increased, the type I error rates for (iii) inclusion of covariance between ηCL–ηV were inflated if the underlying residual distribution was lognormal, or if a normal distribution was combined with too little information in the data (too few samples per subject or sampling at uninformative time-points). For inclusion of (iv)ηV, the type I error rates were affected by the underlying residual error distribution; with a normal distribution the estimated type I error rates were close to the expected, while if a non-normal distribution was used the type I errors rates increased with increasing residual variability. When the first-order (FO) estimation method was used the estimated type I error rates were higher than the expected in most situations. For the FOCE INTER method, but not the FO method, the LR test is appropriate when the underlying assumptions of normality of residuals, and of enough information in the data, hold true. Deviations from these assumptions may lead to inflated type I error rates.