Nonlinearity detection: Advantages of nonlinear mixed-effects modeling

The purpose of this study was to address the question of whether the use of nonlinear mixed-effect models has an impact on the detection and characterization of nonlinear processes (pharmacokinetic and pharmacodynamic) in rich data obtained from a few subjects. Simulations were used to assess the difference between applying population analysis, ie, nonlinear mixed-effects models as implemented in NONMEM, and the standard 2-stage (STS) method as the data analysis method for detection and characterization of nonlinearities. Three situations were considered, 2 pharmacokinetic and 1 pharmacodynamic. Both the first-order (FO) and FO conditional estimation (FOCE) algorithms were used for the population analyses. Within each situation, rich data were simulated for 8 subjects at multiple dose levels. The true nonlinear model and a simpler linear model were fit to each data set using each of the STS, FO, and FOCE methods. Criteria were prespecified to determine when each data analysis method detected the true nonlinear model. For all 3 simulated situations, the application of population analysis with the FOCE algorithm enabled the detection and characterization of the true nonlinear models in at least a 4-fold lower dose level than the STS approach. For both of the pharmacokinetic settings, population analysis with the FO algorithm performed much more poorly than the STS approach. The superior detection and characterization of nonlinearities provided by population analysis with the FOCE algorithm should allow drug developers to better predict and define how a drug should be used in clinical practice in such situations.     

Detection of a drug–drug interaction on population-based phenobarbitone clearance using nonlinear mixed-effects modeling

Objective: Nonlinear mixed-effects modeling (NONMEM) was used to estimate the effects of drug–drug interaction on phenobarbitone clearance values, using 648 serum levels gathered during the routine clinical care of 349 pediatric and adult epileptic patients (age range, 0.4–33.3 years). Patients received phenobarbitone as monotherapy or in combination with either of the antiepileptic drugs carbamazepine or valproic acid. Results: The final model describing phenobarbitone clearance was CL = 52.3 · TBW^–0.567 · CO, where CL is clearance (ml · kg⁻¹ · h⁻¹), TBW is total body weight (kg) and CO is a scaling factor for concomitant medication with a value of 1 for patients on phenobarbitone monotherapy, 46.4^(−1/TBW)for those patients receiving concomitant carbamazepine and 0.642 for those patients receiving concomitant valproic acid. Phenobarbitone CL was highest in the very young and decreased in a weight-related fashion in children, with minimal changes observed in adults. This pattern was consistent whether phenobarbitone was administered alone or coadministered with carbamazepine or valproic acid. When phenobarbitone was coadministered with carbamazepine or valproic acid, phenobarbitone CL decreased compared with that in monotherapy. Its magnitudes in the presence of carbamazepine are maximal in early childhood (about 54%) and decreased in a weight-related fashion in older children, with minimal changes observed in adults. Concomitant administration of phenobarbitone and valproic acid resulted in a 35.8% decrease of phenobarbitone CL. Received: 17 February 1997 / Accepted in revised form: 21 October 1997     

Propranolol pharmacodynamic modeling using unbound and total concentrations in healthy volunteers

In an attempt to evaluate the propranolol (P) concentration-effect relationship, percentage reduction in exercise heart rate was modeled as a function of unbound and total P concentrations using the linear, E _max ,and sigmoid E _max models. Nine volunteers underwent repeated treadmill exercise tests over 48 hr during a control period, after receiving 160 mg of P orally and again after receiving 160 mg once daily for 7 days. Beta blockade was assessed as the percentage reduction in exercise heart rate compared to control. Total serum P concentrations were determined by HPLC and unbound fractions by equilibrium dialysis. Using nonlinear least-squares regression, the E _max model was best in describing the concentration-effect relationship in each subject. Mean parameters for combined single dose and steady state were E _max 33.6±4.5% and EC₅₀ 18.2±15.6ng/ml for total P and E _max 33.5±4.3% and EC₅₀ 1.66±1.56 for unbound P. Model fits were not significantly better for unbound versus total P and EC₅₀ values showed similar intersubject variability. The observed unbound EC₅₀ values are consistent with reported receptor dissociation constants. Therefore the large intersubject variability in EC₅₀ could not be accounted for by variability in P protein binding.     

Propranolol pharmacodynamic modeling using unbound and total concentrations in healthy volunteers

In an attempt to evaluate the propranolol (P) concentration-effect relationship, percentage reduction in exercise heart rate was modeled as a function of unbound and total P concentrations using the linear, Emax, and sigmoid Emax models. Nine volunteers underwent repeated treadmill exercise tests over 48 hr during a control period, after receiving 160 mg of P orally and again after receiving 160 mg once daily for 7 days. Beta blockade was assessed as the percentage reduction in exercise heart rate compared to control. Total serum P concentrations were determined by HPLC and unbound fractions by equilibrium dialysis. Using nonlinear least-squares regression, the Emax model was best in describing the concentration-effect relationship in each subject. Mean parameters for combined single dose and steady state were Emax 33.6 +/- 4.5% and EC50 18.2 +/- 15.6 ng/ml for total P and Emax 33.5 +/- 4.3% and EC50 1.66 +/- 1.56 for unbound P. Model fits were not significantly better for unbound versus total P and EC50 values showed similar intersubject variability. The observed unbound EC50 values are consistent with reported receptor dissociation constants. Therefore the large intersubject variability in EC50 could not be accounted for by variability in P protein binding.     

Accounting for dropout bias using mixed-effects models.

Treatment effects are often evaluated by comparing change over time in outcome measures. However, valid analyses of longitudinal data can be problematic when subjects discontinue (dropout) prior to completing the study. This study assessed the merits of likelihood-based repeated measures analyses (MMRM) compared with fixed-effects analysis of variance where missing values were imputed using the last observation carried forward approach (LOCF) in accounting for dropout bias. Comparisons were made in simulated data and in data from a randomized clinical trial. Subject dropout was introduced in the simulated data to generate ignorable and nonignorable missingness. Estimates of treatment group differences in mean change from baseline to endpoint from MMRM were, on average, markedly closer to the true value than estimates from LOCF in every scenario simulated. Standard errors and confidence intervals from MMRM accurately reflected the uncertainty of the estimates, whereas standard errors and confidence intervals from LOCF underestimated uncertainty.     

Adjustment of endogenous concentrations in pharmacokinetic modeling

Purpose

Estimating pharmacokinetic parameters in the presence of an endogenous concentration is not straightforward as cross-reactivity in the analytical methodology prevents differentiation between endogenous and dose-related exogenous concentrations. This article proposes a novel intuitive modeling approach which adequately adjusts for the endogenous concentration.

Methods

Monte Carlo simulations were carried out based on a two-compartment population pharmacokinetic (PK) model fitted to real data following intravenous administration. A constant and a proportional error model were assumed. The performance of the novel model and the method of straightforward subtraction of the observed baseline concentration from post-dose concentrations were compared in terms of terminal half-life, area under the curve from 0 to infinity, and mean residence time.

Results

Mean bias in PK parameters was up to 4.5 times better with the novel model assuming a constant error model and up to 6.5 times better assuming a proportional error model.

Conclusions

The simulation study indicates that this novel modeling approach results in less biased and more accurate PK estimates than straightforward subtraction of the observed baseline concentration and overcomes the limitations of previously published approaches.     

An application of nonlinear mixed-effects modeling to pharmacokinetic data exhibiting nonlinear and time-dependent behavior

A population pharmacokinetic (PK) analysis was performed on plasma concentrations of GW468816 observed in dogs after 10, 25, and 50 mg/kg/day repeated intravenous administration. A two-compartment model was fitted to the concentration-time data using the NONMEM program. Dose and time dependency of PK parameters was investigated. Selection of the best model was performed using a stepwise approach. A Michaelis-Menten elimination process was used to describe the PK dose dependency, whereas an interoccasion variability on V(m) (the maximum elimination rate of the Michaelis-Menten elimination process) was initially used to describe the time dependency of the PKs, and the final model included an exponential function to account for time variance on V(m). The K(m) value of the final model was 29.6 microg/mL, whereas V(m) was estimated to vary with time from 4.97 microg/h/kg at day 1 to a maximum mean value of 9.64 microg/h/kg at day 14. This approach can be applied to either rich or sparse data leading to estimates of individual parameters by using Bayesian feedback. The overall information obtained can be used to interpret toxicological and pharmacological endpoints and integrated with further in vitro-in vivo studies to supply a comprehensive PK behavior before the first time in human studies.     

Population pharmacokinetics of gentamicin in neonates using a nonlinear, mixed-effects model.

The population pharmacokinetics of gentamicin in neonates was determined using a nonlinear, mixed-effects model (NONMEM). The final regression equations derived to estimate clearance (Cl) and volume of distribution (Vd) were Cl = 0.120 * (WT/2.4)1.36 L/hr and Vd = 0.429 * (WT) L. The interindividual variability (% CV) for clearance was 26.2% and for volume of distribution 15.9%. Intraindividual variability was 11.0%. In a separate group of 30 neonates, the predictive ability of the NONMEM-generated population variables was compared to the predictions from a standard two-stage population analysis. The trough concentrations predicted using NONMEM-generated parameters were significantly less biased and more precise; there were no significant differences between the methods in predicting peaks. NONMEM is a useful tool for determining population pharmacokinetics and appears to be consistent across populations using routine clinical data and limited observation.     

Pharmacokinetics and concentration-effect analysis of intravenous RGD891, a platelet GPIIb/IIIa antagonist, using mixed-effects modeling (NONMEM)

RGD891 is a platelet GPIIb/IIIa receptor antagonist and potent inhibitor of platelet aggregation. This compound is biotransformed in vivo to RGD039, which also exhibits high affinity for the GPIIb/IIIa receptor. Pharmacokinetic/pharmacodynamic modeling was employed to describe the concentration-effect relationship of both compounds following the intravenous administration of RGD891 to healthy volunteers. The overall objectives of this work were to support the dose selection process for future intravenous RGD891 safety and efficacy studies. Various intravenous regimens of RGD891 were administered to healthy volunteers enrolled in three Phase I studies. Frequent plasma samples were collected at regular intervals for later measurement of RGD891 and RGD039 concentrations (validated LC/MS/MS methods). The pharmacokinetics of RGD891 and RGD039 were simultaneously analyzed by nonlinear mixed-effect modeling (NONMEM). Pharmacodynamic activity was assessed in all three studies by the degree to which ADP (20 microM)-induced platelet aggregation was inhibited. Population parameters describing the concentration-effect relationship of RGD891 and RGD039 were then generated using a modified competitive Emax-based model. RESULTS: Parent compound is by far the predominant active compound circulating in the plasma following intravenous administration of RGD891. The plasma RGD891 concentration-time data were best fit by a two-compartment structural model. The fit of the basic model was improved when total body weight was introduced as a covariate for RGD891 distribution. Between-subject variability in the RGD891 pharmacokinetic parameters--V1, K10, and K21--was less than 17% (coefficient of variation). Formation of the active metabolite (RGD039; Km) and its elimination (Kem) were assumed to be first-order processes (i.e., one-compartment model). The population pharmacokinetic model could only provide a rough estimate of the plasma concentration-time profile for RGD039 after administration of a given intravenous dosage regimen of RGD891 since metabolite concentrations were relatively low and highly variable. The first-order rate constant describing the formation of RGD039 from RGD891 (Km) was also associated with a substantial degree of between-subject variability (44.9%). The potency of RGD891 toward the inhibition of ADP-induced platelet aggregation was described by the population IC50 value (plasma concentration yielding 50% of maximal inhibition), which ranged from 58.0 to 95.4 ng/mL, depending on the pharmacokinetic-pharmacodynamic (PK-PD) model and the data set used. The relatively low concentrations of the active metabolite achieved following intravenous administration of RGD891 did not permit independent estimation of a population IC50 value for RGD039. Therefore, its potency was fixed at 2.2-fold greater than that of the parent compound (based on previous PK-PD analyses). Intersubject variability in the IC50 values was 30%. CONCLUSIONS: Antagonism of the platelet IIb/IIIa receptors by intravenously administered RGD891 was effective in inhibiting ADP-induced platelet aggregation in a reversible and dose-dependent manner. Pharmacodynamic activity was largely attributed to the parent compound and less to the active metabolite based on the relative potencies of both compounds and the plasma concentrations of each achieved following intravenous administration. Intravenous bolus plus maintenance infusion regimens resulted in rapid attainment of steady-state plasma RGD891 concentrations. This combination regimen also provided for a marked and sustained inhibition of platelet aggregation that reached 90% or greater (relative to baseline values) in the higher dose groups. The modified Emax model adequately described inhibition of platelet aggregation following a particular intravenous dosage regimen of RGD891 (within the range of doses administered in the present studies). (ABSTRACT TRUNCATED)     

Semiparametric mixed-effects analysis of PK/PD models using differential equations

Motivated by the use of semiparametric nonlinear mixed-effects modeling on longitudinal data, we develop a new semiparametric modeling approach to address potential structural model misspecification for population pharmacokinetic/pharmacodynamic (PK/PD) analysis. Specifically, we use a set of ordinary differential equations (ODEs) with form dx/dt = A(t)x + B(t) where B(t) is a nonparametric function that is estimated using penalized splines. The inclusion of a nonparametric function in the ODEs makes identification of structural model misspecification feasible by quantifying the model uncertainty and provides flexibility for accommodating possible structural model deficiencies. The resulting model will be implemented in a nonlinear mixed-effects modeling setup for population analysis. We illustrate the method with an application to cefamandole data and evaluate its performance through simulations.     

A linear mixed-effects calibration in qualifying experiments

In many applications, controls are used to monitor the process or experiment and to assess whether the process is in control or the experiment is valid. In this case, the traditional fixed-effects calibration is usually not adequate, but a mixed-effects model is appropriate. In this article, a linear mixed-effects calibration model is considered to qualify an experiment. Two estimating methods for the controls based on maximum likelihood and restricted maximum likelihood are proposed. The bias and mean squared error performances are studied by simulation. Five different methods to construct confidence intervals for the controls are compared. A dataset is used to demonstrate the advantages of the mixed-effects model.     

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.     

Mathematical modeling of circadian cortisol concentrations using indirect response models: comparison of several methods.

Six mathematical functions to describe the chronobiology of cortisol concentrations were assessed. Mean data from a dose-proportionality study of inhaled fluticasone propionate were fitted with an indirect response model using various biorhythmic functions (single cosine, dual ramps, dual zero-order, dual cosines, and Fourier series with 2 and n-harmonics) for production rate. Data with known parameters and random variation were also generated and fitted using the ADAPT II program. Fitted parameters, model estimation criteria, and runs tests were compared. Models with preassigned functions: the dual ramps, the dual zero-order and the dual cosines provide maximum and minimum times for cortisol release rate, were suitable for describing asymmetric circadian patterns and yielding IC50 values. Fourier analysis differs from the other methods in that it uses the placebo data to recover equations for cortisol secretion rate rather than by postulation. Nonlinear regression for Fourier analysis, instead of the L2-norm method, was useful to characterize the baseline cortisol data but was restricted to a maximum of two harmonics. Apart from the single cosine function, which predicts symmetrical cortisol concentrations, all methods were satisfactory in describing the baseline and suppressed cortisol concentrations. On the other hand, Fourier series with L2-norm produced the best unbiased estimate for baseline patterns. The Fourier method is flexible, accurate, and can be extended to other drug-induced changes in normal periodic rhythms.     

Human plasma concentrations of cytochrome P450 probes extrapolated from pharmacokinetics in cynomolgus monkeys using physiologically based pharmacokinetic modeling

Abstract

1.?Cynomolgus monkeys are widely used in preclinical studies as non-human primate species. Pharmacokinetics of human cytochrome P450 probes determined in cynomolgus monkeys after single oral or intravenous administrations were extrapolated to give human plasma concentrations.

2.?Plasma concentrations of slowly eliminated caffeine and R-/S-warfarin and rapidly eliminated omeprazole and midazolam previously observed in cynomolgus monkeys were scaled to human oral biomonitoring equivalents using known species allometric scaling factors and in vitro metabolic clearance data with a simple physiologically based pharmacokinetic (PBPK) model. Results of the simplified human PBPK models were consistent with reported experimental PK data in humans or with values simulated by a fully constructed population-based simulator (Simcyp).

3.?Oral administrations of metoprolol and dextromethorphan (human P450 2D probes) in monkeys reportedly yielded plasma concentrations similar to their quantitative detection limits. Consequently, ratios of in vitro hepatic intrinsic clearances of metoprolol and dextromethorphan determined in monkeys and humans were used with simplified PBPK models to extrapolate intravenous PK in monkeys to oral PK in humans.

4.?These results suggest that cynomolgus monkeys, despite their rapid clearance of some human P450 substrates, could be a suitable model for humans, especially when used in conjunction with simple PBPK models.     

Use of nonlinear, mixed-effects modeling for population analysis of ofloxacin: effects of age on oral drug pharmacokinetics.

To compare the effect of age on pharmacokinetics of orally administered ofloxacin, two separate studies were reanalyzed using mixed-effect modeling with the program NONMEM. Subjects were male volunteers, 36 age 65 years or greater and 24 age 18-40 years. The younger group received three 100-mg tablets and the older group received two 200-mg tablets of ofloxacin. Serial blood samples obtained throughout dosing were assayed for drug concentrations using high-performance liquid chromatography. A pharmacostatistical model was developed for the data using mixed-effect modeling with NONMEM. A one-compartment open model with first-order absorption, which included the covariables weight and age, best fit the data. Mean (SE) population values were clearance/F 0.219 (0.009) L/hr/kg, volume of distribution/F 1.50 (0.071) L/kg, and absorption rate constant 2.26 (0.048) hr-1. Older subjects had a 29% lower clearance and 13% lower volume of distribution then the younger subjects.     

Population pharmacodynamic modeling without plasma concentrations of rocuronium in children.

Using the pharmacodynamic model without plasma concentrations described by Bragg et al, an individual approach resulted in highly variable parameters for rocuronium. Using a population approach of the model, the time course of the effect of an IV bolus dose of 400, 600, and 800 microg/kg of rocuronium was studied. Response was measured by accelerometry (TOF-Guard) in 45 low-risk surgical children, ages 2 to 14 years, who were receiving general anesthesia with isoflurane. Using a Bayesian approach and the software P-PHARM, response (the first twitch of the TOF) was modeled. The apparent rate constant of elimination, the rate constant for equilibrium between plasma and the effect compartment, the sigmoidicity factor of the relationship between drug concentration in the effect compartment and the effect, and the infusion rate that produces 50% of the effect at steady state were obtained. Population and individual post hoc parameters were similar among groups and variability was reduced.     

Predicting brain concentrations of drug using positron emission tomography and venous input: modeling of arterial-venous concentration differences

Objective In a positron emission tomography (PET) study, the concentrations of the labeled drug (radiotracer) are often different in arterial and venous plasma, especially immediately following administration. In a PET study, the transfer of the drug from plasma to brain is usually described using arterial plasma concentrations, whereas venous sampling is standard in clinical pharmacokinetic studies of new drug candidates. The purpose of the study was to demonstrate the modeling of brain drug kinetics based on PET data in combination with venous blood sampling and an arterio-venous transform (T_av).Methods Brain kinetics (C_br) was described as the convolution of arterial plasma kinetics (C_ar) with an arterial-to-brain impulse response function (T_br). The arterial plasma kinetics was obtained as venous plasma kinetics (C_ve) convolved with the inverse of the arterio-venous transform (T_av ⁻¹). The brain kinetics was then given by C_br=C_ve*T_av ⁻¹*T_br. This concept was applied on data from a clinical PET study in which both arterial and venous plasma sampling was done in parallel to PET measurement of brain drug kinetics. The predictions of the brain kinetics based on an arterial input were compared with predictions using a venous input with and without an arterio-venous transform.Results The venous based models for brain distribution, including a biexponential arterio-venous transform, performed comparably to models based on arterial data and better than venous based models without the transform. It was also shown that three different brain regions with different shaped concentration curves could be modeled with a common arterio-venous transform together with an individual brain distribution model.Conclusion We demonstrated the feasibility of modeling brain drug kinetics based on PET data in combination with venous blood sampling and an arterio-venous transform. Such a model can in turn be used for the calculation of brain kinetics resulting from an arbitrary administration mode by applying this model on venous plasma pharmacokinetics. This would be an important advantage in the development of drugs acting in the brain, and in other circumstances when the effect is likely to be closer related to the brain than the plasma concentration.     

Human plasma concentrations of five cytochrome P450 probes extrapolated from pharmacokinetics in dogs and minipigs using physiologically based pharmacokinetic modeling

1. The pharmacokinetics of cytochrome P450 probes in humans can be extrapolated from corresponding data in cynomolgus monkeys using simplified physiologically based pharmacokinetic (PBPK) modeling. In the current study, despite some species difference in drug clearances, this modeling methodology was adapted to estimate human plasma concentrations of P450 probes based on data from commonly used medium-sized experimental animals, namely dogs and minipigs.

2. Using known species allometric scaling factors and in vitro metabolic clearance data, the observed plasma concentrations of slowly eliminated caffeine and warfarin and rapidly eliminated omeprazole, metoprolol and midazolam in two young dogs were scaled to human oral monitoring equivalents. Using the same approach, the previously reported pharmacokinetics of the five P450 probes in minipigs was also scaled to human monitoring equivalents.

3. The human plasma concentration profiles of the five P450 probes estimated by the simplified human PBPK models based on observed/reported pharmacokinetics in dogs/minipigs were consistent with previously published pharmacokinetic data in humans.

4. These results suggest that dogs and minipigs, in addition to monkeys, could be suitable models for humans during research into new drugs, especially when used in combination with simple PBPK models.

     

用SAS软件实现配对设计定量资料的统计分析

配对设计是药学科研中经常用到的一种实验设计方法,在临床药物疗效研究方面具有十分广泛的适用性.本文主要从配对设计的概念、配对设计统计分析方法的合理选用、如何使用SAS程序进行分析,以及如何解释结果几个方面作一概述.     

Aerosol deposition modeling using ACSL

An aerosol deposition model has been written for inclusion into physiologically based pharmacokinetic (PBPK) models, allowing PBPK model based risk assessments to be performed for aerosolized materials. Previously, PBPK models could only treat inhaled gases and vapors. The deposition model employs a semi-empirical equation to describe extrathoracic deposition and employs data concerning the geometry of the thoracic conducting airways as well as that of the gas exchange regions of the lung to compute the deposited aerosol mass based on aerosol diffusion, sedimentation, and impaction. Provisions are made to allow calculations for polydisperse aerosols whose size distribution and mass vary with time. Variations in the model subject's respiration can be accommodated through selection of respiratory parameters at model startup as well as through consideration of carbon dioxide stimulation of respiration. The model is compared with other similar calculations and experimental data to validate the calculations. An example model application is presented in the form of a comparison of two inhalation atmospheres, one from an inhalation toxicity study and one from a similar atmosphere produced for fire extinguishing agent testing.