Pharmacokinetic-Pharmacodynamic Modeling and Simulation

In the previous chapters, we discussed autoregressive linear mixed effects models. In this section, we discuss the relationships between the autoregressive linear mixed effects models and nonlinear mixed effects models, growth curves, and differential equations. The autoregressive model shows a profile approaching an asymptote, where the change is proportional to the distance remaining to the asymptote. Autoregressive models in discrete time correspond to monomolecular curves in continuous time. Autoregressive linear mixed effects models correspond to monomolecular curves with random effects in the baseline and asymptote, and special error terms. The autoregressive coefficient is a nonlinear parameter, but all random effects parameters in the model are linear. Therefore, autoregressive linear mixed effects models are nonlinear mixed effects models without nonlinear random effects and have a closed form of likelihood. When there are time-dependent covariates, autoregressive linear mixed effects models are represented by a differential equation and random effects. The monomolecular curve is one of the popular growth curves. We introduce other growth curves, such as the logistic curves and von Bertalanffy curves, and generalizations of growth curves. Re-parameterization is often performed in nonlinear models, and various representations of re-parameterization in monomolecular and other curves are provided herein.

Different mixed-effects models were compared to evaluate the population dose-response and relative potency of two albuterol inhalers. Bronchodilator response was measured after ascending doses of each inhaler in 37 asthmatic patients. A linear mixed-effects model was developed based on the approach proposed by Finney for the evaluation of bioassay data. A nonlinear mixed-effects (Emax) model with interindividual and interoccasion variability (IOV) in the different pharmacodynamic parameters was also fit to the data. Both methods produced a similar estimate of relative potency. However, the estimate of relative potency was 22% lower with the nonlinear mixed-effects model if IOV was not taken into account. Monte Carlo simulations based on a similar study design demonstrated that more biased and variable estimates of ED50 and relative potency were obtained when the nonlinear mixed-effects model ignored the presence of IOV in the data. Furthermore, the linear mixed-effects model that did not account for IOV produced confidence intervals for relative potency that were too narrow and thus could lead to erroneous conclusions. These problems were avoided when the estimation model could account for IOV. Results of the simulations were consistent with those of the experimental data. Although the linear or the nonlinear mixed-effects model may be used to evaluate population dose-response and relative potency, there are important differences in the assumptions made by each method.

Longitudinal data are data collected repeatedly from each subject for a particular response variable over a certain time period. Specifically, in longitudinal data analysis, the researchers are interested in changes in the response levels over time and the differences in these changes among factor levels or covariates. Because of within-subject correlations, analysis methods considering the correlations or variance-covariance structures have been developed. One of the approaches is the use of mixed effects models that take into account between-subject heterogeneity by random effects. In population pharmacokinetics, the response variable corresponds to drug concentration and is analysed typically using nonlinear mixed effects models. In this article, longitudinal data analysis with a continuous response variable is introduced focusing on population pharmacokinetics. Longitudinal data analysis, linear mixed effects models, nonlinear mixed effects models, and population pharmacokinetics are discussed from a biostatistical point of view. This article is expected to be of interest to biostatisticians, pharmacologists, pharmacokineticists, and those in related fields.

3567 Background: ABT-869 is an orally bioavailable, potent and specific inhibitor of all vascular endothelial growth factor and platelet derived growth factor family receptor tyrosine kinases. The objectives of this analysis were to understand the population pharmacokinetics of ABT-869 and explore the effect of several demographic/disease state covariates influencing ABT-869 disposition. Methods: A population PK analysis of 181 patients (pts) enrolled in two phase 1 (multiple types of solid tumors and AML) and three phase 2 monotherapy studies (non-small cell lung cancer, hepatocellular carcinoma [HCC] and renal cell carcinoma) was conducted. Approximately 90% of pts received ABT-869 based on body-weight dosing while the remaining pts had flat dosing. Available plasma concentrations obtained after intensive and sparse pre-dose PK sampling were analyzed by population PK using the non linear mixed effects modeling (NONMEM) approach. Potential covariates including body weight, body surface area (BSA), age, sex, creatinine clearance (CrCL) and disease state (HCC vs. non-HCC pts) were tested. Results: The mean body weight of enrolled pts was 71 kg and 57% were Asian, 36% Caucasian and 7% other races. The ABT-869 plasma concentration time profile was well described by a one-compartment model with first order absorption and elimination process. Oral clearance (CL/F) was not affected by body weight (range 35–177 kg); however, apparent volume of distribution (V/F) increased by 6L per 0.1 mg/m2 increase in BSA. CrCL (39.9–290.3 ml/min) was not a significant covariate on V/F and CL/F suggesting renally impaired pts do not require a different dose/dosing regimen. HCC pts had ∼40% lower CL/F values than pts with other malignancies suggesting a lower dose would be appropriate for HCC (Child Pugh A and B) pts. Conclusions: Population PK analysis showed that ABT-869 PK can be well described by a one-compartment model with first order absorption and elimination. Race and impaired renal function does not appear to alter PK. HCC pts had lower CL/F value therefore a lower dose may be recommended in these patients. Implications of increased V/F with increasing body size and appropriate dosing strategy are undergoing further analysis. [Table: see text]

Long-Term Growth of the Neoaortic Root After Arterial Switch Operation

Population pharmacokinetic study of tacrolimus in pediatric patients with primary nephrotic syndrome: A comparison of linear and nonlinear Michaelis–Menten pharmacokinetic 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.

This work is motivated by a meta-analysis case study on antipsychotic medications. The Michaelis-Menten curve is employed to model the nonlinear relationship between the dose and D2 receptor occupancy across multiple studies. An intraclass correlation coefficient (ICC) is used to quantify the heterogeneity across studies. To interpret the size of heterogeneity, an accurate estimate of ICC and its confidence interval is required. The goal is to apply a recently proposed generic beta-approach for construction the confidence intervals on ICCs for linear mixed effects models to nonlinear mixed effects models using four estimation methods. These estimation methods are the maximum likelihood, second-order generalized estimating equations and two two-step procedures. The beta-approach is compared with a large sample normal approximation (delta method) and bootstrapping. The confidence intervals based on the delta method and the nonparametric percentile bootstrap with various resampling strategies failed in our settings. The beta-approach demonstrates good coverages with both two-step estimation methods and consequently, it is recommended for the computation of confidence interval for ICCs in nonlinear mixed effects models for small studies.

Animal growth models are used to identify alternative strategies to improve the efficiency of livestock production and to estimate daily nutrient requirements for the animal of different age and sex group. In this study, the efficiency of nonlinear mixed effects models were explored and a comparison was made between the predictive power of fixed effects models and the mixed effects models. Three hundred body weight (BW) data including male and female pigs were used for model fitting. One pig specific random effect was included in each of the models. The random function was a random deviation of mature BW of the individual from average mature BW of its genotype. Logistic, Gompertz and Von-Bertalanffy fixed and mixed models were explored for these data. It was found that Logistic mixed effects model performed better than the other nonlinear mixed effects models based on mean square error (MSE) and root mean square error (RMSE).

The aim of this study was to investigate the use of nonlinear mixed effects (NLME) models in a real bioequivalence study and compare it to noncompartmental analysis (NCA) which is proposed by regulatory agencies. NCA requires few hypotheses but a large number of samples per subject. On the other hand, NLME approach is more complex than NCA but it has some advantages such as it requires few samples per subject. A real data application was provided for the study, which was get from Ege University Drug Development and Pharmacokinetics Research Center. For NLME, we used the stochastic approach to expectation-maximization (SAEM) algorithm, whereas linear trapezoidal rule was used for NCA. We estimate pharmacokinetic parameters, area under the curve (AUC0-∞) and maximum concentration (Cmax), and perform a bioequivalence tests using NCA and NLME. According to real data analysis, NLME approach has smaller within subject error, narrower confidence intervals than non-compartmental analysis. However, NLME models have some limitations because of increasing type I error. Therefore, caution is needed for small sample size and data with high variability.

The statistical methodology for the design and analysis of clinical Phase II dose‐response studies, with related software implementation, is well developed for the case of a normally distributed, homoscedastic response considered for a single timepoint in parallel group study designs. In practice, however, binary, count, or time‐to‐event endpoints are encountered, typically measured repeatedly over time and sometimes in more complex settings like crossover study designs. In this paper, we develop an overarching methodology to perform efficient multiple comparisons and modeling for dose finding, under uncertainty about the dose‐response shape, using general parametric models. The framework described here is quite broad and can be utilized in situations involving for example generalized nonlinear models, linear and nonlinear mixed effects models, Cox proportional hazards models, with the main restriction being that a univariate dose‐response relationship is modeled, that is, both dose and response correspond to univariate measurements. In addition to the core framework, we also develop a general purpose methodology to fit dose‐response data in a computationally and statistically efficient way. Several examples illustrate the breadth of applicability of the results. For the analyses, we developed theRadd‐on packageDoseFinding, which provides a convenient interface to the general approach adopted here. Copyright © 2013 John Wiley & Sons, Ltd.

Aripiprazole is one of the most commonly prescribed antipsychotic drugs to children and adolescents worldwide, but it is associated with serious side effects, including weight gain. This study assessed the population pharmacokinetics of aripiprazole and its active metabolite and investigated the relationship between PK parameters and BMI in children and adolescents with ASD and behavioral problems. Secondary outcomes were metabolic, endocrine, extrapyramidal and cardiac side effects and drug effectiveness. Twenty-four children and adolescents (15 males, 9 females) aged 6-18 years were included in a 24-week prospective observational trial. Drug plasma concentrations, side effects and drug effectiveness were measured at several time points during follow-up. Relevant pharmacokinetic covariates, including CYP2D6, CYP3A4, CYP3A5 and P-glycoprotein (ABCB1) genotypes, were determined. Nonlinear mixed-effects modelling (NONMEM®) was used for a population pharmacokinetic analysis with 92 aripiprazole and 91 dehydro-aripiprazole concentrations. Subsequently, model-based trough concentrations, maximum concentrations and 24-hour AUCs were analyzed to predict outcomes using generalized and linear mixed-effects models. For both aripiprazole and de-hydro-aripiprazole, one-compartment models best described the measured concentrations, with albumin and BMI as significant covariates. Of all the pharmacokinetic parameters, higher sum (aripiprazole plus dehydro-aripiprazole) trough concentrations best predicted higher BMI z-scores (P < .001) and higher Hb1Ac levels (p=0.03) during follow-up. No significant association was found between sum concentrations and effectiveness. Our results indicate a threshold with regard to safety, which suggests that therapeutic drug monitoring of aripiprazole could potentially increase safety in children and adolescents with ASD and behavioral problems.

e13011 Background: Serdemetan is a compound that can cause replicative stress type responses in tumor cells and it has been administered to patients with solid tumors. ECG data from an ongoing first-in-human study revealed effects on QT interval, related to serdemetan exposure. The aim of this project was to develop a PK-PD model to quantify the observed effects on QTc interval. Furthermore, model-based simulations were performed with different dosing scenarios to support the dose and regimen selection of next study cohorts. Methods: Clinical data from 36 subjects (doses from 4-300 mg QD) from the phase I study JNJ-26854165-CAN-1001 were used for PK and PKPD modeling. Plasma concentrations were used as input for the pharmacokinetic modeling. QTcF data were used as input for the PK-PD model. Modeling and simulations were performed using nonlinear mixed effect modeling in NONMEM version 6.2. Results: A two-compartment model with combined first- and zero-order absorption best described the pharmacokinetics of serdemetan after oral solution and tablet formulation. A small effect of food intake was observed on the absorption. QTcF effects over time were described by several components, including baseline QTc, heart rate correction (Fridericia's formulae), circadian rhythm, and the drug-induced effect, as described by a linear function of the plasma concentration. The developed PK-PD model was used to address the impact of different dosing schedules (QD, BID, Q2D) on the number of patients with a delta QTcF of > 60 ms. Simulations indicated that BID dosing had increased safety margin for QTcF effects, compared to QD or less frequent dosing at the proposed therapeutic range. Conclusions: PK-PD modeling enables the quantification of QTcF effects of serdemetan in a first-in-human study. Optimization of treatment schedules can be facilitated based upon simulation scenarios as proposed by the PK-PD model. PK-PD modeling in an early stage in drug development can be a valuable tool for dose and schedule selection. Author Disclosure Employment or Leadership Position Consultant or Advisory Role Stock Ownership Honoraria Research Funding Expert Testimony Other Remuneration Johnson & Johnson Johnson & Johnson

Voriconazole is a widely used antifungal agent in immunocompromised patients, but its utility is limited by its variable exposure and narrow therapeutic index. Population pharmacokinetic (PK) models have been used to characterize voriconazole PK and derive individualized dosing regimens. However, determinants of temporal within-patient variability of voriconazole PK were not well established. We aimed to characterize temporal variability of voriconazole PK within individuals and identify predictive clinical factors. This study was conducted as a part of a single-institution, phase I study of intravenous voriconazole in children undergoing hematopoietic cell transplantation (NCT02227797). We analyzed voriconazole PK study data collected at week 1 and again at week 2 after the start of voriconazole therapy in 59 pediatric patients undergoing HCT (age <21 years). Population PK analysis using nonlinear mixed effect modeling was performed to analyze temporal within-individual variability of voriconazole PK by incorporating a between-occasion variability term in the model. A 2-compartment linear elimination model incorporating body weight and cytochrome P450 2C19 phenotype described the data. The ratio of individual voriconazole clearance between weeks 1 and 2 ranged from 0.11 to 3.3 (-9.1 to +3.3-fold change). Incorporation of covariate effects by serum C-reactive protein and albumin levels decreased between-occasion variability of clearance as compared to the model without them (coefficient of variation, 41.2% and 59.5%, respectively) and improved the model fit (P < .05). As significant covariates on voriconazole PK, C-reactive protein and albumin concentrations may potentially serve as useful biomarkers as part of therapeutic drug monitoring.

A multivariate nonlinear mixed effects model for longitudinal image analysis: Application to amyloid imaging