Mixture models and subpopulation classification: a pharmacokinetic simulation study and application to metoprolol CYP2D6 phenotype

Evaluation of the estimation and classification performance of NONMEM when applying mixture model for drug clearance

Maximum likelihood estimation of parameters involving mixture model is known to have significant and specific patterns of errors. Population pharmacokinetic (PopPK) modeling using NONMEM is no exception. A few relevant studies on estimation and classification performance were done, but a comprehensive study was not yet available. The current study aims to evaluate performance and likelihood ratio test (LRT)‐based true covariate detection rate when fitting a bimodal mixture of drug clearance (CL) in NONMEM. A large number of PopPK datasets with various settings were simulated and then estimated. The estimates were compared to the simulated values and summarized. The separation between the CL distributions of the two subpopulations is systematically overestimated. The major factor associated with the performance is the change in the minimum objective function value after removing the mixture component (dOFV). Other significant factors include estimated disparity index (DI), estimated mixing proportion, and number of subjects in the dataset. Small dOFV and large estimated DI are associated with the worst performance. Omitting a true mixture resulted in reduced true covariate detection rates. It is recommended that on top of routinely generated standard errors and model diagnostics, dOFV, and other factors when necessary, should be taken into account for the evaluation of performance when fitting mixture model using NONMEM. In addition, when fitting mixture model for CL is intended, the mixture component should be introduced prior to LRT‐based covariate model development for CL.

Application of Deep Neural Networks as a Prescreening Tool to Assign Individualized Absorption Models in Pharmacokinetic Analysis

A specific model for drug absorption is necessarily assumed in pharmacokinetic (PK) analyses following extravascular dosing. Unfortunately, an inappropriate absorption model may force other model parameters to be poorly estimated. An added complexity arises in population PK analyses when different individuals appear to have different absorption patterns. The aim of this study is to demonstrate that a deep neural network (DNN) can be used to prescreen data and assign an individualized absorption model consistent with either a first-order, Erlang, or split-peak process. Ten thousand profiles were simulated for each of the three aforementioned shapes and used for training the DNN algorithm with a 30% hold-out validation set. During the training phase, a 99.7% accuracy was attained, with 99.4% accuracy during in the validation process. In testing the algorithm classification performance with external patient data, a 93.7% accuracy was reached. This algorithm was developed to prescreen individual data and assign a particular absorption model prior to a population PK analysis. We envision it being used as an efficient prescreening tool in other situations that involve a model component that appears to be variable across subjects. It has the potential to reduce the time needed to perform a manual visual assignment and eliminate inter-assessor variability and bias in assigning a sub-model.

Development of visual predictive checks accounting for multimodal parameter distributions in mixture models

The assumption of interindividual variability being unimodally distributed in nonlinear mixed effects models does not hold when the population under study displays multimodal parameter distributions. Mixture models allow the identification of parameters characteristic to a subpopulation by describing these multimodalities. Visual predictive check (VPC) is a standard simulation based diagnostic tool, but not yet adapted to account for multimodal parameter distributions. Mixture model analysis provides the probability for an individual to belong to a subpopulation (IPmix) and the most likely subpopulation for an individual to belong to (MIXEST). Using simulated data examples, two implementation strategies were followed to split the data into subpopulations for the development of mixture model specific VPCs. The first strategy splits the observed and simulated data according to the MIXEST assignment. A shortcoming of the MIXEST-based allocation strategy was a biased allocation towards the dominating subpopulation. This shortcoming was avoided by splitting observed and simulated data according to the IPmix assignment. For illustration purpose, the approaches were also applied to an irinotecan mixture model demonstrating 36% lower clearance of irinotecan metabolite (SN-38) in individuals with UGT1A1 homo/heterozygote versus wild-type genotype. VPCs with segregated subpopulations were helpful in identifying model misspecifications which were not evident with standard VPCs. The new tool provides an enhanced power of evaluation of mixture models.

Metoprolol Dose Equivalence in Adult Men and Women Based on Gender Differences: Pharmacokinetic Modeling and Simulations

Recent meta-analyses and publications over the past 15 years have provided evidence showing there are considerable gender differences in the pharmacokinetics of metoprolol. Throughout this time, there have not been any research articles proposing a gender stratified dose-adjustment resulting in an equivalent total drug exposure. Metoprolol pharmacokinetic data was obtained from a previous publication. Data was modeled using nonlinear mixed effect modeling using the MONOLIX software package to quantify metoprolol concentration–time data. Gender-stratified dosing simulations were conducted to identify equivalent total drug exposure based on a 100 mg dose in adults. Based on the pharmacokinetic modeling and simulations, a 50 mg dose in adult women provides an approximately similar metoprolol drug exposure to a 100 mg dose in adult men.

Gender based Dosing of Metoprolol in the Elderly using Population Pharmacokinetic Modeling and Simulations

INTRODUCTION

This article seeks to clarify if gender-based differences occur in the pharmacokinetics of metoprolol in the elderly patients. There are a series of physiologic changes that occur in the elderly ranging from decreased hepatic blood flow to increased adiposity causing higher plasma concentrations at therapeutic doses as compared to the healthy young population.

METHODS

Population pharmacokinetic modeling were performed using MONOLIX and Monte-Carlo simulations were conducted using MATLAB. The data was based from a previously published dataset where elderly patients, having multiple comorbidities, were administered a 50mg dose of metoprolol.

RESULTS

Metoprolol was modeled using a one-compartment model and resulted in the following population pharmacokinetic parameters: volume of distribution, V=38L (CV=155%), clearance rates, CL-Men=105L/hour and CL-Women=59.1L/hour (38%), time lag, Tlag=0.469 hour (CV=17%), and the absorption rate constant, Ka=0.235 hr^-1 (CV=23%).

CONCLUSION

Gender stratified doses resulting in an equivalent systemic metoprolol exposure in geriatric patients have been identified. Metoprolol doses resulting a similar AUC in a healthy young male administered 50mg tablet were 15mg for geriatric women and 25mg for geriatric men. Further, Metoprolol doses of 25mg for geriatric women and 50mg for geriatric men resulted in an equivalent AUC to a healthy young males dosed with a 100mg tablet. A 15mg Metoprolol tablet may need to be compounded to account for the gender differences in Metoprolol pharmacokinetics.

Evaluation of Approaches to Deal with Low-Frequency Nuisance Covariates in Population Pharmacokinetic Analyses

Clinical studies include occurrences of rare variables, like genotypes, which due to their frequency and strength render their effects difficult to estimate from a dataset. Variables that influence the estimated value of a model-based parameter are termed covariates. It is often difficult to determine if such an effect is significant, since type I error can be inflated when the covariate is rare. Their presence may have either an insubstantial effect on the parameters of interest, hence are ignorable, or conversely they may be influential and therefore non-ignorable. In the case that these covariate effects cannot be estimated due to power and are non-ignorable, then these are considered nuisance, in that they have to be considered but due to type 1 error are of limited interest. This study assesses methods of handling nuisance covariate effects. The specific objectives include (1) calibrating the frequency of a covariate that is associated with type 1 error inflation, (2) calibrating its strength that renders it non-ignorable and (3) evaluating methods for handling these non-ignorable covariates in a nonlinear mixed effects model setting. Type 1 error was determined for the Wald test. Methods considered for handling the nuisance covariate effects were case deletion, Box-Cox transformation and inclusion of a specific fixed effects parameter. Non-ignorable nuisance covariates were found to be effectively handled through addition of a fixed effect parameter.

Tetrahydrobiopterin (BH4) responsiveness in neonates with hyperphenylalaninemia: a semi-mechanistically-based, nonlinear mixed-effect modeling

Neonatal loading studies with tetrahydrobiopterin (BH4) are used to detect hyperphenylalaninemia due to BH4 deficiency by evaluating decreases in blood phenylalanine (Phe) concentrations post BH4 load. BH4 responsiveness in phenylalanine hydroxylase (PAH)-deficient patients introduced a new diagnostic aspect for this test. In older children, a broad spectrum of different levels of responsiveness has been described. The primary objective of this study was to develop a pharmacodynamic model to improve the description of individual sensitivity to BH4 in the neonatal period. Secondary objectives were to evaluate BH4 responsiveness in a large number of PAH-deficient patients from a neonatal screening program and in patients with various confirmed BH4 deficiencies from the BIODEF database. Descriptive statistics in patients with PAH deficiency with 0-24-h data available showed that 129 of 340 patients (37.9%) had a >30% decrease in Phe levels post load. Patients with dihydropteridine reductase deficiency (n = 53) could not be differentiated from BH4-responsive patients with PAH deficiency. The pharmacologic turnover model, "stimulation of loss" of Phe following BH4 load, fitted the data best. Using the model, 193 of 194 (99.5%) patients with a proven BH4 synthesis deficiency or recycling defect were classified as BH4 sensitive. Among patients with PAH deficiency, 216 of 375 (57.6%) patients showed sensitivity to BH4, albeit with a pronounced variability; PAH-deficient patients with blood Phe <1200 μmol/L at time 0 showed higher sensitivity than patients with blood Phe levels >1200 μmol/L. External validation showed good correlation between the present approach, using 0-24-h blood Phe data, and the published 48-h prognostic test. Pharmacodynamic modeling of Phe levels following a BH4 loading test is sufficiently powerful to detect a wide range of responsiveness, interpretable as a measure of sensitivity to BH4. However, the clinical relevance of small responses needs to be evaluated by further studies of their relationship to long-term response to BH4 treatment.

Nanocomposites of graphene and cytochrome P450 2D6 isozyme for electrochemical-driven tramadol metabolism

Cytochrome P450 enzymes (cyt P450s) with an active center of iron protoheme are involved in most clinical drugs metabolism process. Herein, an electrochemical platform for the investigation of drug metabolism in vitro was constructed by immobilizing cytochrome P450 2D6 (CYP2D6) with cyt P450 reductase (CPR) on graphene modified glass carbon electrode. Direct and reversible electron transfer of the immobilized CYP2D6 with the direct electron transfer constant of 0.47 s(-1) and midpoint potential of -0.483 V was obtained. In the presence of substrate tramadol, the electrochemical-driven CYP2D6 mediated catalytic behavior toward the conversion of tramadol to o-demethyl-tramadol was confirmed. The Michaelis-Menten constant (Km(app)) and heterogeneous reaction rate constant during the metabolism of tramadol were calculated to be 23.85 μM and 1.96 cm s(-1), respectively. The inhibition effect of quinidine on CYP2D6 catalyze-cycle was also investigated. Furthermore, this system was applied to studying the metabolism of other drugs.

Disease progression model in subjects with mild cognitive impairment from the Alzheimer's disease neuroimaging initiative: CSF biomarkers predict population subtypes

AIM

The objective is to develop a semi-mechanistic disease progression model for mild cognitive impairment (MCI) subjects. The model aims to describe the longitudinal progression of ADAS-cog scores from the Alzheimer's disease neuroimaging initiative trial that had data from 198 MCI subjects with cerebrospinal fluid (CSF) information who were followed for 3 years.

METHOD

Various covariates were tested on disease progression parameters and these variables fell into six categories: imaging volumetrics, biochemical, genetic, demographic, cognitive tests and CSF biomarkers.

RESULTS

CSF biomarkers were associated with both baseline disease score and disease progression rate in subjects with MCI. Baseline disease score was also correlated with atrophy measured using hippocampal volume. Progression rate was also predicted by executive functioning as measured by the Trail B-test.

CONCLUSION

CSF biomarkers have the ability to discriminate MCI subjects into sub-populations that exhibit markedly different rates of disease progression on the ADAS-cog scale. These biomarkers can therefore be utilized for designing clinical trials enriched with subjects that carry the underlying disease pathology.

A pregnancy physiologically based pharmacokinetic (p-PBPK) model for disposition of drugs metabolized by CYP1A2, CYP2D6 and CYP3A4

AIMS

Pregnant women are usually not part of the traditional drug development programme. Pregnancy is associated with major biological and physiological changes that alter the pharmacokinetics (PK) of drugs. Prediction of the changes to drug exposure in this group of patients may help to prevent under- or overtreatment. We have used a pregnancy physiologically based pharmacokinetic (p-PBPK) model to assess the likely impact of pregnancy on three model compounds, namely caffeine, metoprolol and midazolam, based on the knowledge of their disposition in nonpregnant women and information from in vitro studies.

METHODS

A perfusion-limited form of a 13-compartment full-PBPK model (Simcyp® Simulator) was used for the nonpregnant women, and this was extended to the pregnant state by applying known changes to all model components (including the gestational related activity of specific cytochrome P450 enzymes) and through the addition of an extra compartment to represent the fetoplacental unit. The uterus and the mammary glands were grouped into the muscle compartment. The model was implemented in Matlab Simulink and validated using clinical observations.

RESULTS

The p-PBPK model predicted the PK changes of three model compounds (namely caffeine, metoprolol and midazolam) for CYP1A2, CYP2D6 and CYP3A4 during pregnancy within twofold of observed values. The changes during the third trimester were predicted to be a 100% increase, a 30% decrease and a 35% decrease in the exposure of caffeine, metoprolol and midazolam, respectively, compared with the nonpregnant women.

CONCLUSIONS

In the absence of clinical data, the in silico prediction of PK behaviour during pregnancy can provide a valuable aid to dose adjustment in pregnant women. The performance of the model for drugs metabolized by a single enzyme to different degrees (high and low extraction) and for drugs that are eliminated by several different routes warrants further study.

Ethnic differences in the population pharmacokinetics and pharmacodynamics of warfarin

Ethnic differences in warfarin maintenance doses have been documented amongst the three major Asian ethnic groups (Chinese, Malay and Indian) in Singapore. Studies have shown that cytochrome P450 2C9 (CYP2C9) polymorphisms alone did not entirely account for these differences. Recent reports suggest that VKORC1 (subunit of vitamin K epoxide reductase) haplotypes are more predictive of warfarin response. Population pharmacokinetic/pharmacodynamic (PK/PD) modelling techniques were employed to characterise the PK and PD of warfarin in a healthy volunteer study of 16 Chinese and Indian subjects following a single 25 mg dose of warfarin. To further investigate the underlying differences in warfarin response, a semi-mechanistic modelling approach (using an indirect response model for PCA activity) incorporating the vitamin K cycle was attempted using population methods with Bayesian inference. All eight Indian subjects had H7H7 VKORC1 haplotypes and three had either *2/wt or *3/wt CYP2C9 genotypes. Six Chinese subjects had H1H1 VKORC1 haplotypes and one had H1H7. All Chinese subjects were homozygous wt/wt for CYP2C9. Simulations to steady state were performed to examine warfarin response in subjects with different CYP2C9 and VKORC1 polymorphisms. The presence of a single *2 or *3 CYP2C9 allele reduced mean [SE (standard error)] S-warfarin clearance by 35% from 0.276 (0.04) to 0.180 (0.11) l/h. Subjects with VKORC1 haplotype groups of H7H7 had increased mean (SE) C (50,S) (concentration of S-warfarin required to achieve 50% of maximum effect) of 479 (7.3) compared to 206 (6.7) ng/ml in subjects with the H1H1 groups. For subjects with the H1H7 haplotype, mean (SE) C (50,S) increased 1.4 times to 288 (1.3) ng/ml compared to subjects with H1H1 haplotypes. Steady state simulations showed that whilst CYP2C9 polymorphisms affect the PK of warfarin, VKORC1 haplotypes may be better predictors of warfarin response. Since 90% of Chinese subjects had the VKORC1 H1 haplotype and 100% of Indian subjects the H7 haplotype in this study, ethnic differences in warfarin response in this study appear to be linked to differences in VKORC1 haplotypes.

Population Pharmacokinetic/Pharmacodyanamic Mixture Models via Maximum a Posteriori Estimation

Pharmacokinetic/pharmacodynamic phenotypes are identified using nonlinear random effects models with finite mixture structures. A maximum a posteriori probability estimation approach is presented using an EM algorithm with importance sampling. Parameters for the conjugate prior densities can be based on prior studies or set to represent vague knowledge about the model parameters. A detailed simulation study illustrates the feasibility of the approach and evaluates its performance, including selecting the number of mixture components and proper subject classification.