Michael Van Guilder

Accurate detection of outliers and subpopulations with Pmetrics, a nonparametric and parametric pharmacometric modeling and simulation package for R.

Introduction: Nonparametric population modeling algorithms have a theoretical superiority over parametric methods to detect pharmacokinetic and pharmacodynamic subgroups and outliers within a study population. Methods: The authors created “Pmetrics,” a new Windows and Unix R software package that updates the older MM-USCPACK software for nonparametric and parametric population modeling and simulation of pharmacokinetic and pharmacodynamic systems. The parametric iterative 2-stage Bayesian and the nonparametric adaptive grid (NPAG) approaches in Pmetrics were used to fit a simulated population with bimodal elimination (Kel) and unimodal volume of distribution (Vd), plus an extreme outlier, for a 1-compartment model of an intravenous drug. Results: The true means (SD) for Kel and Vd in the population sample were 0.19 (0.17) and 102 (22.3), respectively. Those found by NPAG were 0.19 (0.16) and 104 (22.6). The iterative 2-stage Bayesian estimated them to be 0.18 (0.16) and 104 (24.4). However, given the bimodality of Kel, no subject had a value near the mean for the population. Only NPAG was able to accurately detect the bimodal distribution for Kel and to find the outlier in both the population model and in the Bayesian posterior parameter estimates. Conclusions: Built on over 3 decades of work, Pmetrics adopts a robust, reliable, and mature nonparametric approach to population modeling, which was better than the parametric method at discovering true pharmacokinetic subgroups and an outlier.

Model-based, goal-oriented, individualised drug therapy : Linkage of population modelling, new 'multiple model' dosage design, Bayesian feedback and individualised target goals

SummaryThis article examines the use of population pharmacokinetic models to store experiences about drugs in patients and to apply that experience to the care of new patients. Population models are the Bayesian prior. For truly individualised therapy, it is necessary first to select a specific target goal, such as a desired serum or peripheral compartment concentration, and then to develop the dosage regimen individualised to best hit that target in that patient.One must monitor the behaviour of the drug by measuring serum concentrations or other responses, hopefully obtained at optimally chosen times, not only to see the raw results, but to also make an individualised (Bayesian posterior) model of how the drug is behaving in that patient. Only then can one see the relationship between the dose and the absorption, distribution, effect and elimination of the drug, and the patient’s clinical sensitivity to it; one must always look at the patient. Only by looking at both the patient and the model can it be judged whether the target goal was correct or needs to be changed. The adjusted dosage regimen is again developed to hit that target most precisely starting with the very next dose, not just for some future steady state.Nonparametric population models have discrete, not continuous, parameter distributions. These lead naturally into the multiple model method of dosage design, specifically to hit a desired target with the greatest possible precision for whatever past experience and present data are available on that drug — a new feature for this goal-oriented, model-based, individualised drug therapy. As clinical versions of this new approach become available from several centres, it should lead to further improvements in patient care, especially for bacterial and viral infections, cardiovascular therapy, and cancer and transplant situations.

Population Modeling and Monte Carlo Simulation Study of the Pharmacokinetics and Antituberculosis Pharmacodynamics of Rifampin in Lungs

ABSTRACT Little information exists on the pulmonary pharmacology of antituberculosis drugs. We used population pharmacokinetic modeling and Monte Carlo simulation to describe and explore the pulmonary pharmacokinetics and pharmacodynamics of rifampin (RIF; rifampicin). A population pharmacokinetic model that adequately described the plasma, epithelial lining fluid (ELF), and alveolar cell (AC) concentrations of RIF in a population of 34 human volunteers was made by use of the nonparametric adaptive grid (NPAG) algorithm. The estimated concentrations correlated well with the measured concentrations, and there was little bias and good precision. The results obtained with the NPAG algorithm were then imported into Matlab software to perform a 10,000-subject Monte Carlo simulation. The ability of RIF to suppress the development of drug resistance and to induce a sufficient bactericidal effect against Mycobacterium tuberculosis was evaluated by calculating the proportion of subjects achieving specific target values for the maximum concentration of drug (Cmax)/MIC ratio and the area under the concentration-time curve from time zero to 24 h (AUC0-24)/MIC ratio, respectively. At the lowest MIC (0.01 mg/liter), after the administration of one 600-mg oral dose, the rates of target attainment for Cmax/MIC (≥175) were 95% in ACs, 48.8% in plasma, and 35.9% in ELF. Under the same conditions, the target attainment results for the killing effect were 100% in plasma (AUC0-24/MIC ≥ 271) but only 54.5% in ELF (AUC0-24/MIC ≥ 665). The use of a 1,200-mg RIF dose was associated with better results for target attainment. The overall results suggest that the pulmonary concentrations obtained with the standard RIF dose are too low in most subjects. This work supports the need to evaluate higher doses of RIF for the treatment of patients with tuberculosis.

Two general methods for population pharmacokinetic modeling: non-parametric adaptive grid and non-parametric Bayesian

Population pharmacokinetic (PK) modeling methods can be statistically classified as either parametric or nonparametric (NP). Each classification can be divided into maximum likelihood (ML) or Bayesian (B) approaches. In this paper we discuss the nonparametric case using both maximum likelihood and Bayesian approaches. We present two nonparametric methods for estimating the unknown joint population distribution of model parameter values in a pharmacokinetic/pharmacodynamic (PK/PD) dataset. The first method is the NP Adaptive Grid (NPAG). The second is the NP Bayesian (NPB) algorithm with a stick-breaking process to construct a Dirichlet prior. Our objective is to compare the performance of these two methods using a simulated PK/PD dataset. Our results showed excellent performance of NPAG and NPB in a realistically simulated PK study. This simulation allowed us to have benchmarks in the form of the true population parameters to compare with the estimates produced by the two methods, while incorporating challenges like unbalanced sample times and sample numbers as well as the ability to include the covariate of patient weight. We conclude that both NPML and NPB can be used in realistic PK/PD population analysis problems. The advantages of one versus the other are discussed in the paper. NPAG and NPB are implemented in R and freely available for download within the Pmetrics package from www.lapk.org.

Achieving Target Voriconazole Concentrations More Accurately in Children and Adolescents

ABSTRACT Despite the documented benefit of voriconazole therapeutic drug monitoring, nonlinear pharmacokinetics make the timing of steady-state trough sampling and appropriate dose adjustments unpredictable by conventional methods. We developed a nonparametric population model with data from 141 previously richly sampled children and adults. We then used it in our multiple-model Bayesian adaptive control algorithm to predict measured concentrations and doses in a separate cohort of 33 pediatric patients aged 8 months to 17 years who were receiving voriconazole and enrolled in a pharmacokinetic study. Using all available samples to estimate the individual Bayesian posterior parameter values, the median percent prediction bias relative to a measured target trough concentration in the patients was 1.1% (interquartile range, −17.1 to 10%). Compared to the actual dose that resulted in the target concentration, the percent bias of the predicted dose was −0.7% (interquartile range, −7 to 20%). Using only trough concentrations to generate the Bayesian posterior parameter values, the target bias was 6.4% (interquartile range, −1.4 to 14.7%; P = 0.16 versus the full posterior parameter value) and the dose bias was −6.7% (interquartile range, −18.7 to 2.4%; P = 0.15). Use of a sample collected at an optimal time of 4 h after a dose, in addition to the trough concentration, resulted in a nonsignificantly improved target bias of 3.8% (interquartile range, −13.1 to 18%; P = 0.32) and a dose bias of −3.5% (interquartile range, −18 to 14%; P = 0.33). With the nonparametric population model and trough concentrations, our control algorithm can accurately manage voriconazole therapy in children independently of steady-state conditions, and it is generalizable to any drug with a nonparametric pharmacokinetic model. (This study has been registered at ClinicalTrials.gov under registration no. NCT01976078.)

Analysis of Combination Drug Therapy to Develop Regimens with Shortened Duration of Treatment for Tuberculosis

Rationale Tuberculosis remains a worldwide problem, particularly with the advent of multi-drug resistance. Shortening therapy duration for Mycobacterium tuberculosis is a major goal, requiring generation of optimal kill rate and resistance-suppression. Combination therapy is required to attain the goal of shorter therapy. Objectives Our objective was to identify a method for identifying optimal combination chemotherapy. We developed a mathematical model for attaining this end. This is accomplished by identifying drug effect interaction (synergy, additivity, antagonism) for susceptible organisms and subpopulations resistant to each drug in the combination. Methods We studied the combination of linezolid plus rifampin in our hollow fiber infection model. We generated a fully parametric drug effect interaction mathematical model. The results were subjected to Monte Carlo simulation to extend the findings to a population of patients by accounting for between-patient variability in drug pharmacokinetics. Results All monotherapy allowed emergence of resistance over the first two weeks of the experiment. In combination, the interaction was additive for each population (susceptible and resistant). For a 600 mg/600 mg daily regimen of linezolid plus rifampin, we demonstrated that >50% of simulated subjects had eradicated the susceptible population by day 27 with the remaining organisms resistant to one or the other drug. Only 4% of patients had complete organism eradication by experiment end. Discussion These data strongly suggest that in order to achieve the goal of shortening therapy, the original regimen may need to be changed at one month to a regimen of two completely new agents with resistance mechanisms independent of the initial regimen. This hypothesis which arose from the analysis is immediately testable in a clinical trial.

Recombinant human erythropoietin for the treatment of renal anaemia in children: no justification for bodyweight-adjusted dosage.

AbstractBackground: Drug doses for children are usually calculated by reducing adult doses in proportion to bodyweight. The clinically effective dose of recombinant human erythropoietin (epoetin) in children, however, seems to be higher than predicted by this calculation. Objective: To determine the quantitative relationship between epoetin dose, bodyweight and response in children with end-stage renal disease. Patients and Methods: The time-course of haemoglobin in 52 children during long-term treatment with epoetin beta was analysed by population pharmacodynamic modelling. Patients were 5–20 years old and weighed 16–53kg at the beginning of treatment. Epoetin beta was given intravenously three times per week after haemodialysis. Doses ranged from 110 to 7500IU (3–205 IU/kg). Haemoglobin versus time was described by assuming that the haemoglobin level rises after each dose due to the formation of new red blood cells, which then survive according to a logistic function. The initial rise after each dose was modelled in terms of absolute dose (not dose/kg). A parametric analysis was done with NONMEM, followed by a nonparametric analysis with NPAG. Results: Dose-response was best described by a sigmoid maximum-effect (Emax) model with median Emax = 0.29 g/dL, median 50% effective dose (ED50) = 2400IU and shape parameter γ = 2. The estimated median survival time of the epoetin-induced red blood cells, τ, was 76 days. Neither of the dose-response parameters Emax and ED50 showed dependence on bodyweight. The median haemoglobin response to a standard dose, 0.042 g/dL for 1000IU, was similar to that reported for adults with intravenous administration. Conclusions: Doses for children in this age range should be specified as absolute amounts rather than amounts per unit bodyweight. Initial doses can be calculated individually, based on haemoglobin level before treatment, the desired haemoglobin at steady state and the median population parameters Emax, ED50 and τ.

Nonparametric population modeling and Bayesian analysis

We read with great interest the article by Premaud et al., in your ournal [1], The nonparametric (NP) population modeling approach stimated the model parameter values and predicted the observed ycophenolic acid concentrations more precisely than the paraetric method did. We expect this because the NP method makes, s the authors say, no assumptions about the shape of the model arameter distributions, as parametric methods do. We would like o respectfully offer the comments below in the hope that they will e well taken by a group we respect very highly.

A two-compartment population pharmacokinetic-pharmacodynamic model of digoxin in adults, with implications for dosage.

Abstract: A population pharmacokinetic/pharmacodynamic model of digoxin in adult subjects was originally developed by Reuning et al in 1973. They clearly described the 2-compartment behavior of digoxin, the lack of correlation of effect with serum concentrations, and the close correlation of the observed inotropic effect of digoxin with the calculated amount of drug present in the peripheral nonserum compartment. Their model seemed most attractive for clinical use. However, to make it more applicable for maximally precise dosage, its model parameter values (means and SDs) were converted into discrete model parameter distributions using a computer program developed especially for this purpose using the method of maximum entropy. In this way, the parameter distributions became discrete rather than continuous, suitable for use in developing maximally precise digoxin dosage regimens, individualized to an adult patients age, gender, body weight, and renal function, to achieve desired specific target goals either in the central (serum) compartment or in the peripheral (effect) compartment using the method of multiple model dosage design. Some illustrative clinical applications of this model are presented and discussed. This model with a peripheral compartment reflecting clinical effect has contributed significantly to an improved understanding of the clinical behavior of digoxin in patients than is possible with models having only a single compartment, and to the improved management of digoxin therapy for more than 20 years.

A population pharmacokinetic model of epidural lidocaine in geriatric patients: effects of low-dose dopamine.

The purposes of this study were to develop a population pharmacokinetic (PK) model of epidural lidocaine in geriatric patients, to search for any difference in the PK behavior of epidural lidocaine when dopamine is given concurrently, and to develop a descriptive PK model from which to calculate dosage and infusion regimens of epidural lidocaine to define and achieve desired target goals in either the epidural or the serum compartment. Twenty patients over age 65 years, undergoing peripheral vascular surgery using continuous epidural lidocaine anesthesia, were studied. Ten patients also received an intravenous infusion of placebo (normal saline), whereas 10 other patients received an intravenous infusion of dopamine at 2 μg/kg per minute. Total plasma lidocaine concentrations (gas-chromatographic assay) were measured from arterial samples just before injecting the first epidural dose (baseline) and then at 5, 15, 30, 60, 90, and 120 minutes and hourly thereafter. Samples were also taken when the lidocaine infusion was stopped at the end of the surgery and at 30 minutes, 60 minutes, 90 minutes, 2 hours, 3 hours, 4 hours, and 5 hours after surgery. The nonparametric adaptive grid (BigNPAG) computer program in the MM-USCPACK collection was used for population PK modeling to obtain the entire discrete maximum likelihood joint parameter distribution. The assay error polynomial was determined to be 0.2 + 0.05*C. The structural population PK model was linear and had three compartments, each with first-order transfer kinetics. Lidocaine had a very fast transfer rate constant (Ka part + K20) from the epidural space to the serum compartment. This rate was slowed, by over 41%, by dopamine. The mean rate constant of elimination from the serum compartment (K20) was increased by 9.7% by dopamine. The mean rate constant for drug movement from central to peripheral compartment (K23) was increased by 47% in the patients receiving dopamine. The mean rate constant back from the peripheral to the central compartment (K32) was slowed 46% by dopamine. There was no obvious difference in the apparent volume of distribution of the central compartment between the patients given placebo and the patients receiving dopamine. In this model, there was no specific compartment for lidocaine in the cerebrospinal fluid. Cerebrospinal fluid is probably one of the components of the overall peripheral, nonserum compartment in our model. In this first population model of epidural lidocaine using a statistically consistent method, low-dose dopamine appears to decrease the rate of transfer of lidocaine from the epidural to the serum compartment and to increase both the rate of elimination of lidocaine as well as its transfer between the central (serum) and peripheral compartment presumably by increasing tissue perfusion. Serum lidocaine concentrations were slightly less in the patients receiving dopamine. Dosage requirements (overall hourly weight-adjusted infusion rates) were slightly less for the patients receiving dopamine, consistent with the slower removal of lidocaine from the epidural compartment. This model should be useful to design more optimal and individualized epidural lidocaine infusion regimens to define and achieve desired target goals in the epidural or the serum compartment.