Prospective Trial on the Use of Trough Concentration versus Area under the Curve To Determine Therapeutic Vancomycin Dosing.

We hypothesized that dosing vancomycin to achieve trough concentrations of >15 mg/liter overdoses many adults compared to area under the concentration-time curve (AUC)-guided dosing. We conducted a 3-year, prospective study of vancomycin dosing, plasma concentrations, and outcomes. In year 1, nonstudy clinicians targeted trough concentrations of 10 to 20 mg/liter (infection dependent) and controlled dosing. In years 2 and 3, the study team controlled vancomycin dosing with BestDose Bayesian software to achieve a daily, steady-state AUC/MIC ratio of ≥400, with a maximum AUC value of 800 mg · h/liter, regardless of trough concentration. For Bayesian estimation of AUCs, we used trough samples in years 1 and 2 and optimally timed samples in year 3. We enrolled 252 adults who were ≥18 years old with ≥1 available vancomycin concentration. Only 19% of all trough concentrations were therapeutic versus 70% of AUCs (P < 0.0001). After enrollment, median trough concentrations by year were 14.4, 9.7, and 10.9 mg/liter (P = 0.005), with 36%, 7%, and 6% over 15 mg/liter (P < 0.0001). Bayesian AUC-guided dosing in years 2 and 3 was associated with fewer additional blood samples per subject (3.6, 2.0, and 2.4; P = 0.003), shorter therapy durations (8.2, 5.4, and 4.7 days; P = 0.03), and reduced nephrotoxicity (8%, 0%, and 2%; P = 0.01). The median inpatient stay was 20 days among nephrotoxic patients versus 6 days (P = 0.002). There was no difference in efficacy by year, with 42% of patients having microbiologically proven infections. Compared to trough concentration targets, AUC-guided, Bayesian estimation-assisted vancomycin dosing was associated with decreased nephrotoxicity, reduced per-patient blood sampling, and shorter length of therapy, without compromising efficacy. These benefits have the potential for substantial cost savings. (This study has been registered at ClinicalTrials.gov under registration no. NCT01932034.).

Accurately Achieving Target Busulfan Exposure in Children and Adolescents With Very Limited Sampling and the BestDose Software.

BACKGROUND: Busulfan dose adjustment is routinely guided by plasma concentration monitoring using 4-9 blood samples per dose adjustment, but a pharmacometric Bayesian approach could reduce this sample burden. METHODS: The authors developed a nonparametric population model with Pmetrics. They used it to simulate optimal initial busulfan dosages, and in a blinded manner, they compared dosage adjustments using the model in the BestDose software to dosage adjustments calculated by noncompartmental estimation of area under the time-concentration curve at a national reference laboratory in a cohort of patients not included in model building. RESULTS: Mean (range) age of the 53 model-building subjects was 7.8 years (0.2-19.0 years) and weight was 26.5 kg (5.6-78.0 kg), similar to nearly 120 validation subjects. There were 16.7 samples (6-26 samples) per subject to build the model. The BestDose cohort was also diverse: 10.2 years (0.25-18 years) and 46.4 kg (5.2-110.9 kg). Mean bias and imprecision of the 1-compartment model-predicted busulfan concentrations were 0.42% and 9.2%, and were similar in the validation cohorts. Initial dosages to achieve average concentrations of 600-900 ng/mL were 1.1 mg/kg (≤12 kg, 67% in the target range) and 1.0 mg/kg (>12 kg, 76% in the target range). Using all 9 concentrations after dose 1 in the Bayesian estimation of dose requirements, the mean (95% confidence interval) bias of BestDose calculations for the third dose was 0.2% (-2.4% to 2.9%, P = 0.85), compared with the standard noncompartmental method based on 9 concentrations. With 1 optimally timed concentration 15 minutes after the infusion (calculated with the authors' novel MMopt algorithm) bias was -9.2% (-16.7% to -1.5%, P = 0.02). With 2 concentrations at 15 minutes and 4 hours bias was only 1.9% (-0.3% to 4.2%, P = 0.08). CONCLUSIONS: BestDose accurately calculates busulfan intravenous dosage requirements to achieve target plasma exposures in children up to 18 years of age and 110 kg using only 2 blood samples per adjustment compared with 6-9 samples for standard noncompartmental dose calculations.

Combination treatment with meropenem plus levofloxacin is synergistic against Pseudomonas aeruginosa infection in a murine model of pneumonia.

BACKGROUND: Meropenem plus levofloxacin treatment was shown to be a promising combination in our in vitro hollow fiber infection model. We strove to validate this finding in a murine Pseudomonas pneumonia model. METHODS: A dose-ranging study with meropenem and levofloxacin alone and in combination against Pseudomonas aeruginosa was performed in a granulocytopenic murine pneumonia model. Meropenem and levofloxacin were administered to partially humanize their pharmacokinetic profiles in mouse serum. Total and resistant bacterial populations were estimated after 24 hours of therapy. Pharmacokinetic profiling of both drugs was performed in plasma and epithelial lining fluid, using a population model. RESULTS: Meropenem and levofloxacin penetrations into epithelial lining fluid were 39.3% and 64.3%, respectively. Both monotherapies demonstrated good exposure responses. An innovative combination-therapy analytic approach demonstrated that the combination was statistically significantly synergistic (α = 2.475), as was shown in the hollow fiber infection model. Bacterial resistant to levofloxacin and meropenem was seen in the control arm. Levofloxacin monotherapy selected for resistance to itself. No resistant subpopulations were observed in any combination therapy arm. CONCLUSIONS: The combination of meropenem plus levofloxacin was synergistic, producing good bacterial kill and resistance suppression. Given the track record of safety of each agent, this combination may be worthy of clinical trial.

Achieving target voriconazole concentrations more accurately in children and adolescents.

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.).

Describing Assay Precision-Reciprocal of Variance Is Correct, Not CV Percent: Its Use Should Significantly Improve Laboratory Performance.

BACKGROUND: Describing assay error as percent coefficient of variation (CV%) fails as measurements approach zero. Results are censored if below some arbitrarily chosen lower limit of quantification (LLOQ). CV% gives incorrect weighting to data obtained by therapeutic drug monitoring, with incorrect parameter values in the resulting pharmacokinetic models, and incorrect dosage regimens for patient care. METHODS: CV% was compared with the reciprocal of the variance (1/var) of each assay measurement. This method has not been considered by the laboratory community. A simple description of assay standard deviation (SD) as a polynomial function of the assay measurement over its working range was developed, the reciprocal of the assay variance determined, and its results compared with CV%. RESULTS: CV% does not provide correct weighting of measured serum concentrations as required for optimal therapeutic drug monitoring. It does not permit optimally individualized models of the behavior of a drug in a patient, resulting in incorrect dosage regimens. The assay error polynomial described here, using 1/var, provides correct weighting of such data, all the way down to and including zero. There is no need to censor low results, and no need to set any arbitrary LLOQ. CONCLUSIONS: Reciprocal of variance is the correct measure of assay precision and should replace CV%. The information is easily stored as an assay error polynomial. The laboratory can serve the medical community better. There is no longer any need for LLOQ, a significant improvement. Regulatory agencies should implement this more informed policy.

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

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 SD's) 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 patient's 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.

RPEM: Randomized Monte Carlo parametric expectation maximization algorithm.

Inspired from quantum Monte Carlo, by sampling discrete and continuous variables at the same time using the Metropolis-Hastings algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). We compared RPEM with NONMEM's Importance Sampling Method (IMP), Monolix's Stochastic Approximation Expectation Maximization (SAEM), and Certara's Quasi-Random Parametric Expectation Maximization (QRPEM) for a realistic two-compartment voriconazole model with ordinary differential equations using simulated data. We show that RPEM is as fast and as accurate as the algorithms IMP, QRPEM, and SAEM for the voriconazole model in reconstructing the population parameters, for the normal and log-normal cases.

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.

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.

An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics.

Population pharmacokinetic (PK) modeling has become a cornerstone of drug development and optimal patient dosing. This approach offers great benefits for datasets with sparse sampling, such as in pediatric patients, and can describe between-patient variability. While most current algorithms assume normal or log-normal distributions for PK parameters, we present a mathematically consistent nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions without any assumption about the shape of the distribution. This approach can handle distributions with any shape for all PK parameters. It is shown in convexity theory that the NPML estimator is discrete, meaning that it has finite number of points with nonzero probability. In fact, there are at most N points where N is the number of observed subjects. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. In the simplest case, each point essentially represents the set of PK parameters for one patient. The probability of the points is found by a primal-dual interior-point method; the location of the support points is found by an adaptive grid method. Our method is able to handle high-dimensional and complex multivariate mixture models. An important application is discussed for the problem of population pharmacokinetics and a nontrivial example is treated. Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics. Thereby, this approach presents an important addition to the pharmacometric toolbox for drug development and optimal patient dosing.

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.

Kullback-Leibler Markov chain Monte Carlo--a new algorithm for finite mixture analysis and its application to gene expression data.

In this paper, we study Bayesian analysis of nonlinear hierarchical mixture models with a finite but unknown number of components. Our approach is based on Markov chain Monte Carlo (MCMC) methods. One of the applications of our method is directed to the clustering problem in gene expression analysis. From a mathematical and statistical point of view, we discuss the following topics: theoretical and practical convergence problems of the MCMC method; determination of the number of components in the mixture; and computational problems associated with likelihood calculations. In the existing literature, these problems have mainly been addressed in the linear case. One of the main contributions of this paper is developing a method for the nonlinear case. Our approach is based on a combination of methods including Gibbs sampling, random permutation sampling, birth-death MCMC, and Kullback-Leibler distance.

Nonlinear Random Effects Mixture Models: Maximum Likelihood Estimation via the EM Algorithm.

Nonlinear random effects models with finite mixture structures are used to identify polymorphism in pharmacokinetic/pharmacodynamic phenotypes. An EM algorithm for maximum likelihood estimation approach is developed and uses sampling-based methods to implement the expectation step, that results in an analytically tractable maximization step. A benefit of the approach is that no model linearization is performed and the estimation precision can be arbitrarily controlled by the sampling process. A detailed simulation study illustrates the feasibility of the estimation approach and evaluates its performance. Applications of the proposed nonlinear random effects mixture model approach to other population pharmacokinetic/pharmacodynamic problems will be of interest for future investigation.

Parametric and nonparametric population methods: their comparative performance in analysing a clinical dataset and two Monte Carlo simulation studies.

BACKGROUND AND OBJECTIVES: This study examined parametric and nonparametric population modelling methods in three different analyses. The first analysis was of a real, although small, clinical dataset from 17 patients receiving intramuscular amikacin. The second analysis was of a Monte Carlo simulation study in which the populations ranged from 25 to 800 subjects, the model parameter distributions were Gaussian and all the simulated parameter values of the subjects were exactly known prior to the analysis. The third analysis was again of a Monte Carlo study in which the exactly known population sample consisted of a unimodal Gaussian distribution for the apparent volume of distribution (V(d)), but a bimodal distribution for the elimination rate constant (k(e)), simulating rapid and slow eliminators of a drug. METHODS: For the clinical dataset, the parametric iterative two-stage Bayesian (IT2B) approach, with the first-order conditional estimation (FOCE) approximation calculation of the conditional likelihoods, was used together with the nonparametric expectation-maximisation (NPEM) and nonparametric adaptive grid (NPAG) approaches, both of which use exact computations of the likelihood. For the first Monte Carlo simulation study, these programs were also used. A one-compartment model with unimodal Gaussian parameters V(d) and k(e) was employed, with a simulated intravenous bolus dose and two simulated serum concentrations per subject. In addition, a newer parametric expectation-maximisation (PEM) program with a Faure low discrepancy computation of the conditional likelihoods, as well as nonlinear mixed-effects modelling software (NONMEM), both the first-order (FO) and the FOCE versions, were used. For the second Monte Carlo study, a one-compartment model with an intravenous bolus dose was again used, with five simulated serum samples obtained from early to late after dosing. A unimodal distribution for V(d) and a bimodal distribution for k(e) were chosen to simulate two subpopulations of 'fast' and 'slow' metabolisers of a drug. NPEM results were compared with that of a unimodal parametric joint density having the true population parameter means and covariance. RESULTS: For the clinical dataset, the interindividual parameter percent coefficients of variation (CV%) were smallest with IT2B, suggesting less diversity in the population parameter distributions. However, the exact likelihood of the results was also smaller with IT2B, and was 14 logs greater with NPEM and NPAG, both of which found a greater and more likely diversity in the population studied. For the first Monte Carlo dataset, NPAG and PEM, both using accurate likelihood computations, showed statistical consistency. Consistency means that the more subjects studied, the closer the estimated parameter values approach the true values. NONMEM FOCE and NONMEM FO, as well as the IT2B FOCE methods, do not have this guarantee. Results obtained by IT2B FOCE, for example, often strayed visibly away from the true values as more subjects were studied. Furthermore, with respect to statistical efficiency (precision of parameter estimates), NPAG and PEM had good efficiency and precise parameter estimates, while precision suffered with NONMEM FOCE and IT2B FOCE, and severely so with NONMEM FO. For the second Monte Carlo dataset, NPEM closely approximated the true bimodal population joint density, while an exact parametric representation of an assumed joint unimodal density having the true population means, standard deviations and correlation gave a totally different picture. CONCLUSIONS: The smaller population interindividual CV% estimates with IT2B on the clinical dataset are probably the result of assuming Gaussian parameter distributions and/or of using the FOCE approximation. NPEM and NPAG, having no constraints on the shape of the population parameter distributions, and which compute the likelihood exactly and estimate parameter values with greater precision, detected the more likely greater diversity in the parameter values in the population studied. In the first Monte Carlo study, NPAG and PEM had more precise parameter estimates than either IT2B FOCE or NONMEM FOCE, as well as much more precise estimates than NONMEM FO. In the second Monte Carlo study, NPEM easily detected the bimodal parameter distribution at this initial step without requiring any further information. Population modelling methods using exact or accurate computations have more precise parameter estimation, better stochastic convergence properties and are, very importantly, statistically consistent. Nonparametric methods are better than parametric methods at analysing populations having unanticipated non-Gaussian or multimodal parameter distributions.

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.

NPEST: a nonparametric method and a database for transcription start site prediction.

In this paper we present NPEST, a novel tool for the analysis of expressed sequence tags (EST) distributions and transcription start site (TSS) prediction. This method estimates an unknown probability distribution of ESTs using a maximum likelihood (ML) approach, which is then used to predict positions of TSS. Accurate identification of TSS is an important genomics task, since the position of regulatory elements with respect to the TSS can have large effects on gene regulation, and performance of promoter motif-finding methods depends on correct identification of TSSs. Our probabilistic approach expands recognition capabilities to multiple TSS per locus that may be a useful tool to enhance the understanding of alternative splicing mechanisms. This paper presents analysis of simulated data as well as statistical analysis of promoter regions of a model dicot plant Arabidopsis thaliana. Using our statistical tool we analyzed 16520 loci and developed a database of TSS, which is now publicly available at www.glacombio.net/NPEST.

IMPLICIT DUAL CONTROL BASED ON PARTICLE FILTERING AND FORWARD DYNAMIC PROGRAMMING.

This paper develops a sampling-based approach to implicit dual control. Implicit dual control methods synthesize stochastic control policies by systematically approximating the stochastic dynamic programming equations of Bellman, in contrast to explicit dual control methods that artificially induce probing into the control law by modifying the cost function to include a term that rewards learning. The proposed implicit dual control approach is novel in that it combines a particle filter with a policy-iteration method for forward dynamic programming. The integration of the two methods provides a complete sampling-based approach to the problem. Implementation of the approach is simplified by making use of a specific architecture denoted as an H-block. Practical suggestions are given for reducing computational loads within the H-block for real-time applications. As an example, the method is applied to the control of a stochastic pendulum model having unknown mass, length, initial position and velocity, and unknown sign of its dc gain. Simulation results indicate that active controllers based on the described method can systematically improve closed-loop performance with respect to other more common stochastic control approaches.