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.

Influence of renal function estimation on pharmacokinetic modeling of vancomycin in elderly patients.

Vancomycin is a renally excreted drug, and its body clearance correlates with creatinine clearance. However, the renal function estimation equation that best predicts vancomycin clearance has not been established yet. The objective of this study was to compare the abilities of different renal function estimation equations to describe vancomycin pharmacokinetics in elderly patients. The NPAG algorithm was used to perform population pharmacokinetic analysis of vancomycin concentrations in 78 elderly patients. Six pharmacokinetic models of vancomycin clearance were built, based on the following equations: Cockcroft-Gault (CG), Jelliffe (JEL), Modification of Diet in Renal Disease (MDRD), Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) (both in milliliters per minute per 1.73 m(2)), and modified MDRD and CKD-EPI equations (both in milliliters per minute). Goodness-of-fit and predictive performances of the six PK models were compared in a learning set (58 subjects) and a validation set (20 patients). Final analysis was performed to estimate population parameters in the entire population. In the learning step, the MDRD-based model best described the data, but the CG- and JEL-based models were the least biased. The mean weighted errors of prediction were significantly different between the six models (P = 0.0071). In the validation group, predictive performances were not significantly different. However, the use of a renal function estimation equation different from that used in the model building could significantly alter predictive performance. The final analysis showed important differences in parameter distributions and AUC estimation across the six models. This study shows that methods used to estimate renal function should not be considered interchangeable for pharmacokinetic modeling and model-based estimation of vancomycin concentrations in elderly patients.

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.

Are vancomycin trough concentrations adequate for optimal dosing?

The current vancomycin therapeutic guidelines recommend the use of only trough concentrations to manage the dosing of adults with Staphylococcus aureus infections. Both vancomycin efficacy and toxicity are likely to be related to the area under the plasma concentration-time curve (AUC). We assembled richly sampled vancomycin pharmacokinetic data from three studies comprising 47 adults with various levels of renal function. With Pmetrics, the nonparametric population modeling package for R, we compared AUCs estimated from models derived from trough-only and peak-trough depleted versions of the full data set and characterized the relationship between the vancomycin trough concentration and AUC. The trough-only and peak-trough depleted data sets underestimated the true AUCs compared to the full model by a mean (95% confidence interval) of 23% (11 to 33%; P = 0.0001) and 14% (7 to 19%; P < 0.0001), respectively. In contrast, using the full model as a Bayesian prior with trough-only data allowed 97% (93 to 102%; P = 0.23) accurate AUC estimation. On the basis of 5,000 profiles simulated from the full model, among adults with normal renal function and a therapeutic AUC of ≥400 mg · h/liter for an organism for which the vancomycin MIC is 1 mg/liter, approximately 60% are expected to have a trough concentration below the suggested minimum target of 15 mg/liter for serious infections, which could result in needlessly increased doses and a risk of toxicity. Our data indicate that adjustment of vancomycin doses on the basis of trough concentrations without a Bayesian tool results in poor achievement of maximally safe and effective drug exposures in plasma and that many adults can have an adequate vancomycin AUC with a trough concentration of <15 mg/liter.

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.

Software for dosage individualization of voriconazole for immunocompromised patients.

The efficacy of voriconazole is potentially compromised by considerable pharmacokinetic variability. There are increasing insights into voriconazole concentrations that are safe and effective for treatment of invasive fungal infections. Therapeutic drug monitoring is increasingly advocated. Software to aid in the individualization of dosing would be an extremely useful clinical tool. We developed software to enable the individualization of voriconazole dosing to attain predefined serum concentration targets. The process of individualized voriconazole therapy was based on concepts of Bayesian stochastic adaptive control. Multiple-model dosage design with feedback control was used to calculate dosages that achieved desired concentration targets with maximum precision. The performance of the software program was assessed using the data from 10 recipients of an allogeneic hematopoietic stem cell transplant (HSCT) receiving intravenous (i.v.) voriconazole. The program was able to model the plasma concentrations with a high level of precision, despite the wide range of concentration trajectories and interindividual pharmacokinetic variability. The voriconazole concentrations predicted after the last dosages were largely concordant with those actually measured. Simulations provided an illustration of the way in which the software can be used to adjust dosages of patients falling outside desired concentration targets. This software appears to be an extremely useful tool to further optimize voriconazole therapy and aid in therapeutic drug monitoring. Further prospective studies are now required to define the utility of the controller in daily clinical practice.

Inclusion of CYP3A5 genotyping in a nonparametric population model improves dosing of tacrolimus early after transplantation.

Following organ engraftment, initial dosing of tacrolimus is based on recipient weight and adjusted by measured C(0) concentrations. The bioavailability and elimination of tacrolimus are affected by the patients CYP3A5 genotype. Prospective data of the clinical advantage of knowing patient's CYP3A5 genotype prior to transplantation are lacking. A nonparametric population model was developed for tacrolimus in renal transplant recipients. Data from 99 patients were used for model development and validation. A three-compartment model with first-order absorption and lag time from the dosing compartment described the data well. Clearances and volumes of distribution were allometrically scaled to body size. The final model included fat-free mass, body mass index, hematocrit, time after transplantation, and CYP3A5 genotype as covariates. The bias and imprecision were 0.35 and 1.38, respectively, in the external data set. Patients with functional CYP3A5 had 26% higher clearance and 37% lower bioavailability. Knowledge of CYP3A5 genotype provided an initial advantage, but only until 3-4 tacrolimus concentrations were known. After this, a model without CYP3A5 genotype predicted just as well. The present models seem applicable for clinical individual dose predictions but need a prospective evaluation.

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.

Comparison of four renal function estimation equations for pharmacokinetic modeling of gentamicin in geriatric patients.

Most aminoglycoside pharmacokinetic models include an index of renal function, such as creatinine clearance, to describe drug clearance. However, the best clinical descriptor of renal function for the pharmacokinetic modeling of aminoglycosides has not been established. This analysis was based on 412 gentamicin concentrations from 92 geriatric patients who received intravenous gentamicin for various infectious diseases. Four two-compartment population models were fitted to gentamicin concentrations in a learning set of 64 patients using the nonparametric adaptive grid (NPAG) algorithm. Each model included an index of renal function, namely, the Cockcroft-Gault (CG), Jelliffe (JEL), modification of diet in renal disease (MDRD), or modified MDRD (MDRDm; adjusted to individual body surface area) equation as a covariate influencing gentamicin serum clearance. Goodness of fit and predictive performance of the four models were compared using standard criteria in both the learning set and in a validation set of 28 patients. A final analysis was performed to estimate the population pharmacokinetic parameter values of the entire 92-patient group. In the learning set, the CG-based model best fit the data, followed by JEL-, MDRD-, and MDRDm-based models, with relative reductions of the Akaike information criterion of 29.4, 20.2, 14.2, and 4.2, respectively. Bias and precision of population predictions were significantly different among the four models. In the validation set, individual predictions from the four models showed marginally different biases. The final estimation confirmed the previous results. Specifically, the CG-based model showed predictive performance that was comparable to or better than that of the MDRD-based model at each stage of the analysis. This study shows that methods used to estimate renal function should not be considered interchangeable for the model-based estimation of gentamicin concentrations.

Some comments and suggestions concerning population pharmacokinetic modeling, especially of digoxin, and its relation to clinical therapy.

Population pharmacokinetic and dynamic modeling is often employed to analyze data of steady-state trough serum digoxin concentrations in the course of what is frequently regarded as routine therapeutic drug monitoring (TDM). Such a monitoring protocol is extremely uninformative. It permits only the estimation of a single parameter of a 1-compartment model, such as clearance. The use of D-optimal design strategies permits much more information to be obtained, employing models having a really meaningful structure. Strategies and protocols for routine TDM policies greatly need to be improved, incorporating these principles of optimal design. Software for population pharmacokinetic modeling has been dominated by NONMEM. However, because NONMEM is a parametric method, it must assume a shape for the model parameter distributions. If the assumption is not correct, the model will be in error, and the most likely results given the raw data will not be obtained. In addition, the likelihood as computed by NONMEM is only approximate, not exact. This impairs statistical consistency and reduces statistical efficiency and the resulting precision of model parameter estimates. Other parametric methods are superior, as they provide exact likelihoods. However, they still suffer from the constraints of assuming the shape of the model parameter distributions. Nonparametric methods are more flexible. One need not make any assumptions about the shape of the parameter distributions. Nonparametric methods also provide exact likelihoods and are statistically consistent, efficient, and precise. They also permit maximally precise dosage regimens to be developed for patients using multiple model dosage design, something parametric modeling methods cannot do. Laboratory assay errors are better described by the reciprocal of the assay variance of each measurement rather than by coefficient of variation. This is easy to do and permits more precise models to be made. This also permits estimation of assay error separately from the other sources of uncertainty in the clinical environment. This is most useful scientifically. Digoxin has at least 2-compartment behavior. Its pharmacologic and clinical effects correlate not with serum digoxin concentrations but with those in the peripheral nonserum compartment. Some illustrative clinical examples are discussed. It seems that digitalis therapy, guided by TDM and our 2 compartment models based on that of Reuning et al, can convert at least some patients with atrial fibrillation and flutter to regular sinus rhythm. Investigators have often used steady-state trough concentrations only to make a 1-compartment model and have sought only to predict future steady-state trough concentrations. Much more than this can be done, and clinical care can be much improved. Further work along these lines is greatly to be desired.

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.

Individualized Patient Care Through Model-Informed Precision Dosing: Reflections on Training Future Practitioners.

Prior to his passing, Dr. Roger Jelliffe, expressed the need for educating future physicians and clinical pharmacists on the availability of computer-based tools to support dose optimization in patients in stable or unstable physiological states. His perspectives were to be captured in a commentary for the AAPS J with a focus on incorporating population pharmacokinetic (PK)/pharmacodynamic (PD) models that are designed to hit the therapeutic target with maximal precision. Unfortunately, knowing that he would be unable to complete this project, Dr. Jelliffe requested that a manuscript conveying his concerns be completed upon his passing. With this in mind, this final installment of the AAPS J theme issue titled "Alternative Perspectives for Evaluating Drug Exposure Characteristics in a Population - Avoiding Analysis Pitfalls and Pigeonholes" is an effort to honor Dr. Jelliffe's request, conveying his concerns and the need to incorporate modeling and simulation into the training of physicians and clinical pharmacists. Accordingly, Dr. Jelliffe's perspectives have been integrated with those of the other three co-authors on the following topics: the clinical utility of population PK models; the role of multiple model (MM) dosage regimens to identify an optimal dose for an individual; tools for determining dosing regimens in renal dialysis patients (or undergoing other therapies that modulate renal clearance); methods to analyze and track drug PK in acutely ill patients presenting with high inter-occasion variability; implementation of a 2-cycle approach to minimize the duration between blood samples taken to estimate the changing PK in an acutely ill patient and for the generation of therapeutic decisions in advance for each dosing cycle based on an analysis of the previous cycle; and the importance of expressing therapeutic drug monitoring results as 1/variance rather than as the coefficient of variation. Examples showcase why, irrespective of the overall approach, the combination of therapeutic drug monitoring and computer-informed precision dosing is indispensable for maximizing the likelihood of achieving the target drug concentrations in the individual patient.

Mathematical modeling of pulmonary tuberculosis therapy: Insights from a prototype model with rifampin.

There is a critical need for improved and shorter tuberculosis (TB) treatment. Current in vitro models of TB, while valuable, are poor predictors of the antibacterial effect of drugs in vivo. Mathematical models may be useful to overcome the limitations of traditional approaches in TB research. The objective of this study was to set up a prototype mathematical model of TB treatment by rifampin, based on pharmacokinetic, pharmacodynamic and disease submodels. The full mathematical model can simulate the time-course of tuberculous disease from the first day of infection to the last day of therapy. Therapeutic simulations were performed with the full model to study the antibacterial effect of various dosage regimens of rifampin in lungs. The model reproduced some qualitative and quantitative properties of the bactericidal activity of rifampin observed in clinical data. The kill curves simulated with the model showed a typical biphasic decline in the number of extracellular bacteria consistent with observations in TB patients. Simulations performed with more simple pharmacokinetic/pharmacodynamic models indicated a possible role of a protected intracellular bacterial compartment in such a biphasic decline. This modeling effort strongly suggests that current dosage regimens of RIF may be further optimized. In addition, it suggests a new hypothesis for bacterial persistence during TB treatment.

Voriconazole pharmacokinetics and pharmacodynamics in children.

BACKGROUND: Voriconazole pharmacokinetic and pharmacodynamic data are lacking in children. METHODS: Records at the Childrens Hospital Los Angeles were reviewed for children with > or =1 serum voriconazole concentration measured from 1 May 2006 through 1 June 2007. Information on demographic characteristics, dosing histories, serum concentrations, toxicity and survival, and outcomes was obtained. RESULTS: A total of 207 voriconazole measurements were obtained from 46 patients (age, 0.8-20.5 years). A 2-compartment Michaelis-Menten pharmacokinetic model fit the data best but explained only 80% of the observed variability. The crude mortality rate was 28%, and each trough serum voriconazole concentration <1000 ng/mL was associated with a 2.6-fold increased odds of death (95% confidence interval, 1.6-4.8; P=.002). Serum voriconazole concentrations were not associated with hepatotoxicity. Simulations predicted an intravenous dose of 7 mg/kg or an oral dose of 200 mg twice daily would achieve a trough >1000 ng/mL in most patients, but with a wide range of possible concentrations. CONCLUSIONS: We found a pharmacodynamic association between a voriconazole trough >1000 ng/mL and survival and marked pharmacokinetic variability, particularly after enteral dosing, justifying the measurement of serum concentrations.

Pharmacokinetics and pharmacogenomics of once-daily raltegravir and atazanavir in healthy volunteers.

Atazanavir inhibits UDP-glucuronyl-transferase-1A1 (UGT1A1), which metabolizes raltegravir, but the magnitude of steady-state inhibition and role of the UGT1A1 genotype are unknown. Sufficient inhibition could lead to reduced-dose and -cost raltegravir regimens. Nineteen healthy volunteers, age 24 to 51 years, took raltegravir 400 mg twice daily (arm A) and 400 mg plus atazanavir 400 mg once daily (arm B), separated by ≥3 days, in a crossover design. After 1 week on each regimen, raltegravir and raltegravir-glucuronide plasma and urine concentrations were measured by liquid chromatography-tandem mass spectrometry in multiple samples obtained over 12 h (arm A) or 24 h (arm B) and analyzed by noncompartmental methods. UGT1A1 promoter variants were detected with a commercially available kit and published primers. The primary outcome was the ratio of plasma raltegravir C(tau), or concentration at the end of the dosing interval, for arm B (24 h) versus arm A (12 h). The arm B-to-arm A geometric mean ratios (95% confidence interval, P value) for plasma raltegravir C(tau), area under the concentration-time curve from 0 to 12 h (AUC(0-12)), and raltegravir-glucuronide/raltegravir AUC(0-12) were 0.38 (0.22 to 0.65, 0.001), 1.32 (0.62 to 2.81, 0.45), and 0.47 (0.38 to 0.59, <0.001), respectively. Nine volunteers were heterozygous and one was homozygous for a UGT1A1 reduction-of-function allele, but these were not associated with metabolite formation. Although atazanavir significantly reduced the formation of the glucuronide metabolite, its steady-state boosting of plasma raltegravir did not render the C(tau) with a once-daily raltegravir dose of 400 mg similar to the C(tau) with the standard twice-daily dose. UGT1A1 promoter variants did not significantly influence this interaction.

Intrapulmonary pharmacokinetics and pharmacodynamics of micafungin in adult lung transplant patients.

Invasive pulmonary aspergillosis is a life-threatening infection in lung transplant recipients; however, no studies of the pharmacokinetics and pharmacodynamics (PKPD) of echinocandins in transplanted lungs have been reported. We conducted a single-dose prospective study of the intrapulmonary and plasma PKPD of 150 mg of micafungin administered intravenously in 20 adult lung transplant recipients. Epithelial lining fluid (ELF) and alveolar cell (AC) samples were obtained via bronchoalveolar lavage performed 3, 5, 8, 18, or 24 h after initiation of infusion. Micafungin concentrations in plasma, ELF, and ACs were determined using high-pressure liquid chromatography. Noncompartmental methods, population analysis, and multiple-dose simulations were used to calculate PKPD parameters. Cmax in plasma, ELF, and ACs was 4.93, 1.38, and 17.41 microg/ml, respectively. The elimination half-life in plasma was 12.1 h. Elevated concentrations in ELF and ACs were sustained during the 24-h sampling period, indicating prolonged compartmental half-lives. The mean micafungin concentration exceeded the MIC90 of Aspergillus fumigatus (0.0156 microg/ml) in plasma (total and free), ELF, and ACs throughout the dosing interval. The area under the time-concentration curve from 0 to 24 h (AUC0-24)/MIC90 ratios in plasma, ELF, and ACs were 5,077, 923.1, and 13,340, respectively. Multiple-dose simulations demonstrated that ELF and AC concentrations of micafungin would continue to increase during 14 days of administration. We conclude that a single 150-mg intravenous dose of micafungin resulted in plasma, ELF, and AC concentrations that exceeded the MIC90 of A. fumigatus for 24 h and that these concentrations would continue to increase during 14 days of administration, supporting its potential activity for prevention and early treatment of pulmonary aspergillosis.

Expert Discussion of the Role of Rate Constant Versus Clearance Approaches to Define Drug Pharmacokinetics: Theoretical and Clinical Considerations.

This article provides a dialogue covering an ongoing controversy on the use of clearance versus rate constant approaches for model parameterization when assessing pharmacokinetic (PK) data. It reflects the differences in opinions that can exist among PK experts. Importantly, this discussion extends beyond theoretical arguments to demonstrate how these different approaches impact the analysis and interpretation of data acquired in clinical situations. By not shying away from such dialogues, this article showcases how dissimilarity in well-grounded perspectives can influence how one applies PK and mathematical principles.

Development of a methodology to make individual estimates of the precision of liquid chromatography-tandem mass spectrometry drug assay results for use in population pharmacokinetic modeling and the optimization of dosage regimens.

BACKGROUND: The clinical value of therapeutic drug monitoring can be increased most significantly by integrating assay results into clinical pharmacokinetic models for optimal dosing. The correct weighting in the modeling process is 1/variance, therefore, knowledge of the standard deviations (SD) of each measured concentration is important. Because bioanalytical methods are heteroscedastic, the concentration-SD relationship must be modeled using assay error equations (AEE). We describe a methodology of establishing AEE's for liquid chromatography-tandem mass spectrometry (LC-MS/MS) drug assays using carbamazepine, fluconazole, lamotrigine and levetiracetam as model analytes. METHODS: Following method validation, three independent experiments were conducted to develop AEE's using various least squares linear or nonlinear, and median-based linear regression techniques. SD's were determined from zero concentration to the high end of the assayed range. In each experiment, precision profiles of 6 ("small" sample sets) or 20 ("large" sample sets) out of 24 independent, spiked specimens were evaluated. Combinatorial calculations were performed to attain the most suitable regression approach. The final AEE's were developed by combining the SD's of the assay results, established in 24 specimens/spiking level and using all spiking levels, into a single precision profile. The effects of gross hyperbilirubinemia, hemolysis and lipemia as laboratory interferences were investigated. RESULTS: Precision profiles were best characterized by linear regression when 20 spiking levels, each having 24 specimens and obtained by performing 3 independent experiments, were combined. Theil's regression with the Siegel estimator was the most consistent and robust in providing acceptable agreement between measured and predicted SD's, including SD's below the lower limit of quantification. CONCLUSIONS: In the framework of precision pharmacotherapy, establishing the AEE of assayed drugs is the responsibility of the therapeutic drug monitoring service. This permits optimal dosages by providing the correct weighting factor of assay results in the development of population and individual pharmacokinetic models.

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.