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.

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.

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.

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.

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.

The Case for Using Higher Doses of First Line Anti-Tuberculosis Drugs to Optimize Efficacy.

Apart from new anti-tuberculosis drug development, another approach for tuberculosis (TB) treatment optimization is to derive maximum benefit from current agents. However, the dosage of current anti-TB drug regimens has never been optimized according to the exposure-effect relationships of each drug. The objective of this article is to review the latest pharmacokinetic, pharmacodynamic, experimental, and clinical data concerning the use of higher doses of first-line anti-TB drugs to improve the efficacy of pulmonary tuberculosis treatment. Exposure-effect relationships have been described for all first-line anti-TB agents. There is convincing evidence that patients would benefit from higher rifamycin exposure. This could be achieved by using higher daily doses of rifampin, or more frequent dosing of rifapentine. The dose-dependent activity of pyrazinamide observed in hollow-fiber and animal models suggests that higher doses of pyrazimamide might be more efficacious, but the tolerability of such higher doses needs to be investigated in humans. It is likely that higher doses of ethambutol would be associated with higher antibacterial effect, but the dose-related ocular toxicity of the drug precludes such practice. For isoniazid, dose individualization is required to optimize patient care. The use of higher than standard doses of isoniazid in fast acetylators should result in greater early bactericidal activity. To conclude, the use of higher doses for some of the firstline anti-TB agents has definite potential for shortening or improving TB treatment.

The role of digitalis pharmacokinetics in converting atrial fibrillation and flutter to regular sinus rhythm.

This report examined the role of digitalis pharmacokinetics in helping to guide therapy with digitalis glycosides with regard to converting atrial fibrillation (AF) or flutter to regular sinus rhythm (RSR). Pharmacokinetic models of digitoxin and digoxin, containing a peripheral non-serum effect compartment, were used to analyze outcomes in a non-systematic literature review of five clinical studies, using the computed concentrations of digitoxin and digoxin in the effect compartment of these models in an analysis of their outcomes. Four cases treated by the author were similarly examined. Three literature studies showed results no different from placebo. Dosage regimens achieved ≤11 ng/g in the model's peripheral compartment. However, two other studies achieved significant conversion to RSR. Their peripheral concentrations were 9-14 ng/g. In the four patients treated by the author, three converted using classical clinical titration with incremental doses, plus therapeutic drug monitoring and pharmacokinetic guidance from the models for maintenance dosage. They converted at peripheral concentrations of 9-18 ng/g, similar to the two studies above. No toxicity was seen. Successful maintenance was achieved, using the models and their pharmacokinetic guidance, by giving somewhat larger than average recommended dosage regimens in order to maintain peripheral concentrations present at conversion. The fourth patient did not convert, but only reached peripheral concentrations of 6-7 ng/g, similar to the studies in which conversion was no better than placebo. Pharmacokinetic analysis and guidance play a highly significant role in converting AF to RSR. To the author's knowledge, this has not been specifically described before. In my experience, conversion of AF or flutter to RSR does not occur until peripheral concentrations of 9-18 ng/g are reached. Results in the four cases correlated well with the literature findings. More work is needed to further evaluate these provocative findings.

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.