Fig 1.
An overview of how therapeutic drug monitoring (TDM) results can be integrated into clinical population and individual pharmacokinetic models on which individualized drug therapy is based.
After the drug is administered (A), blood is drawn at specific times (B) and submitted for analysis to obtain time-concentration data with the aim of determining the subject’s individual pharmacokinetic parameters. This can be done using, for instance, either parametric or nonparametric Bayesian analysis (C). An illustrative input pharmacokinetic model file of Pmetrics™, a nonparametric population modeling software suite [12], is shown (D). The coefficients of the assay error equation are included in the computer script under “#Err”. Ka, Ke, V and Tlag are notations for pharmacokinetic parameters. Line art images are uncopyrighted and were made available by the National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, United States at https://www.niddk.nih.gov/news/media-library.
Fig 2.
Presentation of the experimental design.
3 experiments were performed. The impact of sample size, the number of spiking levels and common interferences was assessed on “small” and”large” sample sets containing 6 and 20 samples, respectively, using a combinatorial approach. The final assay error equations were established by using all of the results obtained in the 3 experiments (N = 24 specimens/spiking level, M = 20 spiking levels+blank).
Table 1.
Mass spectrometry settings applied for the quantitation of carbamazepine, fluconazole, lamotrigine and levetiracetam.
Fig 3.
Representative analytical data.
Ion chromatograms of the analytes (left) and the internal standards (middle), and representative calibration curves (right) obtained in the experiments.
Table 2.
Performance of the calibration curves employed in this study.
Table 3.
Within-run accuracy and relative precision (expressed as the coefficient of variation) obtained for the analytes in spiked independent serum samples in the conducted experiments.
Table 4.
Medians and ranges of linear and constant coefficients of carbamazepine, fluconazole, lamotrigine and levetiracetam assay error equations obtained by developing precision profiles for all combinations of 6 or 20 samples in the three experiments conducted.
(a) unweighted linear least squares regression, (b) unweighted 2nd-order least squares polynomial regression, (c) unweighted 3rd-order least squares polynomial regression, (d) 1/x2-weighted least squares linear regression, (e) Theil’s regression, (f) Theil’s regression using the Siegel estimator. 3rd-order least squares regression was not applied in experiment 1 due to the small number of spiking levels (M = 4). (A) Linear coefficients. High/low, ratio of the highest and the lowest linear coefficients obtained in the combinatorial calculation of SD’s and, subsequently, assay error equations in each experimental setup. ND, not determined. (B) Constant coefficients (intercepts). ND, not determined. NNI, percentage proportions of non-negative intercepts obtained in the combinatorial calculation of SD’s and, subsequently, assay error equations in each experimental setup.
Fig 4.
Regression plots obtained by applying various regression algorithms to the precision profiles of carbamazepine, fluconazole, lamotrigine and levetiracetam and by using all of the serum specimens (N = 24) and spiking levels (M = 20+blank) of the 3 experiments.
Each data point displays the standard deviation of the assay results. Green line: Theil’s regression, black line: unweighted linear least squares, blue line: 1/x2-weighted linear least squares, red curve: unweighted 2nd-order least squares, orange curve: unweighted 3rd-order least squares regression. See Table 5 for a detailed evaluation.
Fig 5.
Accuracy of the prediction of SD’s by applying various regression algorithms to the final precision profiles of (A) carbamazepine, (B) fluconazole, (C) lamotrigine and (D) levetiracetam (M = 20 spiking levels+blank, N = 24 specimens/spiking level).
Red lines indicate perfect (100%) agreement between predicted and experimentally determined SD’s. Insets show results for concentration ranges in which the inaccuracy of the predictions was on the same scale. The applied regression methods are (a) unweighted linear least squares, (b) unweighted 2nd-order least squares, (c) unweighted 3rd-order least squares, (d) 1/x2-weighted linear least squares, (e) Theil’s regression, (f) Theil’s regression with the Siegel estimator.
Table 5.
Regression equations and the normalized sums of squared residuals obtained applying various regression algorithms to the combined results of the 3 experiments performed on carbamazepine, fluconazole, lamotrigine and levetiracetam (N = 24 specimens/spiking level, M = 20 spiking levels+blank).