Procedure for the Selection and Validation of a Calibration Model I—Description and Application

Abstract

Calibration model selection is required for all quantitative methods in toxicology and more broadly in bioanalysis. This typically involves selecting the equation order (quadratic or linear) and weighting factor correctly modelizing the data. A mis-selection of the calibration model will generate lower quality control (QC) accuracy, with an error up to 154%. Unfortunately, simple tools to perform this selection and tests to validate the resulting model are lacking. We present a stepwise, analyst-independent scheme for selection and validation of calibration models. The success rate of this scheme is on average 40% higher than a traditional "fit and check the QCs accuracy" method of selecting the calibration model. Moreover, the process was completely automated through a script (available in Supplemental Data 3) running in RStudio (free, open-source software). The need for weighting was assessed through an F-test using the variances of the upper limit of quantification and lower limit of quantification replicate measurements. When weighting was required, the choice between 1/x and 1/x2 was determined by calculating which option generated the smallest spread of weighted normalized variances. Finally, model order was selected through a partial F-test. The chosen calibration model was validated through Cramer-von Mises or Kolmogorov-Smirnov normality testing of the standardized residuals. Performance of the different tests was assessed using 50 simulated data sets per possible calibration model (e.g., linear-no weight, quadratic-no weight, linear-1/x, etc.). This first of two papers describes the tests, procedures and outcomes of the developed procedure using real LC-MS-MS results for the quantification of cocaine and naltrexone.

Systematic optimisation of ethyl glucuronide extraction conditions from scalp hair by design of experiments and its potential effect on cut‐off values appraisal

“…All the results of significance tests are reported in the Supporting Information, together with the information about the slope and the intercept of the tested calibration model, and its determination coefficient, in the output format provided by the R codes developed and made available by Desharnais et al30,31 The whole procedure was repeatedly tested on a lower number of the already prepared calibration curves (ie, including 4 or 5 replicates only) to test the model robustness and similar results were obtained.From the final calibration model, LOD and LOQ values were calculated following the Hubaux-Vos' algorithm, 37 which yielded the following values: LOD = 0.8 pg/mg and LOQ = 1.7 pg/mg. The first step of the procedure involved the evaluation of data heteroscedasticity by means of F-test; then different statistical tests were executed, including lack-of-fit and normality testing, in order to choose the model order, either linear or quadratic, that best fitted the experimental calibration points (7 levels × 7 replicates), and the corresponding weighting.…”

“…33,34 Determination coefficient (R 2 ), relative standard deviation of the slope, normality of the standardised residuals, and deviation from back-calculated concentrations were also evaluated using in-house spreadsheets, package mvtnorm, 35,36 and the routines developed by B. Desharnais et al 30,31 LOD and LOQ were estimated by the Hubaux-Vos algorithm. Most validation parameters were determined from these data, including linearity range, limit of detection (LOD), LOQ, selectivity, specificity, trueness, accuracy, repeatability, and carry-over effect, in accordance with ISO/IEC 17025 and SWGTOX requirements.…”

“…The stepwise systematic method proposed by Desharnais et al 30,31 was used to select the most appropriate calibration model and validate and Grubbs tests). Lastly, no carry-over effect was observed.…”

“…The new analytical method was validated using a stepwise, analystindependent protocol that required the preparation of 7 independent calibration curves, 30,31 prepared in 3 different days, at 7 calibration levels: 2, 5, 10, 30, 50, 100, and 300 pg/mg. Most validation parameters were determined from these data, including linearity range, limit of detection (LOD), LOQ, selectivity, specificity, trueness, accuracy, repeatability, and carry-over effect, in accordance with ISO/IEC 17025 and SWGTOX requirements.…”

“…The linearity was checked by lack-of-fit and Mandel tests. 33,34 Determination coefficient (R 2 ), relative standard deviation of the slope, normality of the standardised residuals, and deviation from back-calculated concentrations were also evaluated using in-house spreadsheets, package mvtnorm, 35,36 and the routines developed by B. Desharnais et al 30,31 LOD and LOQ were estimated by the Hubaux-Vos algorithm. 37 Specificity was assessed by analysing 7 blank head samples from acknowledged teetotaller individuals; in particular, the presence/ absence of interfering ions on each single-ion chromatogram was evaluated, with reference to EtG pure standard.…”