Evaluation of analytical calibration based on least-squares linear regression for instrumental techniques: A tutorial review

Abstract

Please cite this article as: Francisco Raposo, Evaluation of analytical calibration based on leastsquares linear regression for instrumental techniques: A tutorial review, Trends in Analytical Chemistry (2016), http://dx.doi.org/Highlights  Compilation of analytical calibration information from validation guidelines  Report of very common mistakes in the analytical calibration process  Compilation of methods for assessing linearity of calibration curves  The correlation and determination coefficients are misleading for testing linearity  Deviation from back-calculated concentration is very useful for testing linearity ABSTRACTThe analytical calibration of an instrumental method is very important, being considered as a key point in method validation. There are different validation guidelines; showing that analytical calibration process variety prevails in terms of nomenclature, methodology employed and acceptance criteria.Very common mistakes in the analytical calibration process are the use of correlation and/or determination coefficients as a test for linearity, the negligence in the heteroscedasticity of the experimental data and selection of appropriate weighting factor, misunderstanding about the regression through the origin and using zero-point calibration. Once the calibration function is established, their linearity can be confirmed by using different procedures such as graphical plots, statistical significance tests and numerical parameters. In particular, deviation from back-calculated concentrations expressed in the form of percentage of relative error (%RE) can be considered very useful for unambiguous linearity evaluation. Some case studies were included to explain the linearity assessment from a practical viewpoint.

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

“…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 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.…”

Development and validation of a Partial Least Squares-Discriminant Analysis (PLS-DA) model based on the determination of ethyl glucuronide (EtG) and fatty acid ethyl esters (FAEEs) in hair for the diagnosis of chronic alcohol abuse

“…According to the expected ratio of the four esters in real samples [9], 6-point calibration curves were built at the concentrations of 0.04, 0.08, 0.12, 0.24, 0.36, 0.60 ng/mg for E14:0 and E18:0 and 0.16, 0.32, 0.48, 0.96, 1.44, 2.40 ng/mg for E16:0 and E18:1 The calibration curves proved linear over the whole range for all monitored biomarkers. Several tests were performed to verify the features of the calibration curves calculated with least-squares linear regression, according to Raposo [47]. ANOVA, lack-of-fit, back-calculation and Mandel's tests showed satisfactory results in terms of linearity and homoscedasticity in the calibration ranges considered.…”

Analytical Calibrations: Schemes, Manuals, and Metrological Deliberations

“…The conventional scheme for performing calibration is to prepare a set of standards (plus a blank) followed by quantifying the response signal for such a set [11][12][13]. Common several "How" questions usually evolve as the analyst is getting ready to conduct this study:…”