Comparison of Ordinary, Weighted, and Generalized Least-Squares Straight-Line Calibrations for LC-MS-MS, GC-MS, HPLC, GC, and Enzymatic Assay (original) (raw)
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Linear regression for calibration lines revisited: weighting schemes for bioanalytical methods
Journal of Chromatography B-analytical Technologies in The Biomedical and Life Sciences, 2002
When the assumption of homoscedasticity is not met for analytical data, a simple and effective way to counteract the greater influence of the greater concentrations on the fitted regression line is to use weighted least squares linear regression (WLSLR). The purpose of the present paper is to stress the relevance of weighting schemes for linear regression analysis and to show how this approach can be useful in the bioanalytical field. The steps to be taken in the study of the linear calibration approach are described. The application of weighting schemes was shown by using a high-performance liquid chromatography method for the determination of lamotrigine in biological fluids as a practical example. By using the WLSLR, the accuracy of the analytical method was improved at the lower end of the calibration curve. Bioanalytical methods data analysis was improved by using the WLSLR procedure.
An approach to select linear regression model in bioanalytical method validation
Journal of Analytical Science and Technology, 2019
Background: The accuracy of any bioanalytical method depends on the selection of an appropriate calibration model. The most commonly used calibration model is the unweighted linear regression, where the response (y-axis) is plotted against the corresponding concentration (x-axis). The degree of association between these two variables is expressed in terms of correlation coefficient (r 2). However, the satisfactory r 2 alone is not adequate to accept the calibration model. The wide calibration curve range used in the bioanalytical methods is susceptible to the heteroscedasticity of the calibration curve data. The use of weighted linear regression with an appropriate weighting factor reduces the heteroscedasticity and improves the accuracy over the selected concentration range. Methods: The present work describes a rapid and simple RP-HPLC method for the estimation of chlorthalidone in spiked human plasma. The calibration curve standards were studied in the concentration range of 100-3200 ng/mL. The chromatography was performed on a C18 column (250 × 4.6 mm, 5 μm) in an isocratic mode at a flow rate of 1 mL/min using methanol:water (60:40%, v/v) as a mobile phase. The detection was carried out at 276 nm. Both the unweighted regression model and weighted regression models with different weighting factors (1/x, 1/√x, and 1/x 2) were evaluated for heteroscedasticity. The statistical approach for the selection of a suitable regression model with appropriate weighting factors was discussed and the developed bioanalytical method was further validated, as per US-FDA guidelines. Results: In calibration curve experiments, although the acceptable r 2 of 0.998 was obtained, the % residual plot showed that the data were susceptible to heteroscedasticity. When the weighted linear regression was applied to the same calibration curve data set, no significant difference between % relative residual (% RR) was observed. Furthermore, when % relative error (% RE) was calculated for different weighting factors, it was observed that the regression model with 1/x weighting factor gave a minimum % RE. The calibration curve was found to be linear in the range of 100 to 3200 ng/mL. The validation experiments proved good accuracy, and intra-and inter-day variability and acceptable recovery. Stability studies proved that the drug was stable under tested stability cycles. Conclusions: From the statistical reports obtained from the present work, it was observed that the calibration curve in bioanalytical experiments was susceptible to heteroscedasticity using the unweighted linear regression model. Hence, to obtain homoscedasticity in the calibration curve experiments, there is a need for a weighted linear regression model. The appropriate regression model was further selected by evaluating the % RE for different weighting factors.
Calibration and Validation of Analytical Methods - A Sampling of Current Approaches, 2018
Calibration curve is a regression model used to predict the unknown concentrations of analytes of interest based on the response of the instrument to the known standards. Some statistical analyses are required to choose the best model fitting to the experimental data and also evaluate the linearity and homoscedasticity of the calibration curve. Using an internal standard corrects for the loss of analyte during sample preparation and analysis provided that it is selected appropriately. After the best regression model is selected, the analytical method needs to be validated using quality control (QC) samples prepared and stored in the same temperature as intended for the study samples. Most of the international guidelines require that the parameters, including linearity, specificity, selectivity, accuracy, precision, lower limit of quantification (LLOQ), matrix effect and stability, be assessed during validation. Despite the highly regulated area, some challenges still exist regarding the validation of some analytical methods including methods when no analyte-free matrix is available.
Statistical approach for selection of regression model during validation of bioanalytical method
Macedonian Pharmaceutical Bulletin
The selection of an adequate regression model is the basis for obtaining accurate and reproducible results during the bionalytical method validation. Given the wide concentration range, frequently present in bioanalytical assays, heteroscedasticity of the data may be expected. Several weighted linear and quadratic regression models were evaluated during the selection of the adequate curve fit using nonparametric statistical tests: One sample rank test and Wilcoxon signed rank test for two independent groups of samples. The results obtained with One sample rank test could not give statistical justification for the selection of linear vs. quadratic regression models because slight differences between the error (presented through the relative residuals) were obtained. Estimation of the significance of the differences in the RR was achieved using Wilcoxon signed rank test, where linear and quadratic regression models were treated as two independent groups. The application of this simple...
Rapid Communications in Mass Spectrometry, 2012
RATIONALE: The linear range of a liquid chromatography/tandem mass spectrometry (LC/MS/MS) bioanalytical assay is typically about three orders of magnitude. A broader standard curve range is favored since it can significantly reduce the time, labor and potential errors related to sample dilutionone of the bottlenecks in sample analysis. Using quadratic regression to fit the standard curve can, to a certain degree, extend the dynamic range. However, the use of a quadratic regression is controversial, particularly in regulated bioanalysis. METHODS: A number of compounds, with different physicochemical properties and ionization efficiencies, were evaluated to understand the cause of the non-linear behavior of the standard curve. RESULTS: The standard curve behavior is primarily associated with the absolute analyte response but not the analyte concentration, the properties of the analyte, or the nature of the matrix when a stable-isotope-labeled internal standard (SIL-IS) is used. For all the test compounds, a non-linear curve was observed when signals exceeded a certain response, which depends on the detector used in the mass spectrometer. With typical API4000 instruments used for the experiments, this critical response level was determined to be~1 E+6 counts per second (cps) and it was successfully used to predict the linear ranges for the test compounds. By simultaneously monitoring two selective reaction monitoring (SRM) channels of different intensity and using SIL-IS, a linear range of five orders of magnitude was achieved. CONCLUSIONS: In this work, the root cause of the non-linear behavior of the standard curve when using a SIL-IS was investigated and identified. Based on the findings, an improved multiple SRM channels approach was proposed and successfully applied to obtain a linear dynamic range of five orders of magnitude for one test compound. This approach may work particularly well for LC/MS/MS bioanalytical assay of dried blood spot (DBS) samples, for which a direct dilution is cumbersome.
Journal of Pharmaceutical and Biomedical Analysis, 2003
The Société Française des Sciences et Techniques Pharmaceutiques (SFSTP) published in 1997 a guide on the validation of chromatographic bio-analytical methods, which introduces new concepts in three different areas: stages of the validation, test of acceptability of a method and design of experiments to perform. In 'stages of validation', the SFSTP guide requires two phases to validate a method. The first phase, called 'prevalidation', is intended to (1) identify the model to use for the calibration curve; (2) evaluate the limits of quantitation; and (3) provide good estimates of the precision and bias of the method before designing the 'validation' phase per se. In the 'test of acceptability', the use of the interval hypotheses is envisaged by the SFSTP guide, not on the parameters of bias and precision, but on individual results by mixing mean bias and intermediate precision in a single test. The SFSTP guide also avoids the use of Satterthwaite's df for testing the acceptability. The reasons for those choices are discussed extensively. In 'design of experiments', much effort has been devoted to improving the quality of results by optimally designing and sizing the experiments to perform in validation. The rationale for using near D-optimal designs for the calibration curve is demonstrated and sample sizes are proposed to correctly size the validation experiments. #
Journal of AOAC INTERNATIONAL, 2012
The calibration of an analytical method is a very important part of its development, and only the proper statistical and chemometric evaluation of the results, together with understanding this process, allows good results. The purpose of this minireview is to call the reader's attention to the major problems in calibration: curvilinearity, heteroscedasticity, presence of outliers, transformation of results, and distribution and autocorrelation of residuals. The common misunderstandings and mistakes are emphasized to inform the reader. Additionally, the computational package “quantchem” for GNU R environment, allowing full and automatic calibration evaluation, is presented.
Validation of bias in multianalyte determination methods
Analytica Chimica Acta, 2000
This paper reports a new approach for validating bias in analytical methods that provide simultaneous results on multiple analytes. The validation process is based on a linear regression technique taking into account errors in both axes. The validation approach is used to individually compare two different chromatographic methods with a reference one. Each of the two methods to be tested is applied on a different set of data composed of two real data sets each. In addition, three different kinds of simulated data sets were used. All three methods are based on RP-high-performance liquid chromatography (HPLC) and are used to quantify eight biogenic amines in wine. The two methods to be tested use different derivatizing procedures: precolumn 6-aminoquinolyl-n-hydroxysuccinimidyl carbamate (AQC) and oncolumn o-phtalaldehyde (OPA), respectively. On the other hand, the reference method uses derivatization with OPA precolumn. Various analytes are determined in a set of samples using each of the methods to be tested and their results are regressed independently against the results of the reference method. Bias is detected in the methods to be tested by applying the joint confidence interval test to the slope and the intercept of the regression line which takes into account uncertainties in the two methods being compared. The conclusions about the trueness of the two methods being tested varied according to whether the joint confidence interval test was applied to data obtained from various biogenic amines considered simultaneously or individually.