1. Comparison of ordinary, weighted, and generalized least-squares straight-line calibrations for LC-MS-MS, GC-MS, HPLC, GC, and enzymatic assay.
- Author
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Duer WC, Ogren PJ, Meetze A, Kitchen CJ, Von Lindern R, Yaworsky DC, Boden C, and Gayer JA
- Subjects
- Biological Assay, Calibration, Chromatography, Gas standards, Chromatography, High Pressure Liquid standards, Gas Chromatography-Mass Spectrometry standards, Humans, Least-Squares Analysis, Linear Models, Tandem Mass Spectrometry standards, Chromatography, Gas methods, Chromatography, High Pressure Liquid methods, Enzymes analysis, Gas Chromatography-Mass Spectrometry methods, Tandem Mass Spectrometry methods
- Abstract
The impact of experimental errors in one or both variables on the use of linear least-squares was investigated for method calibrations (response = intercept plus slope times concentration, or equivalently, Y = a(1) + a(2)X ) frequently used in analytical toxicology. In principle, the most reliable calibrations should consider errors from all sources, but consideration of concentration (X) uncertainties has not been common due to complex fitting algorithm requirements. Data were obtained for liquid chromatography-tandem mass spectrometry, gas chromatography-mass spectrometry, high-performance liquid chromatography, gas chromatography, and enzymatic assay. The required experimental uncertainties in response were obtained from replicate measurements. The required experimental uncertainties in concentration were determined from manufacturers' furnished uncertainties in stock solutions coupled with uncertainties imparted by dilution techniques. The mathematical fitting techniques used in the investigation were ordinary least-squares, weighted least-squares (WOLS), and generalized least-squares (GLS). GLS best-fit results, obtained with an efficient iteration algorithm implemented in a spreadsheet format, are used with a modified WOLS-based formula to derive reliable uncertainties in calculated concentrations. It was found that while the values of the intercepts and slopes were not markedly different for the different techniques, the derived uncertainties in parameters were different. Such differences can significantly affect the predicted uncertainties in concentrations derived from the use of the different linear least-squares equations.
- Published
- 2008
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