Abstract
When drugs are poorly soluble then, instead of the potentiometric determination of dissociation constants, pH-spectrophotometric titration can be used along with nonlinear regression of the absorbance response surface data. Generally, regression models are extremely useful for extracting the essential features from a multiwavelength set of data. Regression diagnostics represent procedures for examining the regression triplet (data, model, method) in order to check (a) the data quality for a proposed model; (b) the model quality for a given set of data; and (c) that all of the assumptions used for least squares hold. In the interactive, PC-assisted diagnosis of data, models and estimation methods, the examination of data quality involves the detection of influential points, outliers and high leverages, that cause many problems when regression fitting the absorbance response hyperplane. All graphically oriented techniques are suitable for the rapid estimation of influential points. The reliability of the dissociation constants for the acid drug silybin may be proven with goodness-of-fit tests of the multiwavelength spectrophotometric pH-titration data. The uncertainty in the measurement of the pK a of a weak acid obtained by the least squares nonlinear regression analysis of absorption spectra is calculated. The procedure takes into account the drift in pH measurement, the drift in spectral measurement, and all of the drifts in analytical operations, as well as the relative importance of each source of uncertainty. The most important source of uncertainty in the experimental set-up for the example is the uncertainty in the pH measurement. The influences of various sources of uncertainty on the accuracy and precision are discussed using the example of the mixed dissociation constants of silybin, obtained using the SQUAD(84) and SPECFIT/32 regression programs.
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References
Meloun M, Bordovská S, Syrový T, Vrána A (2006) Anal Chim Acta 580:107–121
Maeder M, Neuhold Y-M, Puxty G, Gemperline P (2006) Chemometr Intell Lab Syst 82:75–82
Meloun M, Militký J, Hill M, Brereton RG (2002) Analyst 127:433–450
Meloun M, Militký J, Forina M (1994) Chemometrics for analytical chemistry, vol 2. PC-aided regression and related methods. Ellis Horwood, Chichester, UK
Leggett DJ (ed)(1985) SQUAD. In: Computational methods for the determination of formation constants. Plenum, New York, pp 99–157, 291–353
Meloun M, Javůrek M, Havel J (1986) Talanta 33:513–524
Leggett DJ, McBryde WAE (1975) Anal Chem 47:1065–1070
Leggett DJ (1977) Anal Chem 49:276–281
Gampp H, Maeder M, Mayer Ch J, Zuberbühler A (1985) Talanta 32:95–101
Gampp H, Maeder M, Meyer Ch J, Zuberbühler A (1985) Talanta 32:251–264
Gampp H, Maeder M, Meyer Ch J, Zuberbühler A (1985) Talanta 33:943–951
Spectrum Software Associates (2004) SPECFIT/32. Spectrum Software Associates, Marlborough, MA (see http://www.bio-logic.info/rapid-kinetics/specfit.html, last accessed 16th November 2006)
Meloun M, Javůrek M, Högfeldt E (1988) Chem Scripta 28:323–329
Meloun M, Havel J, Högfeldt E (1988) Computation of solution equilibria. Ellis Horwood, Chichester, UK
Meloun M, Havel J (1984) Computation of solution equilibria, 1. Spectrophotometry, Folia Fac. Sci. Nat. Univ. Purkyn. Brunensis (Chemia), Brno, XXV
Meloun M, Havel J (1985) Computation of solution equilibria, 2. Potentiometry, Folia Fac. Sci. Nat. Univ. Purkyn. Brunensis (Chemia), Brno, XXVI
Meloun M, Militký J, Forina M (1992) Chemometrics for analytical chemistry, vol 1. PC-aided statistical data analysis. Ellis Horwood, Chichester, UK
Cook RD, Weisberg S (1982) Residuals and influence in regression. Chapman & Hall, London
Atkinson AC (1985) Plots, transformations and regression: an introduction to graphical methods of diagnostic regression analysis. Clarendon, Oxford
Chatterjee S, Hadi AS (1988) Sensitivity analysis in linear regression. Wiley, New York
Anscombe FJ (1961) Proc Fourth Berkeley Symp Math Statist Prob I:1–36
Draper NR, Smith H (1966) Applied regression analysis, 1st edn. Wiley, New York
Carrol RJ, Ruppert D (1988) Transformation and weighting in regression. Chapman and Hall, New York
Meloun M, Burkoňová D, Syrový T, Vrána A (2003) Anal Chim Acta 486:125–141
Meloun M, Syrový T, Vrána A (2003) Anal Chim Acta 489:137–151
OriginLab Corporation (2006) ORIGIN. OriginLab Corporation, Northampton, MA
Insightful Corp. (2006) S-PLUS. Insightful Corp., Seattle, WA, (see http://www.insightful.com/products/splus, last accessed 16th November 2006)
TriloByte Statistical Software Ltd. (2006) ADSTAT 1.25, 2.0, 3.0 (Windows 95). TriloByte Statistical Software Ltd., Pardubice, Czech Republic
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The financial support of the Grant Agency IGA (Grant No NR9055-4/2006) and of the Czech Ministry of Education (Grant No MSM253100002) is gratefully acknowledged.
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Meloun, M., Syrový, T., Bordovská, S. et al. Reliability and uncertainty in the estimation of pK a by least squares nonlinear regression analysis of multiwavelength spectrophotometric pH titration data. Anal Bioanal Chem 387, 941–955 (2007). https://doi.org/10.1007/s00216-006-0993-1
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DOI: https://doi.org/10.1007/s00216-006-0993-1