Sensitivity equation for quantitative analysis with multivariate curve resolution-alternating least-squares: theoretical and experimental approach.

A new equation is derived for estimating the sensitivity when the multivariate curve resolution-alternating least-squares (MCR-ALS) method is applied to second-order multivariate calibration data. The validity of the expression is substantiated by extensive Monte Carlo noise addition simulations. The multivariate selectivity can be derived from the new sensitivity expression. Other important figures of merit, such as limit of detection, limit of quantitation, and concentration uncertainty of MCR-ALS quantitative estimations can be easily estimated from the proposed sensitivity expression and the instrumental noise. An experimental example involving the determination of an analyte in the presence of uncalibrated interfering agents is described in detail, involving second-order time-decaying sensitized lanthanide luminescence excitation spectra. The estimated figures of merit are reasonably correlated with the analytical features of the analyzed experimental system.

[1]  R. Tauler,et al.  Noise propagation and error estimations in multivariate curve resolution alternating least squares using resampling methods , 2004 .

[2]  Rasmus Bro,et al.  Multi-way Analysis with Applications in the Chemical Sciences , 2004 .

[3]  Gary D. Christian,et al.  Application of the method of rank annihilation to fluorescent multicomponent mixtures of polynuclear aromatic hydrocarbons , 1980 .

[4]  M. P. Callao,et al.  Analytical applications of second-order calibration methods. , 2008, Analytica chimica acta.

[5]  R. Tauler,et al.  Estimation of figures of merit using univariate statistics for quantitative second-order multivariate curve resolution , 2001 .

[6]  R. Tauler.  Multivariate curve resolution applied to second order data , 1995 .

[7]  Romà Tauler,et al.  Multivariate resolution of rank‐deficient spectrophotometric data from first‐order kinetic decomposition reactions , 1998 .

[8]  Graciela M. Escandar,et al.  A review of multivariate calibration methods applied to biomedical analysis , 2006 .

[9]  L. A. Currie,et al.  Nomenclature in evaluation of analytical methods including detection and quantification capabilities (IUPAC Recommendations 1995) , 1995 .

[10]  J. Kalivas,et al.  Selectivity and Related Measures for nth-Order Data. , 1996, Analytical chemistry.

[11]  A. Saltelli,et al.  Sensitivity analysis for chemical models. , 2005, Chemical reviews.

[12]  N. M. Faber,et al.  Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report) , 2006 .

[13]  José Manuel Amigo,et al.  ChroMATHography: solving chromatographic issues with mathematical models and intuitive graphics. , 2010, Chemical reviews.

[14]  A. Olivieri,et al.  A closed‐form expression for computing the sensitivity in second‐order bilinear calibration , 2005 .

[15]  S. Wold,et al.  Residual bilinearization. Part 1: Theory and algorithms , 1990 .

[16]  Ronei J. Poppi,et al.  Second- and third-order multivariate calibration: data, algorithms and applications , 2007 .

[17]  Alejandro C. Olivieri,et al.  A simple approach to uncertainty propagation in preprocessed multivariate calibration , 2002 .

[18]  Gabriela A Ibañez,et al.  Second-order analyte quantitation under identical profiles in one data dimension. A dependency-adapted partial least-squares/residual bilinearization method. , 2010, Analytical chemistry.

[19]  Klaas Faber,et al.  New developments for the sensitivity estimation in four-way calibration with the quadrilinear parallel factor model. , 2012, Analytical chemistry.

[20]  Graciela M. Escandar,et al.  Second-order and higher-order multivariate calibration methods applied to non-multilinear data using different algorithms , 2011 .

[21]  Alejandro C Olivieri,et al.  Computing sensitivity and selectivity in parallel factor analysis and related multiway techniques: the need for further developments in net analyte signal theory. , 2005, Analytical chemistry.

[22]  A. Olivieri.  On a versatile second‐order multivariate calibration method based on partial least‐squares and residual bilinearization: Second‐order advantage and precision properties , 2005 .

[23]  W. Windig,et al.  Interactive self-modeling mixture analysis , 1991 .

[24]  Romà Tauler,et al.  Second-order multivariate curve resolution applied to rank-deficient data obtained from acid-base spectrophotometric titrations of mixtures of nucleic bases , 1997 .

[25]  Claus A. Andersson,et al.  PARAFAC2—Part II. Modeling chromatographic data with retention time shifts , 1999 .

[26]  R. Bro.  Review on Multiway Analysis in Chemistry—2000–2005 , 2006 .

[27]  Klaus Danzer,et al.  Guidelines for calibration in analytical chemistry. Part I. Fundamentals and single component calibration (IUPAC Recommendations 1998) , 1998 .

[28]  Romà Tauler,et al.  Multivariate curve resolution applied to three‐way trilinear data: Study of a spectrofluorimetric acid–base titration of salicylic acid at three excitation wavelengths , 1998 .

[29]  Hai-Long Wu,et al.  Alternating penalty trilinear decomposition algorithm for second‐order calibration with application to interference‐free analysis of excitation–emission matrix fluorescence data , 2005 .

[30]  Alejandro C Olivieri,et al.  Analytical advantages of multivariate data processing. One, two, three, infinity? , 2008, Analytical chemistry.

[31]  Alejandro C. Olivieri,et al.  Validation and Error , 2009 .

[32]  Juan A Arancibia,et al.  A review on second- and third-order multivariate calibration applied to chromatographic data. , 2012, Journal of chromatography. B, Analytical technologies in the biomedical and life sciences.

[33]  R. Bro.  PARAFAC. Tutorial and applications , 1997 .

[34]  Yang Li,et al.  A novel trilinear decomposition algorithm for second-order linear calibration , 2000 .

[35]  Rasmus Bro,et al.  Calibration methods for complex second-order data , 1999 .

[36]  A. Lorber.  Error propagation and figures of merit for quantification by solving matrix equations , 1986 .

[37]  B. Kowalski,et al.  Selectivity, local rank, three‐way data analysis and ambiguity in multivariate curve resolution , 1995 .

[38]  B. Kowalski,et al.  Theory of analytical chemistry , 1994 .

[39]  R. Bro,et al.  PARAFAC2—Part I. A direct fitting algorithm for the PARAFAC2 model , 1999 .