Limit of detection for calibration methods MARÍA JOSÉ RODRÍGUEZ CUESTA Doctoral Thesis ROVIRA I VIRGILI UNIVERSITY Tarragona 2006 UNIVERSITAT ROVIRA I VIRGILI LIMIT OF DETECTION FOR SECOND-ORDER CALIBRATION METHODS. M. José Rodríguez Cuesta ISBN: 978-84-690-7787-0 / DL: T.1349-2007 UNIVERSITAT ROVIRA I VIRGILI LIMIT OF DETECTION FOR SECOND-ORDER CALIBRATION METHODS. M. José Rodríguez Cuesta ISBN: 978-84-690-7787-0 / DL: T.1349-2007 Limit of detection for second-order calibration methods Doctoral thesis ROVIRA I VIRGILI UNIVERSITY UNIVERSITAT ROVIRA I VIRGILI LIMIT OF DETECTION FOR SECOND-ORDER CALIBRATION METHODS. M. José Rodríguez Cuesta ISBN: 978-84-690-7787-0 / DL: T.1349-2007 UNIVERSITAT ROVIRA I VIRGILI LIMIT OF DETECTION FOR SECOND-ORDER CALIBRATION METHODS. M. José Rodríguez Cuesta ISBN: 978-84-690-7787-0 / DL: T.1349-2007 Rovira i Virgili University Department of Analytical Chemistry and Organic Chemistry Limit of detection for second-order calibration methods Dissertation presented by María José Rodríguez Cuesta to receive the degree Doctor of the Rovira i Virgili University European PhD Tarragona, 2006 Supervisor Dr. Ricard Boqué i Martí UNIVERSITAT ROVIRA I VIRGILI LIMIT OF DETECTION FOR SECOND-ORDER CALIBRATION METHODS. M. José Rodríguez Cuesta ISBN: 978-84-690-7787-0 / DL: T.1349-2007 UNIVERSITAT ROVIRA I VIRGILI LIMIT OF DETECTION FOR SECOND-ORDER CALIBRATION METHODS. M. José Rodríguez Cuesta ISBN: 978-84-690-7787-0 / DL: T.1349-2007 ROVIRA I VIRGILI UNIVERSITY Department of Analytical Chemistry and Organic Chemistry Dr RICARD BOQUÉ I MARTÍ, Associate professor of the Department of Analytical Chemistry and Organic Chemistry at the Rovira i Virgili University CERTIFIES: That the Doctoral Thesis entitled: ”LIMIT OF DETECTION FOR SECOND- ORDER CALIBRATION METHODS”, presented by MARÍA JOSÉ RODRÍGUEZ CUESTA to receive the degree of Doctor of the Rovira i Virgili University, European PhD, has been carried out under my supervision in the Department of Analytical Chemistry and Organic Chemistry at the Rovira i Virgili University, and that all the results presented in this thesis were obtained in experiments conducted by the above-mentioned student. Tarragona, April 2006 Dr Ricard Boqué i Martí UNIVERSITAT ROVIRA I VIRGILI LIMIT OF DETECTION FOR SECOND-ORDER CALIBRATION METHODS. M. José Rodríguez Cuesta ISBN: 978-84-690-7787-0 / DL: T.1349-2007 UNIVERSITAT ROVIRA I VIRGILI LIMIT OF DETECTION FOR SECOND-ORDER CALIBRATION METHODS. M. José Rodríguez Cuesta ISBN: 978-84-690-7787-0 / DL: T.1349-2007 While writing this thesis I was supervised by Dr. Ricard Boqué, and the work was undertaken in the Chemometrics and Qualimetrics research group, headed by Prof. F. Xavier Rius, of the Analytical Chemistry and Organic Chemistry Department at the Rovira i Virgili University in Tarragona, Spain. The work included a four-month research stay in the winter of 2004 in the Spectroscopy and Chemometrics group of the Quality and Technology Department of Food Science at The Royal Veterinary and Agricultural University (KVL) in Copenhagen, Denmark, where I was supervised by Prof. Rasmus Bro. It also included a scientific collaboration with Prof. J. L. Martínez Vidal, Prof. A. Garrido Frenich, Prof. D. Picón Zamora and Prof. M. Martínez Galera of the Department of Hydrogeology and Analytical Chemistry of the University of Almeria Finally, I appreciate the financial support given by the ‘Agència de Gestió d’Ajusts Universitaris i Recerca’ (2000FI-00632) of the Catalan Government. For those who have helped me to grow as a person and as a researcher, and to all those have helped me to follow my path, each one in their different way. I hope that all of you, friends, family and colleagues, feel identified in these lines. UNIVERSITAT ROVIRA I VIRGILI LIMIT OF DETECTION FOR SECOND-ORDER CALIBRATION METHODS. M. José Rodríguez Cuesta ISBN: 978-84-690-7787-0 / DL: T.1349-2007 UNIVERSITAT ROVIRA I VIRGILI LIMIT OF DETECTION FOR SECOND-ORDER CALIBRATION METHODS. M. José Rodríguez Cuesta ISBN: 978-84-690-7787-0 / DL: T.1349-2007 Table contents Chapter 1. DESCRIPTION OF THE THESIS 1.1. Motivation ...................................................................................-3- 1.2. Objectives ....................................................................................-4- 1.3. Structure .....................................................................................-6- 1.4. Notation and list of symbols ......................................................-8- Chapter 2. INTRODUCTION TO CHEMOMETRICS 2.1. Types of data and instruments used in Analytical Chemistry-13- 2.1.1. Historical Background........................................................................-13- 2.1.2. Tensor Terminology...........................................................................-14- 2.1.3. The Concepts of Bilinearity and Trilinearity .......................................-17- 2.1.4. Deviations from Linearity...................................................................-20- 2.2. Calibration methods....................................................................-22- 2.2.1. From Zeroth- to Second-order Calibration.........................................-22- 2.2.2. Resolution and Calibration Methods for Second-Order Data.............-27- 2.2.2.1 Parallel Factor Analysis (PARAFAC)...................................-31- 2.2.2.2 Iterative Target Transformation Factor Analysis (ITTFA).....-35- 2.2.2.3 Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS)..........................................................................-38- 2.2.2.4 Multi-linear Partial Least Squares (N-PLS)..........................-41- 2.2.3. Uniqueness, Indeterminacies and Constraints ..................................-44- 2.3. Validation of Analytical Methods ..............................................-50- 2.3.1. What is Method Validation? ..............................................................-50- 2.3.2. Figures of Merit. International Recommendations .............................-51- UNIVERSITAT ROVIRA I VIRGILI LIMIT OF DETECTION FOR SECOND-ORDER CALIBRATION METHODS. M. José Rodríguez Cuesta ISBN: 978-84-690-7787-0 / DL: T.1349-2007 2.3.3. Analytical Detection ......................................................................... -55- 2.3.3.1 Hypothesis Testing ............................................................ -55- 2.3.3.2 Critical Level and Detection Limit ...................................... -56- 2.3.3.3 Limit of Detection from Linear Calibration Curves............... -58- 2.3.3.4 Limit of Detection in Multivariate Calibration ....................... -61- Chapter 3. ESTIMATION OF THE LOD FOR PARAFAC 3.1. Introduction..................................................................................-69- 3.2. Paper.............................................................................................-73- Determination of Carbendazim, Fuberidazole and Thiabendazole by Three- Dimensional Excitation–Emission Matrix Fluorescence and Parallel Factor Analysis. Analytica Chimica Acta 491: 47-57 (2003) Chapter 4. ESTIMATION OF THE LOD FOR ITTFA 4.1. Introduction..................................................................................-95- 4.2. Paper.............................................................................................-99- Influence of Selectivity and Sensitivity Parameters on Detection in Multivariate Curve Resolution of Chromatographic Second-Order Data. Analytica Chimica Acta 476: 111-122 (2003) Chapter 5. ESTIMATION OF THE LOD FOR MCR-ALS 5.1. Introduction..................................................................................-125- 5.2. Paper.............................................................................................-129- Development and Validation of a Method for Determining Pesticides in Groundwater from Complex Overlapped HPLC Signals and Multivariate Curve Resolution. Chemometrics and Intelligent Laboratory Systems 77(1- 2): 251-260 (2005) UNIVERSITAT ROVIRA I VIRGILI LIMIT OF DETECTION FOR SECOND-ORDER CALIBRATION METHODS. M. José Rodríguez Cuesta ISBN: 978-84-690-7787-0 / DL: T.1349-2007 Chapter 6. ESTIMATION OF THE LOD FOR N-PLS 6.1. Introduction .................................................................................-157- 6.2. Paper.............................................................................................-161- Standard Error of Prediction at Low Content Levels and Limit of Detection Estimation for Multivariate and Multi-linear Regression. (In press) Chapter 7. CONCLUSIONS 7.1. Introduction .................................................................................-193- 7.2. Conclusions ................................................................................-193- APPENDIX References ...........................................................................................-201- Glossary and abbreviations..................................................................-211- List of papers and meeting contributions .............................................-221- UNIVERSITAT ROVIRA I VIRGILI LIMIT OF DETECTION FOR SECOND-ORDER CALIBRATION METHODS. M. José Rodríguez Cuesta ISBN: 978-84-690-7787-0 / DL: T.1349-2007 UNIVERSITAT ROVIRA I VIRGILI LIMIT OF DETECTION FOR SECOND-ORDER CALIBRATION METHODS. M. José Rodríguez Cuesta ISBN: 978-84-690-7787-0 / DL: T.1349-2007 Chapter DESCRIPTION OF THE THESIS - 1 - UNIVERSITAT ROVIRA I VIRGILI LIMIT OF DETECTION FOR SECOND-ORDER CALIBRATION METHODS. M. José Rodríguez Cuesta ISBN: