The study of the calibration of a series of compounds of environmental concern (six perfluoroalkyl compounds (perfluorooctane sulfonic acid and five perfluoroalkyl carboxylic acids), three preservatives (methyl-, ethyl- and propylparabens) and the brominated flame retardant hexabromocyclododecane) by LC-MS/MS has been carries out, with a view to their simultaneous determination in samples of environmental interest. In some cases nonlinear calibration curves are obtained, but restricting the concentration range a linear model may be used to fit the data. Residual analysis has been performed in order to verify which models fit the data better, opting for a compromise decision given the apparent complexity of residuals plots. As Box states there are no perfect models (but models that work better than others).
KeywordsCalibrationNon Linear CalibrationResidual AnalysisLiquid Chromatography-Tandem Mass SpectrometryEmerging Pollutants
Eurachem Working Group (1998) Eurachem Guide: The Fitness for Purpose of Analytical Methods—A Laboratory Guide to Method Validation and Related Topics. Teddington, 3, 20-21.
Harmonized IUPAC Guidelines (2003) Guidelines for Single-Laboratory Validation of Methods of Analysis. CAC/GL 49-2003, Cambridge, 839, 846-847.
Sanagi, M.M., Nasir, Z., Ling, S.L., Hermawan, D., Ibrahim, W.A.W. and Naim, A.A. (2010) A Practical Approach for Linearity Assessment of Calibration Curves Under the International Union of Pure and Applied Chemistry (IUPAC) Guidelines for an In-House Validation of Method of Analysis. Journal of AOAC International, 93, 1322-1330.
Asnin, L.D. (2016) Peak Measurement and Calibration in Chromatographic Analysis. Trends in Analytical Chemistry, 81, 51-62. https://doi.org/10.1016/j.trac.2016.01.006
Kóscielniak, P. and Wieczorek, M. (2016) Univariate Analytical Calibration Methods and Procedures: A Review. Analytica Chimica Acta, 944, 14-28. https://doi.org/10.1016/j.aca.2016.09.024
Raposo, F. (2016) Evaluation of Analytical Calibration Based on Least Squares Linear Regression for Instrumental Techniques: A Tutorial Review. Trends in Analytical Chemistry, 77, 167-185. https://doi.org/10.1016/j.trac.2015.12.006
Olivieri, A.C. (2015) Practical Guidelines for Reporting Results in Simple and Multi-Component Analytical Calibration: A Tutorial. Analytica Chimica Acta, 868, 10-22. https://doi.org/10.1016/j.aca.2015.01.017
Mermet, J.-M. (2010) Calibration in Atomic Spectrometry: A Tutorial Review Dealing with Quality Criteria, Weighting Procedures and Possible Curvatures. Spectrochimica Acta B, 65, 509-523. https://doi.org/10.1016/j.sab.2010.05.007
Tellinghuisen, J. (2009) Least Squares in Calibration: Weights, Nonlinearity, and Other Nuisances. Methods Enzymology, 454, 259-285. https://doi.org/10.1016/S0076-6879(08)03810-X
Switaj-Zawadha, A., Konieczka, P., Pryk, E. and Namiesnik, J. (2005) Calibration in Metrological Approach. Analytical Letters, 38, 353-376. https://doi.org/10.1081/AL-200043431
Lavagnini, I. and Magno, F. (2007) A Statistical Overview on Univariate Calibration, Inverse Regression, and Detection Limits: Application to Gas Chromatography/Mass Spectrometry Technique. Mass Spectrometry Reviews, 26, 1-18. https://doi.org/10.1002/mas.20100
Lavagnini, I., Magno, F., Seraglia, R. and Traldi, P. (2006) Quantitative Applications of Mass Spectrometry. Wiley, New York. https://doi.org/10.1002/0470029021
Chatterjee, S. and Hadi, A.S. (2012) Regression Analysis by Example. 5th Edition, Wiley, New York, 98.
Draper, N.R. and Smith, H. (1998) Applied Regression Analysis. 3th Edition, Wiley, New York. https://doi.org/10.1002/9781118625590
Cornish-Bowden, A. (2014) Analysis and Interpretation of Enzyme Kinetics Data. Perspectives in Science, 1, 121-125. https://doi.org/10.1016/j.pisc.2014.02.010
Meloun, M. and Militky, J. (2011) Statistical Data Analysis, a Practical Guide. Woodhead Publishing, New Delhy.
Asuero, A.G., Sayago, A. and González, A.G. (2006) The Correlation Coefficient: An Overview. Critical Reviews in Analytical Chemistry, 36, 41-59. https://doi.org/10.1080/10408340500526766
Sayago, A., Boccio, M. and Asuero, A.G. (2004) Fitting Straight Lines with Replicated Observations by Linear Regression: The Least Squares Postulates. Critical Reviews in Analytical Chemistry, 34, 39-50. https://doi.org/10.1080/10408340490273744
Wisniak, J. and Polishuk, A. (1999) Analysis of Residuals—A Useful Tool for Phase Equilibrium Data Analysis. Fluid Phase Equilibria, 164, 61-82. https://doi.org/10.1016/S0378-3812(99)00246-0
Noggle, J.H. (1933) Practical Curve Fitting and Data Analysis. Software and Self-Instructions for Scientists and Engineers, Prentice Hall, Englewood Cliffs.
Asuero, A.G. and González, A.G. (2007) Fitting Straight Lines with Replicated Observations by Linear Regression. III. Weighting Data. Critical Reviews in Analytical Chemistry, 37, 143-172. https://doi.org/10.1080/10408340701244615
Asuero, A.G. and Martin, J. (2011) Fitting Straight Lines with Replicated Observations by Linear Regression. IV. Transforming Data. Critical Reviews in Analytical Chemistry, 41, 36-69. https://doi.org/10.1080/10408347.2010.523589
Asuero, A.G. and González, A.G. (1989) Some Observations on Fitting a Straight Line to Data. Microchemical Journal, 40, 216-225. https://doi.org/10.1016/0026-265X(89)90073-8
Michalowska-Kazcmarcyk, A., Asuero, A.G., Martin, J., Alonso, E., Jurado, J.M. and Michalowski, T. (2014) A Uniform Nonlinearity Criteria for Rational Functions Applied to Calibration Curve and Standard Addition Methods. Talanta, 130, 307-314. https://doi.org/10.1016/j.talanta.2014.04.067
Bates, D.M. and Watt, D.G. (2007) Nonlinear Regression Analysis and Its Applications. 2nd Edition, Wiley, New York, 1.
Martín, J., Santos, J.L., Aparicio, I. and Alonso, E. (2015) Determination of Hormones, a Plasticizer, Preservatives, Perfluoroalkylated Compounds, and a Flame Retardant in Water Samples by Ultrasound-Assisted Dispersive Liquid-Liquid Microextraction Based on the Solidification of a Floating Organic Drop. Talanta, 143, 335-343. https://doi.org/10.1016/j.talanta.2015.04.089
Farré, M., Kantiani, L., Petrovic, M., Pérez, S. and Barceló, D. (2012) Achievements and Future Trends in the Analysis of Emerging Organic Contaminants in Environmental Samples by Mass Spectrometry and Bioanalytical Techniques. Journal of Chromatography A, 1259, 86-99. https://doi.org/10.1016/j.chroma.2012.07.024
Banjac, Z., Ginebreda, A., Kuzmanovic, M., Marcé, R., Nadal, M., Riera, J.M. and Barceló, D. (2015) Emission Factor Estimation of ca. 160 Emerging Organic Microcontaminants by Inverse Modeling in a Mediterranean River Basin (Llobregat, NE Spain). Science of the Total Environment, 520, 241-252. https://doi.org/10.1016/j.scitotenv.2015.03.055
Fromme, H., Becher, G., Hilger, B. and Volkel, W. (2016) Brominated Flame Retardants—Exposure and Risk Assessment for the General Population. International Journal of Hygiene and Environmental Health, 219, 1-23. https://doi.org/10.1016/j.ijheh.2015.08.004
Allgood, J.M., Jimah, T., McClaskey, C.M., La Guardia, M.J., Hammel, S.C., Zeineddine, M.M., Tang, I.W., Runnerstrom, M.G. and Ogunseitan, O.A. (2017) Potential Human Exposure to Halogenated Flame-Retardants in Elevated Surface Dust and Floor Dust in an Academic Environment. Environmental Research, 153, 55-62. https://doi.org/10.1016/j.envres.2016.11.010
Rivière, G., Sirot, V., Tard, A., Jean, J., Marchand, P., Veyrand, B., Le Bizec, B. and Leblanc, J.C. (2014) Food Risk Assessment for Perfluoroalkyl Acids and Brominated Flame Retardants in the French Population: Results from the Second French Total Diet Study. Science of the Total Environment, 491-492, 176-183. https://doi.org/10.1016/j.scitotenv.2014.01.104
Hendriks, H.S. and Westerink, R.H.S. (2015) Neurotoxicity and Risk Assessment of Brominated and Alternative Flame Retardants. Neurotoxicology and Teratology, 52, 248-269. https://doi.org/10.1016/j.ntt.2015.09.002
The European Parliament and the Council of the European Union (2008) Directive 2008/105/EC of the European Parliament and of the Council of 16 December 2008 on Environmental Quality Standards in the Field of Water Policy, Amending and Subsequently Repealing Council Directives 82/176/EEC, 83/513/EEC, 84/156/EEC, 84/491/EEC, 86/280/EEC and Amending Directive 2000/60/EC of the European Parliament and of the Council. Official Journal of the European Union, 348, 84.
Corsini, E., Luebke, R.W., Germolec, D.R. and DeWitt, J.C. (2014) Perfluorinated Compounds: Emerging POPs with Potential Immunotoxicity. Toxicological Letters, 230, 263-270. https://doi.org/10.1016/j.toxlet.2014.01.038
Hekster, F.M., Laane, R.W.P.M. and de Voogt, P. (2003) Environmental and Toxicity Effects of Perfluoroalkylated Substances. Reviews of Environmental Contamination and Toxicology, 179, 99-121. https://doi.org/10.1007/0-387-21731-2_4
Domingo, J.L. (2011) Health Risks of Dietary Exposure to Perfluorinated Compounds. Environment International, 40, 187-195. https://doi.org/10.1016/j.envint.2011.08.001
Soni, M.G., Carabin, I.G. and Burdock, G.A. (2005) Safety Assessment of Esters of p-Hydroxybenzoic Acid (Parabens). Food and Chemical Toxicology, 43, 985-1015. https://doi.org/10.1016/j.fct.2005.01.020
Boberg, J., Taxvig, C., Christiansen, S. and Hass, U. (2010) Possible Endocrine Disrupting Effects of Parabens and Their Metabolites. Reproductive Toxicology, 30, 301-312. https://doi.org/10.1016/j.reprotox.2010.03.011
European Parliament and of the Council of 30 November 2009 on Cosmetic Products; European Union Regulation No. 1223/2009: 2009; 59-209.
Commission Decision (2002/657/EC) of 12 August 2002 Implementing Council Directive 96/23/EC Concerning the Performance of Analytical Methods and the Interpretation of Results, Official Journal of the European Communities L221, Brussels, Belgium, 8-36.
Gorazda, K., Michalowska-Kaczmarcyk, A.M., Asuero, A.G. and Michalowski, T. (2013) Application of Rational Functions for the Standard Addition Method. Talanta, 116, 927-930. https://doi.org/10.1016/j.talanta.2013.07.085
Box, G.E.P. (1976) Science and Statistics. Journal of the American Statistical Association, 71, 791-796. https://doi.org/10.1080/01621459.1976.10480949
Box, G.E.P. and Draper, N.R. (1987) Empirical Model Building and Response Surfaces. Wiley, New York.
Box, G.E.P., Hunter, J.S. and Hunter, W.G. (2005) Statistics for Experimenters. 2nd Edition, Wiley, New York.
Taylor, P.D.P. and Schutyser, P. (1986) Weighted Linear-Regression Applied in Inductively Couple Plasma-Atomic Emission Spectrometry—A Review of the Statistical Considerations Involved. Spectrochimica Acta, 41B, 1051-1061.