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).
References
[1]
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.
[2]
Harmonized IUPAC Guidelines (2003) Guidelines for Single-Laboratory Validation of Methods of Analysis. CAC/GL 49-2003, Cambridge, 839, 846-847.
[3]
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.
[4]
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
[5]
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
[6]
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
[7]
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
[8]
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
[9]
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
[10]
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
[11]
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
[12]
Lavagnini, I., Magno, F., Seraglia, R. and Traldi, P. (2006) Quantitative Applications of Mass Spectrometry. Wiley, New York. https://doi.org/10.1002/0470029021
[13]
Chatterjee, S. and Hadi, A.S. (2012) Regression Analysis by Example. 5th Edition, Wiley, New York, 98.
[14]
Draper, N.R. and Smith, H. (1998) Applied Regression Analysis. 3th Edition, Wiley, New York. https://doi.org/10.1002/9781118625590
[15]
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
[16]
Meloun, M. and Militky, J. (2011) Statistical Data Analysis, a Practical Guide. Woodhead Publishing, New Delhy.
[17]
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
[18]
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
[19]
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
[20]
Noggle, J.H. (1933) Practical Curve Fitting and Data Analysis. Software and Self-Instructions for Scientists and Engineers, Prentice Hall, Englewood Cliffs.
[21]
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
[22]
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
[23]
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
[24]
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
[25]
Bates, D.M. and Watt, D.G. (2007) Nonlinear Regression Analysis and Its Applications. 2nd Edition, Wiley, New York, 1.
[26]
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
[27]
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
[28]
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
[29]
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
[30]
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
[31]
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
[32]
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
[33]
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.
[34]
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
[35]
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
[36]
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
[37]
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
[38]
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
[39]
European Parliament and of the Council of 30 November 2009 on Cosmetic Products; European Union Regulation No. 1223/2009: 2009; 59-209.
[40]
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.
[41]
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
[42]
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
[43]
Box, G.E.P. and Draper, N.R. (1987) Empirical Model Building and Response Surfaces. Wiley, New York.
[44]
Box, G.E.P., Hunter, J.S. and Hunter, W.G. (2005) Statistics for Experimenters. 2nd Edition, Wiley, New York.
[45]
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.
