Verification of the predictive ability of some probability distribution functions in test analysis
Abstract
The increased interest of analytical chemists in test methods of analysis is due to their expressivity and relative simplicity of implementation. There is no doubt about the need for test methods for the analysis of toxic substances in the environment, food products and general consumer goods. Test analyses can also be useful in medical diagnostics, drug and doping control. Along with the increase in the number of test systems on the market, theoretical methods for determining the metrological characteristics of test analysis methods are also developing rapidly. The selection of a probability distribution function and the estimation of their parameters in qualitative analysis procedures with a binary response and semi-quantitative determination methods is a well-studied problem. At the same time, relatively little attention has been paid to such an aspect as the assessment of the predictive ability of such models. Most often, it is necessary to estimate the value of the threshold concentration for the probability of detecting a component that goes beyond the studied area of unreliability of the test reaction. In this work, for this purpose, the cross-evaluation procedure was used - a method for studying the predictive ability of mathematical models.
A comprehensive method for assessing the predictive ability of probability distribution functions for analyte detection in qualitative chemical analysis methods is proposed. Based on the results of calculations, probability distribution functions characterized by maximum predictive ability are determined. The increased interest of analytical chemists in test methods of analysis is due to their expressivity and relative simplicity of implementation. There is no doubt about the need for test methods for the analysis of toxic substances in the environment, food products and general consumer goods. Test analyses can also be useful in medical diagnostics, drug and doping control. Along with the increase in the number of test systems on the market, theoretical methods for determining the metrological characteristics of test analysis methods are also developing rapidly. The selection of a probability distribution function and the estimation of their parameters in qualitative analysis procedures with a binary response and semi-quantitative determination methods is a well-studied problem. At the same time, relatively little attention has been paid to such an aspect as the assessment of the predictive ability of such models. Most often, it is necessary to estimate the value of the threshold concentration for the probability of detecting a component that goes beyond the studied area of unreliability of the test reaction. In this work, for this purpose, the cross-evaluation procedure was used - a method for studying the predictive ability of mathematical models.
A method for testing the predictive ability of exponential, logistic, and normal distribution functions for approximating the uncertainty region of binary response test methods is proposed. A cross-validation procedure was used to define a set of functions that can be used to assess the metrological characteristics of test analysis methods. Analysis of the set of statistical adequacy criteria showed the advantage of using normal and logistic distribution functions. The exponential distribution function is not characterized by acceptable predictive ability.
Downloads
References
Colorimetric water analysis: proven, practical, precise [Електроний ресурс]: https://www.chemetrics.com/colorimetric-water-analysis-proven-practical-precise
Reshetnyak E.A., Nemets N.N., Chernyshova O.S., Panteleimonov A.V., Ostrovskaya V.M. Visual Binary Testing of Hydrogen Sulfide Dissolved in Return Underground Local-Water of Oil and Gas Condensate Fields Methods Objects Chem. Anal. 2019, 14(3), 146-152 https://doi.org/10.17721/moca.2019.146-152
Li Y.D., Chai H.H., Zhang S.J., Lu Z.S., Li C.M., Yu L. Sensitive and portable colorimetric detection of copper in water by cotton thread based pre-concentration Microchemical Journal. 2019, 148, 735-742 https://doi.org/10.1016/j.microc.2019.05.056
Castro R.C., Ribeiro D.S.M., Santos J.L.M. Visual detection using quantum dots sensing platforms Coordination Chemistry Reviews. 2021, 429, 213637 https://doi.org/10.1016/j.ccr.2020.213637
Jeber J.N., Hassan R.F., Hammood M.K., Al-Jeilawi O.H.R. Sensitive and simple colorimetric methods for visual detection and quantitative determination of semicarbazide in flour products using colorimetric reagents. Sensors & Actuators: B. Chemical. 2021, 341, 130009 https://doi.org/10.1016/j.snb.2021.130009
Sukma W., Boonyakong C., Chaiphet T., Chamni S. A simple and rapid colorimetric detection of methanol, ethanol, and isopropanol and its application toward alcohol-based hand sanitizer quality control Green Chemistry Letters and Reviews. 2024, 17(1), 2298982 https://doi.org/10.1080/17518253.2023.2298982
Singh R. Narration and Legacy of Important Chemical Spot Tests in Forensic Investigation. Critical Reviews in Analytical Chemistry. 2020, on-line https://doi.org/10.1080/10408347.2020.1785837
Philp M., Shimmon R., Stojanovska N., Tahtouh M., Fu S. Development and validation of a presumptive colour spot test method for the detection of piperazine analogues in seized illicit materials. Anal. Methods, 2013, 5 (20), 5402. DOI: 10.1039/c3ay40511g
Пантелеймонов А.В. Нові хемометричні засоби обробки даних аналітичного експерименту. Автореферат дисертації на здобуття наук. ступ. канд. хім. наук за спец. 02.00.02 – аналітична хімія, Харківський національний університет імені В.Н. Каразіна, Харків, 2009. – 18 с.
Panteleimonov A.V., Nikitina N.A., Reshetnyak E.A., Loginova L.P., Bugaevskii A.A., Kholin Y.V. Binary response procedures of qualitative analysis: metrological characteristics and calculation aspects. Methods Objects Chem. Anal. 2008, 3 (2), 128-146.
Нікітіна Н.О. Тест-методи хімічного аналізу з візуальною індикацією: метрологічне забезпечення, нові тест-системи. Автореферат дисертації на здобуття наук. ступ. канд. хім. наук за спец. 02.00.02 – аналітична хімія, Харківський національний університет імені В.Н. Каразіна, Харків, 2006. – 18 с.
Ríos A., Barceló D., Buydens L., Cárdenas S., Heydorn K.,Karlberg B., Klemm K., Lendl B., Milman B., Neidhart B., Stephany R.W., Townshend A., Zschunke A., Valcárcel M. Quality assurance of qualitative analysis in the framework of the European project “MEQUALAN”. Accred. Qual. Assur. 2003, 8, 68–77. https://doi.org/10.1007/s00769-002-0556-x
Cárdenas S., Valcárcel M. Analytical features in qualitative analysis. Trends Anal. Chem. 2005, 24(6), 477-487. https://doi.org/10.1016/j.trac.2005.03.006
Ellison S.L.R., Fearn T. Characterizing the performance of qualitative analytical methods: Statistics and terminology. Trends Anal. Chem. 2005, 24(6), 468–476. https://doi.org/10.1016/j.trac.2005.03.007
Trullols E., Ruisánchez I., Rius F.X. and Huguet J. Validation of qualitative methods of analysis that use control samples. Trends in Anal. Chem. 2005, 24, 516. https://doi.org/10.1016/j.trac.2005.04.001
Milman B., Konopel'ko L. Uncertainty of Qualitative Chemical Analysis: General Methodology and Binary Test Methods. Journal of Analytical Chemistry. 2004, 59 (12), 1128-1141 DOI:10.1023/B:JANC.0000049712.88066.e7
Zolotov Y.A., Ivanov V.M., Amelin V.G. Chemical Test Methods of Analysis (Comprehensive Analytical Chemistry, Volume 36) 1st Edition. Publisher: Elsevier Science, 2002, 336 p.
Комарь М.П. Основи якісного хімічного анализу. I. Іонні рівноваги. – Харків: Вид-во Харківського університету, 1955. – 448 с.
Hastings N. A. J., Peacock J. B. Statistical Distributions. Publisher: Architectural Press, 1974, 144 p.
Reshetnyak E.A., Nikitina N.A., Loginova L.P., Ostrovskaya V.M. Limit of detection in test methods of analysis with visual indication: affecting factors. Journal of analytical chemistry. 2005, 60(10), P. 982-989. https://doi.org/10.1007/s10809-005-0221-8
Kohavi R. A study of cross-validation and bootstrap for accuracy estimation and model selection. Artificial Intelligence: Fourteenth International Joint Conference: 2 December 1995.: abstr. – San Mateo, CA, 1995, p. 1137–1143.
Richard R.P., Cook L., Dennis M. Cross-Validation of Regression Models. Journal of the American Statistical Association. 1984, 79 (387), 575–583.
Холін Ю.В. Кількісний фізико-хімічний аналіз комплексоутворення в розчинах і на поверхні хімічно модифікованих кремнеземів: змістовні моделі, математичні методи та їх застосунки. – Харків: Фоліо, 2000. – 288 с.
