Authors: Anton Panteleimonov | Н. А. Никитина
Source: Kharkov University Bulletin Chemical Series (article, 2025-06-25)
Field: Chemistry — Analytical Chemistry

Verification of the predictive ability of some probability distribution functions in test analysis 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. Probability distribution ; Test (biology) ; Selection (genetic algorithm) ; Empirical probability ; Prior probability ; Probability density function ; Distribution (mathematics) ; Function (biology) ; Test method Spectroscopy and Chemometric Analyses ; Advanced Statistical Methods and Models ; Pesticide Residue Analysis and Safety