Methodological approach to verifying and using probabilistic models of the biomarkers of exposure – biomarkers of effect relationship based on kl-divergence: Pilot study

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PDF icon health-risk-analysis-2026-3-13.pdf
UDC: 
614.2:519.226:57.088
DOI: 
10.21668/health.risk/2026.3.13.eng
Authors: 

Е.L. Krotova1, N.V. Zaitseva2, А.А. Savochkina1, М.А. Zemlyanova2

Organization: 

1Perm National Research Polytechnic University, 29 Komsomolskii Av., Perm, 614990, Russian Federation
2Federal Scientific Center for Medical and Preventive Health Risk Management Technologies, 82 Monastyrskaya St., Perm, 614045, Russian Federation

Abstract: 

Linear regression models are traditionally used to estimate the relationship between chemical exposures and biomarkers. Still, they have several considerable limitations: they fail to consider heterogeneity of a population, do not adequately describe non-linear dependences and are not effective when correlated predictors are used. The aim of this study was to develop a methodological approach to verifying and using probabilistic models that describe the ‘biomarkers of exposure – biomarkers of effect’ relationship based on Kullback – Leibler (KL) divergence. This is an integral quality measure, which makes it possible to objective compare linear and non-linear models.

A pilot sample was used to build several models: a linear model, ridge-regression, second-degree polynomial model, GAM, Random Forest, and XGBoost. KL-divergence was calculated for each model between the actual and predicted distribution of three blood indicators: neutrophils, eosinophils, and cortisol. The linear regression showed extremely high

KL-divergence and the XGBoost yielded the best result. Q–Q (quantile-quantile) graphs revealed some discrepancies in distribution tails, which indicated that the sample was heterogeneous and stratification was necessary.

The suggested approach makes it possible to objectively compare models and select the most adequate structure of the relationship. A feedback signal system was developed based on the built models; it used three scenarios (yellow, orange, and red) for automatic communication with services responsible for controlling quality of environmental objects in case serious deviations from safe standards were found in biomarkers in the population. The key advantage is that the method is easily scaled to cover any number of tests (biochemical, immunological, or genetic) and any set of pollutants without any changes in its basic logic. This makes the method a universal instrument for the system for social and hygienic monitoring.

Keywords: 
KL-divergence, model verification, XGBoost, GAM, Random Forest, exposure, biomarkers, neutrophils, eosinophils, cortisol, feedback signal
Krotova Е.L., Zaitseva N.V., Savochkina А.А., Zemlyanova М.А. Methodological approach to verifying and using proba-bilistic models of the biomarkers of exposure – biomarkers of effect relationship based on KL-divergence: pilot study. Health Risk Analysis, 2026, no. 3, pp. 139–148. DOI: 10.21668/health.risk/2026.3.13.eng
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Received: 
07.08.2026
Approved: 
15.09.2026
Accepted for publication: 
28.09.2026

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