REGRESSION-BASED STATISTICAL ANALYSIS OF STRUCTURE–PROPERTY RELATIONSHIPS USING KERNEL AND CLASSICAL PREDICTION MODELS
DOI:
https://doi.org/10.69980/nx5sxf77Keywords:
QSAR, aquatic toxicity, support vector regression, kernel methods, molecular descriptorsAbstract
The study explored quantitative structure–property relationship (QSPR) for aquatic toxicity using regression-based statistical approaches and kernel-based prediction models. The dataset comprised 908 chemical compounds with LC50 [-log(mol/L)] treated as the continuous response variable. Descriptive statistics, Pearson correlation analysis, multicollinearity assessment, multiple linear regression, regularized regression, support vector regression, and kernel ridge regression were applied to characterize descriptor–response relationships and compare predictive performance. Model performance was assessed through 10-fold cross-validation and a held-out test set using R², root mean squared error (RMSE), mean absolute error (MAE), and mean squared error (MSE). Multiple linear regression explained 57.7% of the variability in LC50 [-log(mol/L)], while MLOGP showed the strongest positive bivariate association with the response. Among the evaluated models, radial basis function support vector regression achieved the strongest predictive performance, with test R² = 0.605, RMSE = 0.978, MAE = 0.677, and MSE = 0.957. Ridge, LASSO, and Elastic Net produced performance like conventional linear regression, indicating that regularization alone provided limited predictive improvement. Permutation-based importance identified MLOGP and SM1_Dz(Z) as the most influential predictors, followed by CIC0, NdsCH, GATS1i, and NdssC. The findings indicate that nonlinear kernel modelling can provide modest but meaningful gains over classical regression for medium-sized molecular descriptor datasets. Combining interpretable linear models with flexible kernel methods offers a practical framework for quantitative structure–property analysis, toxicity prediction, comparative model evaluation, and computational chemical screening. The approach enables simultaneous interpretation of descriptor effects and nonlinear predictive patterns, thereby strengthening evidence obtained from complementary modelling strategies.
References
1. Abbod, M., Safaie, N., & Gholivand, K. (2024). Genetic algorithm multiple linear regression and machine learning-driven QSTR modeling for the acute toxicity of sterol biosynthesis inhibitor fungicides. Heliyon, 10(16).
2. Ballabio, D., Cassotti, M., Consonni, V., & Todeschini, R. (2015). QSAR fish toxicity [Data set]. UCI Machine Learning Repository. https://doi.org/10.24432/C5JG7B
3. Belfield, S. J., Cronin, M. T., Enoch, S. J., & Firman, J. W. (2023). Guidance for good practice in the application of machine learning in development of toxicological quantitative structure-activity relationships (QSARs). PLoS One, 18(5), e0282924.
4. Chen, X., Dang, L., Yang, H., Huang, X., & Yu, X. (2020). Machine learning-based prediction of toxicity of organic compounds towards fathead minnow. RSC advances, 10(59), 36174-36180.
5. Collins, S. P., & Barton-Maclaren, T. S. (2022). Novel machine learning models to predict endocrine disruption activity for high-throughput chemical screening. Frontiers in toxicology, 4, 981928.
6. Cronin, M. T., Basiri, H., Chrysochoou, G., Enoch, S. J., Firman, J. W., Spînu, N., & Madden, J. C. (2025). The predictivity of QSARs for toxicity: Recommendations for improving model performance. Computational Toxicology, 33, 100338.
7. Dai, D., Liu, Q., Hu, R., Wei, X., Ding, G., Xu, B., ... & Zhang, H. (2020). Method construction of structure-property relationships from data by machine learning assisted mining for materials design applications. Materials & Design, 196, 109194.
8. Das, M., Ghosh, A., & Sunoj, R. B. (2024). Advances in machine learning with chemical language models in molecular property and reaction outcome predictions. Journal of Computational Chemistry, 45(14), 1160-1176.
9. Dobbelaere, M. R., Lengyel, I., Stevens, C. V., & Van Geem, K. M. (2024). Geometric deep learning for molecular property predictions with chemical accuracy across chemical space. Journal of Cheminformatics, 16(1), 99.
10. Fuadah, Y. N., Pramudito, M. A., Firdaus, L., Vanheusden, F. J., & Lim, K. M. (2024). QSAR Classification modeling using machine learning with a consensus-based approach for multivariate chemical hazard end points. ACS omega, 9(51), 50796.
11. Gajewicz-Skretna, A., Furuhama, A., Yamamoto, H., & Suzuki, N. (2021). Generating accurate in silico predictions of acute aquatic toxicity for a range of organic chemicals: Towards similarity-based machine learning methods. Chemosphere, 280, 130681.
12. Gao, Y., Zhong, S., Torralba-Sanchez, T. L., Tratnyek, P. G., Weber, E. J., Chen, Y., & Zhang, H. (2021). Quantitative structure activity relationships (QSARs) and machine learning models for abiotic reduction of organic compounds by an aqueous Fe (II) complex. Water research, 192, 116843.
13. Gasser, L., Schür, C., Perez-Cruz, F., Schirmer, K., & Baity-Jesi, M. (2024). Machine learning-based prediction of fish acute mortality: implementation, interpretation, and regulatory relevance. Environmental Science: Advances, 3(8), 1124-1138.
14. Haywood, A. L., Redshaw, J., Hanson-Heine, M. W., Taylor, A., Brown, A., Mason, A. M., ... & Hirst, J. D. (2022). Kernel methods for predicting yields of chemical reactions. Journal of Chemical Information and Modeling, 62(9), 2077-2092.
15. Mahmood, S. W., Basheer, G. T., & Algamal, Z. Y. (2025). Quantitative structure–activity relationship modeling based on improving kernel ridge regression. Journal of Chemometrics, 39(5), e70027.
16. Mao, J., Akhtar, J., Zhang, X., Sun, L., Guan, S., Li, X., ... & Wang, G. (2021). Comprehensive strategies of machine-learning-based quantitative structure-activity relationship models. Iscience, 24(9).
17. Marimuthu, A. N., & McGuire, B. A. (2025). Machine learning pipeline for molecular property prediction using chemxploreML. Journal of Chemical Information and Modeling, 65(11), 5424-5437.
18. Martinez-Mayorga, K., Rosas-Jiménez, J. G., Gonzalez-Ponce, K., López-López, E., Neme, A., & Medina-Franco, J. L. (2024). The pursuit of accurate predictive models of the bioactivity of small molecules. Chemical Science, 15(6), 1938-1952.
19. Nath, A., Ojha, P. K., & Roy, K. (2023). QSAR assessment of aquatic toxicity potential of diverse agrochemicals. SAR and QSAR in Environmental Research, 34(11), 923-942.
20. Pang, C., Tong, H. H., & Wei, L. (2023). Advanced deep learning methods for molecular property prediction. Quantitative Biology, 11(4), 395-404.
21. Quadri, T. W., Olasunkanmi, L. O., Fayemi, O. E., Akpan, E. D., Verma, C., Sherif, E. S. M., ... & Ebenso, E. E. (2021). Quantitative structure activity relationship and artificial neural network as vital tools in predicting coordination capabilities of organic compounds with metal surface: a review. Coordination Chemistry Reviews, 446, 214101.
22. Shi, X. X., Wang, Z. Z., Wang, Y. L., Wang, F., & Yang, G. F. (2024). AquaticTox: A web-based tool for aquatic toxicity evaluation based on ensemble learning to facilitate the screening of green chemicals. Environment & Health, 2(4), 202.
23. Shi, Y. (2021). Support vector regression-based QSAR models for prediction of antioxidant activity of phenolic compounds. Scientific reports, 11(1), 8806.
24. Shilpa, S., Kashyap, G., & Sunoj, R. B. (2023). Recent applications of machine learning in molecular property and chemical reaction outcome predictions. The Journal of Physical Chemistry A, 127(40), 8253-8271.
25. Sultan, A., Sieg, J., Mathea, M., & Volkamer, A. (2024). Transformers for molecular property prediction: Lessons learned from the past five years. Journal of Chemical Information and Modeling, 64(16), 6259-6280.
26. Sun, T., Wei, C., Liu, Y., & Ren, Y. (2024). Explainable machine learning models for predicting the acute toxicity of pesticides to sheepshead minnow (Cyprinodon variegatus). Science of The Total Environment, 957, 177399.
27. Tang, M., Li, B., & Chen, H. (2023). Application of message passing neural networks for molecular property prediction. Current Opinion in Structural Biology, 81, 102616.
28. Tinkov, O. V., Grigorev, V. Y., Razdolsky, A. N., Grigoryeva, L. D., & Dearden, J. C. (2020). Effect of the structural factors of organic compounds on the acute toxicity toward Daphnia magna. SAR and QSAR in Environmental Research, 31(8), 615-641.
29. Wu, S., Li, S. X., Qiu, J., Zhao, H. M., Li, Y. W., Feng, N. X., ... & Li, Q. X. (2024). Accurate prediction of rat acute oral toxicity and reference dose for thousands of polycyclic aromatic hydrocarbon derivatives based on chemometric QSAR and machine learning. Environmental Science & Technology, 58(34), 15100-15110.
30. Yu, X. (2020). Quantitative structure-toxicity relationships of organic chemicals against Pseudokirchneriella subcapitata. Aquatic Toxicology, 224, 105496.
31. Yu, X., & Zeng, Q. (2022). Random forest algorithm-based classification model of pesticide aquatic toxicity to fishes. Aquatic Toxicology, 251, 106265.
32. Zeng, X., Xiang, H., Yu, L., Wang, J., Li, K., Nussinov, R., & Cheng, F. (2022). Accurate prediction of molecular properties and drug targets using a self-supervised image representation learning framework. Nature Machine Intelligence, 4(11), 1004-1016.
33. Zubrod, J. P., Galic, N., Vaugeois, M., & Dreier, D. A. (2024). Bio-QSARs 2.0: Unlocking a new level of predictive power for machine learning-based ecotoxicity predictions by exploiting chemical and biological information. Environment International, 186, 108607.
