Robustness Comparison of MLE, Clean-MLE, Bianco–Yohai, and Weighted Bianco–Yohai Estimates in Binary Logistic Regression for Heart Disease Prediction

Muhammad Zulfadhli

doi:10.54065/likelihood.1229

Authors

Muhammad Zulfadhli Institut Teknologi Sepuluh Nopember

DOI:

https://doi.org/10.54065/likelihood.1229

Keywords:

Robust Logistic Regression, Outlier, Bianco-Yohai, Weighted Bianco-Yohai, Cardiovascular

Abstract

Logistic regression is a popular statistical method for modeling the relationship between categorical response variables and one or more explanatory variables. However, standard estimation using Maximum Likelihood Estimation (MLE) is very sensitive to the presence of outliers, which can cause bias in the model parameters. This study aims to compare the performance of classical logistic regression models (MLE and Clean-MLE) with robust logistic regression models using Bianco-Yohai (BY) and Weighted Bianco-Yohai (WBY) estimation in predicting cardiovascular disease. The data used came from the Heart Failure Prediction Dataset, which included 918 observations with response variables of heart disease status and several independent variables such as age, blood pressure, cholesterol, fasting blood sugar, and maximum heart rate. Model goodness was evaluated by comparing the smallest chi-square values through arcsin transformation. The analysis results showed the presence of outliers in the dataset used. The comparison of chi-square values showed that the Weighted Bianco-Yohai (WBY) estimation method provided the lowest value of 1531.44 compared to MLE (1540.88), Clean-MLE (1538.03), and BY (1537.30). Thus, it can be concluded that the Binary Logistic Regression method with Robust Weighted Bianco-Yohai estimation is the best model for handling data containing outliers in heart disease prediction because it produces a more accurate and robust model.

References

Achmad, A. M., Zulfadhli, M., & Nurfaudzan, N. (2025). Binary logistic regression on the status of unemployment rate in West Java Province in 2023. Likelihood: Journal of Statistics and Its Applications, 1(1), 30–34.

Agresti, A. (2013). Categorical data analysis (3rd ed.). John Wiley & Sons.

Akturk, B., Beyaztas, U., & Shang, H. L. (2025). Robust functional logistic regression. Advances in Data Analysis and Classification, 19(1), 121–145.

Bianco, A. M., & Yohai, V. J. (1996). Robust estimation in the logistic regression model. In H. Rieder (Ed.), Robust statistics, data analysis, and computer intensive methods (Lecture Notes in Statistics, Vol. 109, pp. 17–34). Springer. https://doi.org/10.1007/978-1-4612-2380-1_2

Burger, D. A., van der Merwe, S., & Lesaffre, E. (2025). Addressing outliers in mixed-effects logistic regression: A more robust modeling approach. arXiv. https://doi.org/10.48550/arXiv.2504.13781

Croux, C., & Haesbroeck, G. (2003). Implementing the Bianco and Yohai estimator for logistic regression. Computational Statistics & Data Analysis, 44(1–2), 273–295. https://doi.org/10.1016/S0167-9473(03)00042-2

Dey, D., Haque, M. S., Islam, M. M., Aishi, U. I., Shammy, S. S., Mayen, M. S. A., Noor, S. T. A., & Uddin, M. J. (2025). The proper application of logistic regression model in complex survey data: A systematic review. BMC Medical Research Methodology, 25(1), Article 15. https://doi.org/10.1186/s12874-024-02454-5

Hosmer, D. W., Jr., Lemeshow, S., & Sturdivant, R. X. (2013). Applied logistic regression (3rd ed.). John Wiley & Sons. https://doi.org/10.1002/9781118548387

Hossain, S., Hasan, M. K., Faruk, M. O., Aktar, N., Hossain, R., & Hossain, K. (2024). Machine learning approach for predicting cardiovascular disease in Bangladesh. BMC Cardiovascular Disorders.

Idris, H. I., Mohammed, A., Salisu, U. F., Balansana, K. I., Abdulazeez, D., & Danrimi, N. H. (2024). Evaluating the performances of robust logistic regression models in the presence of outliers. African Journal of Mathematics and Statistics Studies, 7(4), 320–327. https://doi.org/10.52589/AJMSS-YKDFCYQS

Lukman, A. F., Mohammed, S., Olaluwoye, O., & Farghali, R. A. (2025). Handling multicollinearity and outliers in logistic regression using the robust Kibria–Lukman estimator. Axioms, 14(1), Article 19. https://doi.org/10.3390/axioms14010019

Ma, Q. (2024). Recent applications and perspectives of logistic regression modelling in healthcare. Theoretical and Natural Science, 36, 185–190.

Nwohiri, A. M., Laguda, A. A., Olanite, A. A., & Olabamire, D. D. (2024). Logistic regression technique for cardiovascular disease prediction. FUDMA Journal of Sciences, 8(4), 266–275. https://doi.org/10.33003/fjs-2024-0804-2624

Otok, B. W., Zulfadhli, M., Pangesti, R. D., Kurniawan, M. I., Haryanto, A. E. P., & Kurniawan, I. (2026). Comparison of binary probit regression and Fourier series nonparametric logistic regression in modeling diabetes status at Hajj General Hospital Surabaya. BAREKENG, 20(1), 255–270.

Pregibon, D. (1981). Logistic regression diagnostics. The Annals of Statistics, 9(4), 705–724. https://doi.org/10.1214/aos/1176345513

Saida, S., Zulfadhli, M., & Jurais, M. (2022). Analisis faktor-faktor yang mempengaruhi vaccine hesitancy (keragu-raguan vaksin) pada mahasiswa di era pandemi Covid-19. Preventif: Jurnal Kesehatan Masyarakat, 13(1), 144–154.

Suriaslan, A. S., Budiantara, I. N., Ratnasari, V., Zulfadhli, M., & Dhewy, R. C. (2025). An empirical study on unmet need: A statistical inference framework for truncated spline nonparametric binary logistic regression (TSNLBR). Journal of Cultural Analysis and Social Change, 10, 868–877. https://doi.org/10.20897/jcasc/2025.868

Tong, P., Hu, H., & Tong, L. (2025). Explainable logistic regression for heart disease risk prediction in community and clinical populations: Development and external validation study. JMIR Cardio. https://doi.org/10.2196/82462

Wang, H. (2024). Using logistic regression model to predict the future coronary heart disease. Theoretical and Natural Science, 50, 83–90. https://doi.org/10.54254/2753-8818/50/2024AU0147

Wu, H. (2024). Using logistic regression model to predict the future coronary heart disease. Theoretical and Natural Science, 50, 83–90. https://doi.org/10.54254/2753-8818/50/2024AU0147

Wulandari, R. (2018). Penerapan model regresi logistik robust pada status hiperkolesterolemia di RSUD Dr. Moewardi Surakarta menggunakan estimasi Bianco–Yohai. Jurnal UNS.

Zulfadhli, M. (2025). Estimator regresi nonparametrik deret Fourier multivariabel untuk data kategori [Doctoral dissertation, Institut Teknologi Sepuluh Nopember].

Zulfadhli, M., Budiantara, I. N., & Ratnasari, V. (2024). Nonparametric regression estimator of multivariable Fourier series for categorical data. MethodsX, 13, Article 102983. https://doi.org/10.1016/j.mex.2024.102983

Zulfadhli, M., Budiantara, I. N., Ratnasari, V., & Suriaslan, A. S. (2025a). Fourier series nonparametric regression estimator for modeling status of unmet need in East Java Province in 2023. Communications in Mathematical Biology and Neuroscience, Article 2025.

Zulfadhli, M., Budiantara, I. N., Ratnasari, V., & Suriaslan, A. S. (2025b). Semiparametric regression estimator of Fourier series for categorical data. IAENG International Journal of Applied Mathematics, 55(7), 2157–2164.

Zulfadhli, M., Budiantara, I. N., Ratnasari, V., Suriaslan, A. S., & Dhewy, R. C. (2025c). A statistical inference framework for FSNBLR: Modeling underdeveloped regional status in Eastern Indonesia. MethodsX, Article 103746. https://doi.org/10.1016/j.mex.2025.103746