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

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.