Work

Improving Confidence Interval Estimation in Logistic Regression with Multicollinear Predictors: A Comparative Study of Shrinkage Estimators and Application to Prostate Cancer Data

Year: 2026

Type: article

Abstract: In logistic regression with finite binary samples and multicollinear predictors, the maximum likelihood estimator often results in overfitting and high mean squared error (MSE). Shrinkage methods like ridge, Liu, and Kibria–Lukman offer improved MSE performance but are typically evaluated only on this criterion, which overlooks their inferential capability. This study shifts the focus toward confidence interval coverage, using simulations to assess the coverage probability, interval width, and MSE of several shrinkage estimators under varying conditions. The results show that, while shrinkage methods generally reduce interval width and MSE, many fail to maintain adequate coverage. However, certain ridge and Kibria–Lukman estimators achieve a favorable balance between narrow interval width and consistent coverage, making them preferable. The findings are further validated using a prostate cancer dataset, contributing to more reliable inference in logistic regression under multicollinearity. Overall, the results demonstrate that well-chosen shrinkage estimators can serve as effective alternatives to the MLE in biostatistical modeling, improving the stability and interpretability of regression analyses in studies pertaining to public health and medicine.

Source: Stats

DOI: 10.3390/stats9010011

Authors: Sultana Mubarika Rahman Chowdhury, Zoran Bursac, B. M. Golam Kibria

Institution: Florida International University

Language: English

Topic: Advanced Statistical Methods and Models

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

SDG: Good health and well-being

Open Access status: gold

Estimated APC paid: $1,930