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

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.