A0598
Title: Suppressing odds ratio inflation: Detection and correction of perfect separation in logistic regression
Authors: Liangliang Zhang - Case Western Reserve University (United States) [presenting]
Abstract: Logistic regression is a core method for modeling binary outcomes, but it struggles when perfect separation occurs, leading to inflated odds ratios and unstable predictions. Most existing methods address this issue post hoc. In contrast, a pre-hoc linear programming approach is proposed that assesses the extent to which predictor combinations are separated by the binary outcome. When separation arises from a linear combination of multiple variables, this is defined as latent perfect separation. The method detects both direct and latent separation. It is shown that although latent separation results in infinite estimates for individual coefficients, the ratio of coefficients converges to a fixed constant that reflects the true underlying relationship. This finding is incorporated into a Bayesian power prior framework to correct inflated estimates and guide them toward realistic values. The Bayesian method also integrates additional statistical criteria to ensure convergence. Simulations show that our approach significantly outperforms the widely used Firth correction, and real-world applications confirm that our adjusted coefficients better reflect true effects. By detecting and addressing separation before model fitting, the method improves both interpretability and accuracy in logistic regression, especially in complex settings like disease association studies.
