31: DISCO: Diagnosis of Separation and Correction of Odds-ratio Inflation in Logistic Regression

Thomas M. Menino Convention & Exhibition Center 

Logistic regression models binary outcomes in biomedical studies to obtain interpretable odds ratios. Separation occurs when predictors perfectly or nearly perfectly classify cases and controls, causing maximum likelihood estimates to diverge. We develop DISCO (DIagnosis of Separation and Correction of Odds-ratio inflation), a detection-and-estimation framework. DISCO provides pre-hoc diagnosis to detect separation, identify problematic predictors, and quantify severity. A key theoretical insight is that under separation, the coefficient vector's direction remains identifiable, so pairwise ratios of nonzero coefficients are well-defined despite individual magnitudes diverging. We propose a Bayesian estimator with multivariate exponential power prior that penalizes coefficients. We construct a simulation framework generating separation cases with ground truth for fair comparison. Simulations show DISCO detects more problematic data than existing methods, and our estimator controls bias better than alternatives. In HIV-risk data, DISCO outperforms competitors by identifying problematic variables and producing finite, sign-preserving odds ratios.

Logistic regression

Separation Problem

Bayesian methods

Multivariate exponential-power prior 

ENAR