Detection of and Adjustment for Multiple Unmeasured Confounding Variables in Logistic Regression by Bayesian Structural Equation Modeling

Abstract

Aim: To compare the bias magnitude between logistic regression and Bayesian structural equation modeling (SEM) in a small sample with strong unmeasured confounding from two correlated latent variables. Study Design : Statistical analysis of artificial data. Methodology: Artificial binary data with above characteristics were generated and analyzed by logistic regression and Bayesian SEM over a plausible range of model parameters deduced by comparing the paramete r bounds for two extreme scenarios of no versus maximum confounding. Results: Bayesian SEM with flat priors achieved almost fourfold absolute bias reduction for the effects of observed independent variables on binary outcome in the presence of two correla ted unmeasured confounders in comparison with standard logistic regression which ignored the confounding. The reduction was achieved despite a relatively small sample (N=100) and large bias and variance of the factor loadings for the latent confounding var iables. However, the magnitude of