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 parameter 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 correlated 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 variables. However, the magnitude of residual confounding was still high.  Conclusion: Logistic regression bias due to unmeasured confounding may be considerably reduced with Bayesian SEM even in small samples with multiple confounders. The assumptions for Bayesian SEM are far less restrictive than those for the instrumental variable method aimed at correcting the effect size bias due to unmeasured confounders.