Detection of Unknown Confounders by Bayesian Confirmatory Factor Analysis

Artificial data with known covariance structure was used to directly test confounding hypothesis using Bayesian confirmatory factor analysis with small variance informative priors. The priors were derived from two extreme scenarios of no versus maximum confounding via exposure variables. Large (N=5000) and small (N=100) sample analyses were performed for both continuous and binary variable models. Both models showed large biases for all parameters in all analyses except for the direct effect of unobserved confounding on the outcome. Multivariate regression analyses yielded severely biased estimates of the exposure variables’ effects. This problem was to some extent attenuated in Bayesian confirmatory factor analysis but the bias magnitude still remained large for the parameters in question. In conclusion, Bayesian confirmatory factor analysis was shown reasonably precise to estimate direct confounding effect on the outcome but less so when this effect was mediated via exposure variables in both linear and binary regression models. It may be used a viable method for identifying unknown confounding variables and their relationship with the observed variables in the model.