57: Penalized Mixed Models to Adjust for Unobserved Confounding in High Dimensional Regression

Music City Center 

Confounding can lead to spurious associations. Typically, one must observe confounders in order to adjust for them, but in high-dimensional settings, recent research has shown that it becomes possible to adjust even for unobserved confounders. The methods for carrying out these adjustments, however, have not been thoroughly investigated. In this study, we explore various forms of unobserved confounding and assess how they introduce bias and variability into the data. We quantify the magnitude and structure of these effects by examining the ratios between bias, signal, and noise. We then construct various scenarios to demonstrate the impact of the amount and complexity of unobserved confounding on the performance of competing methods, including the LASSO, principal components LASSO (PC-LASSO), and penalized linear mixed models (PLMMs). Our findings highlight the importance of adjusting for unobserved confounding. In addition, we find that PLMM approaches are more robust than PC-LASSO in handling complex confounding structures while preventing the inclusion of spurious features into the model.

Penalized Regression

Linear mixed models

Unobserved confounding 

ENAR