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October 10, 20250 citationsOpen Access

Penalized mixed models to adjust for batch effects and unobserved confounding in high dimensional regression

YLY. J. LuUniversity of Iowa PBPatrick BrehenyUniversity of Iowa

Key Points

Penalized linear mixed models are shown to outperform other methods in handling unobserved confounding.
The study derives a confounding framework to quantify signal, bias, and variability in high-dimensional regression settings.
Simulations examine how bias-to-signal ratios affect performance across LASSO, PC-LASSO, and PLMM methods.
Results indicate that PLMM is the most robust in various scenarios involving unobserved confounders.

Abstract

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 derive a confounding framework in which the signal, bias, and variability can be cleanly partitioned and quantified, thereby enabling simulations in which one varies the bias-to-signal ratio while holding the signal-to-noise ratio fixed. Using this construction, we 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). We identify scenarios in which each method outperforms the others and find that overall, PLMM is the most robust approach.

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