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Abstract:
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In large scale gene expression studies, latent variables or confounding factors can have substantial effects on the responses. When searching for associations between gene-expression levels and primary variables of interest, it is necessary to adjust for these latent variables to improve estimation and control for false discovery rate. We take a two-step approach for estimation and testing in the presence of confounding factors. The first step estimates the coefficients of the confounding factors using factor analysis, and the second step applies an empirical Bayes approach to shrink the effect estimates. We assume the distribution of the effects of the primary variables are unimodal with mode at 0 and estimate this unimodal density. We prove that our estimate of the unimodal density depends on the estimated coefficients only through their row space, thereby accounting for the usual identifiability issues in factor analysis. We present results on our method, called MOUTHWASH (Maximizing Over Unobservables To Help With Adaptive SHrinkage), and its ability to estimate FDR and improve estimation over other confounder adjustment methods when the effects are unimodally distributed.
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