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Abstract:
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We consider large-scale studies in which thousands of significance tests are performed simultaneously. The multiple testing procedure can be severely biased by latent confounding factors such as batch effects and unmeasured covariates that correlate with both primary variable(s) of interest and the outcome. Over the past decade, many statistical methods have been proposed to adjust for the confounders in hypothesis testing. We unify these methods in the same framework and analyze their statistical properties. In particular, we provide theoretical guarantees for RUV-4 (Gagnon-Bartsch et al., 2013) and LEAPP (Sun et al., 2012), which correspond to two different identification conditions in the framework: the first requires a set of "negative controls" that are known a priori to follow the null distribution; the second requires the true non-nulls to be sparse. We show that if the confounding factors are strong, the resulting estimators can be asymptotically as powerful as the oracle estimator. For hypothesis testing, we show the asymptotic z-tests based on the estimators can control FWER. Numerical experiments show that FDR can also be well controlled.
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