Unifying and generalizing methods for removing unwanted variation based on negative controls

Unwanted variation, including hidden confounding, is a well-known problem in many fields, but particularly in large-scale gene expression studies. Recent proposals to use control genes, genes assumed to be unassociated with the covariates of interest, have led to new methods to deal with this problem. Several versions of these removing unwanted variation (RUV) methods have been proposed, including RUV1, RUV2, RUV4, RUVinv, RUVrinv, and RUVfun. Here, we introduce a general framework, RUV*, that both unites and generalizes these approaches. This unifying framework helps clarify the connections between existing methods. In particular, we provide conditions under which RUV2 and RUV4 are equivalent. The RUV* framework preserves an advantage of the RUV approaches, namely, their modularity, which facilitates the development of novel methods based on existing matrix imputation algorithms. We illustrate this by implementing RUVB, a version of RUV* based on Bayesian factor analysis. In realistic simulations based on real data, we found RUVB to be competitive with existing methods in terms of both power and calibration. However, providing a consistently reliable calibration among the data sets remains challenging.