Various Ideas for Confounder Adjustment in Regression
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Various Ideas for Confounder Adjustment in Regression

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Y = XB + ZA + E,


  • Y an n by p matrix of gene expression data with n samples and p genes,
  • X an n by q matrix of q covariates,
  • B a q by p matrix of unobserved coefficients for the observed covariates,
  • Z an n by k matrix of hidden confounders,
  • A a k by p matrix of hidden coefficients for the hidden confounders, and
  • E an n by p matrix of independent normal errors with column variances s1,...,sp.

Not accounting for the hidden covariates, Z, can reduce power and result in poor control of false discovery rate. This package provides a suite of functions to adjust for hidden confounders, both when one has and does not have access to control genes.

The functions mouthwash and backwash can adjust for hidden confounding when one does not have access to control genes. They do so via non-parametric empirical Bayes methods that use the powerful methodology of Adaptive SHrinkage (Stephens 2016) within the factor-augmented regression framework described in Wang et al. (2015). backwash is a slightly more Bayesian version of mouthwash.

When one has control genes, there are many approaches to take. Such methods include RUV2 (J. A. Gagnon-Bartsch and Speed 2012), RUV4 (J. Gagnon-Bartsch, Jacob, and Speed 2013), and CATE (Wang et al. 2015). This package adds to the field of confounder adjustment with control genes by

  1. Implementing a version of CATE that is calibrated using control genes similarly to the method in J. Gagnon-Bartsch, Jacob, and Speed (2013). The function is called vruv4.
  2. Introduces RUV3, a version of RUV that can be considered both RUV2 and RUV4. The function is called ruv3.
  3. Introduces RUV-impute, a more general framework for accounting for hidden confounders in regression. The function is called ruvimpute
  4. Introduces RUV-Bayes, a Bayesian version of RUV. The function is called ruvb.

See also the related R packages cate (Wang and Zhao 2015) and ruv (J. Gagnon-Bartsch 2015).

Check out to see what's new with each version.

How to cite

If you use any of the control-gene based methods, please cite:

Gerard, D., & Stephens, M. 2017. Unifying and Generalizing Methods for Removing Unwanted Variation Based on Negative Controls. arXiv preprint arXiv:1705.08393

Or, using BibTex:

  title={Unifying and Generalizing Methods for Removing Unwanted Variation Based on Negative Controls},
  author={Gerard, David and Stephens, Matthew},
  journal={arXiv preprint arXiv:1705.08393},

If you use either MOUTHWASH or BACKWASH, please cite:

Gerard, D., & Stephens, M. 2017. Empirical Bayes Shrinkage and False Discovery Rate Estimation, Allowing For Unwanted Variation. arXiv preprint arXiv:1709.10066

Or, using BibTex:

  title={Empirical {B}ayes Shrinkage and False Discovery Rate Estimation, Allowing For Unwanted Variation},
  author={Gerard, David and Stephens, Matthew},
  journal={arXiv preprint arXiv:1709.10066},

Otherwise, please cite this package as:

Gerard, David. 2016. vicar: Various Ideas for Confounder Adjustment in Regression.

Or, using BibTex:

    title = {{vicar}: Various Ideas for Confounder Adjustment in Regression},
    author = {David Gerard},
    year = {2016},
    note = {R package version 0.1-9},
    url = {},


To install, first install sva and limma from Bioconductor in R:

## try http:// if https:// URLs are not supported
biocLite(c("limma", "sva"))

Also install the cate R package:


Then run in R:

# install.packages("devtools")

A note about matrix computations in vicar: Some of the methods in the vicar package such as mouthwash and backwash rely heavily on matrix-vector operations. The speed of these operations can have a big impact on vicar's performance, especially in large-scale data sets. If you are applying vicar to large data sets, I recommend that you set up R with optimized BLAS (optionally, LAPACK) libraries, especially if you have a multicore computer (most modern laptops and desktops are multicore). See here and here for advice and technical details on this. For example, in our experiments on a high-performance compute cluster we set up R with multithreaded OpenBLAS.


I've provided three vignettes to help you get started with vicar. By default, the vignettes are not built when you use install_github. To build the vignettes during installation, run

# install.packages("devtools")
devtools::install_github("dcgerard/vicar", build_vignettes = TRUE)

Note that this will result in a somewhat slower install. The first vignette, sample_analysis, gives a sample analysis using vicar to account for hidden confounding. The second vignette, customFA, gives a few instructions on how to incorporate user-defined factor analyses with the confounder adjustment procedures implemented in vicar. The third vignette, custom_prior, gives instructions and examples on incorporating a user-specified prior into ruvb. To see these vignettes after install, run

utils::vignette("sample_analysis", package = "vicar")
utils::vignette("customFA", package = "vicar")
utils::vignette("custom_prior", package = "vicar")


Gagnon-Bartsch, Johann. 2015. ruv: Detect and Remove Unwanted Variation Using Negative Controls.

Gagnon-Bartsch, Johann A, and Terence P Speed. 2012. “Using Control Genes to Correct for Unwanted Variation in Microarray Data.” Biostatistics 13 (3). Biometrika Trust: 539–52. doi:10.1093/biostatistics/kxr034.

Gagnon-Bartsch, Johann, Laurent Jacob, and Terence Speed. 2013. “Removing Unwanted Variation from High Dimensional Data with Negative Controls.” Technical Report 820, Department of Statistics, University of California, Berkeley.

Stephens, Matthew. 2016. “False Discovery Rates: A New Deal.” Biostatistics. doi:10.1093/biostatistics/kxw041.

Wang, Jingshu, and Qingyuan Zhao. 2015. cate: High Dimensional Factor Analysis and Confounder Adjusted Testing and Estimation.

Wang, Jingshu, Qingyuan Zhao, Trevor Hastie, and Art B Owen. 2015. “Confounder Adjustment in Multiple Hypothesis Testing.” arXiv Preprint arXiv:1508.04178.