Covariance adjustment for batch effect in gene expression data

Batch bias has been found in many microarray gene expression studies that involve multiple batches of samples. A serious batch effect can alter not only the distribution of individual genes but also the inter-gene relationships. Even though some efforts have been made to remove such bias, there has been relatively less development on a multivariate approach, mainly because of the analytical difficulty due to the high-dimensional nature of gene expression data. We propose a multivariate batch adjustment method that effectively eliminates inter-gene batch effects. The proposed method utilizes high-dimensional sparse covariance estimation based on a factor model and a hard thresholding. Another important aspect of the proposed method is that if it is known that one of the batches is produced in a superior condition, the other batches can be adjusted so that they resemble the target batch. We study high-dimensional asymptotic properties of the proposed estimator and compare the performance of the proposed method with some popular existing methods with simulated data and gene expression data sets. Copyright (c) 2014 John Wiley & Sons, Ltd.