Abstract
The RNA-sequencing (RNA-seq) is becoming increasingly popular for quantifying gene expression levels. Since the RNA-seq measurements are relative in nature, between-sample normalization is an essential step in differential expression (DE) analysis. The normalization step of existing DE detection algorithms is usually ad hoc and performed only once prior to DE detection, which may be suboptimal since ideally normalization should be based on non-DE genes only and thus coupled with DE detection. We propose a unified statistical model for joint normalization and DE detection of RNA-seq data. Sample-specific normalization factors are modeled as unknown parameters in the gene-wise linear models and jointly estimated with the regression coefficients. By imposing sparsity-inducing L1 penalty (or mixed L1/L2 penalty for multiple treatment conditions) on the regression coefficients, we formulate the problem as a penalized least-squares regression problem and apply the augmented Lagrangian method to solve it. Simulation and real data studies show that the proposed model and algorithms perform better than or comparably to existing methods in terms of detection power and false-positive rate. The performance gain increases with increasingly larger sample size or higher signal to noise ratio, and is more significant when a large proportion of genes are differentially expressed in an asymmetric manner.