  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 of counts is an essential step in differential
expression (DE) analysis. The normalization of existing DE detection algorithms
is ad hoc and performed once for all 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 log-transformed 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-norm 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 studies show that the proposed model
and algorithms outperform existing methods in terms of detection power and
false-positive rate when more than half of the genes are differentially
expressed and/or when the up- and down-regulated genes among DE genes are
unbalanced in amount.
