Joint between-sample normalization and differential expression detection through ℓ₀-regularized regression

A fundamental problem in RNA-seq data analysis is to identify genes or exons that are differentially expressed with varying experimental conditions based on the read counts. The relativeness of RNA-seq measurements makes the between-sample normalization of read counts an essential step in differential expression (DE) analysis. In most existing methods, the normalization step is performed prior to the DE analysis. Recently, Jiang and Zhan proposed a statistical method which introduces sample-specific normalization parameters into a joint model, which allows for simultaneous normalization and differential expression analysis from log-transformed RNA-seq data. Furthermore, an ℓ₀ penalty is used to yield a sparse solution which selects a subset of DE genes. The experimental conditions are restricted to be categorical in their work.

In this paper, we generalize Jiang and Zhan's method to handle experimental conditions that are measured in continuous variables. As a result, genes with expression levels associated with a single or multiple covariates can be detected. As the problem being high-dimensional, non-differentiable and non-convex, we develop an efficient algorithm for model fitting.

Experiments on synthetic data demonstrate that the proposed method outperforms existing methods in terms of detection accuracy when a large fraction of genes are differentially expressed in an asymmetric manner, and the performance gain becomes more substantial for larger sample sizes. We also apply our method to a real prostate cancer RNA-seq dataset to identify genes associated with pre-operative prostate-specific antigen (PSA) levels in patients.