Identification of gene pairs through penalized regression subject to constraints

• Published in: BMC bioinformatics Vol. 18; no. 1; pp. 466 - 11
• Main Authors: Shen, Rex, Luo, Lan, Jiang, Hui
• Format: Journal Article
• Language: English
• Published: London BioMed Central 03.11.2017; BioMed Central Ltd; BMC
• Subjects: ADMM; Algorithms; Analysis; Bioinformatics; Biomarker; Biomarkers, Tumor - genetics; Biomarkers, Tumor - metabolism; Biomedical and Life Sciences; Computational biology; Computational Biology/Bioinformatics; Computer Appl. in Life Sciences; Gene pair; Genetic aspects; Genotype; Humans; Identification and classification; Keratin-15 - genetics; Keratin-15 - metabolism; Life Sciences; Linear Models; Male; Methodology; Methodology Article; Methods; Microarrays; Penalized regression; Phenotype; Prostate cancer; Prostate-Specific Antigen - genetics; Prostate-Specific Antigen - metabolism; Prostatic Neoplasms - diagnosis; Prostatic Neoplasms - genetics; Prostatic Neoplasms - metabolism; Real-Time Polymerase Chain Reaction; RNA, Neoplasm - genetics; RNA, Neoplasm - metabolism; Transcriptome analysis; Biomarker; Gene pair; Penalized regression; ADMM
• ISSN: 1471-2105; 1471-2105
• DOI: 10.1186/s12859-017-1872-9

Background This article concerns the identification of gene pairs or combinations of gene pairs associated with biological phenotype or clinical outcome, allowing for building predictive models that are not only robust to normalization but also easily validated and measured by qPCR techniques. However, given a small number of biological samples yet a large number of genes, this problem suffers from the difficulty of high computational complexity and imposes challenges to the accuracy of identification statistically. Results In this paper, we propose a parsimonious model representation and develop efficient algorithms for identification. Particularly, we derive an equivalent model subject to a sum-to-zero constraint in penalized linear regression, where the correspondence between nonzero coefficients in these models is established. Most importantly, it reduces the model complexity of the traditional approach from the quadratic order to the linear order in the number of candidate genes, while overcoming the difficulty of model nonidentifiablity. Computationally, we develop an algorithm using the alternating direction method of multipliers (ADMM) to deal with the constraint. Numerically, we demonstrate that the proposed method outperforms the traditional method in terms of the statistical accuracy. Moreover, we demonstrate that our ADMM algorithm is more computationally efficient than a coordinate descent algorithm with a local search. Finally, we illustrate the proposed method on a prostate cancer dataset to identify gene pairs that are associated with pre-operative prostate-specific antigen. Conclusion Our findings demonstrate the feasibility and utility of using gene pairs as biomarkers.