Identification of gene pairs through penalized regression subject to constraints

Abstract

BackgroundThis 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.ResultsIn 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.ConclusionOur findings demonstrate the feasibility and utility of using gene pairs as biomarkers.

Modeling Between-Study Heterogeneity for Improved Replicability in Gene Signature Selection and Clinical Prediction

“…Such ideal gene pairs are less likely to be observed purely due to technical biases, as this flip in expression is specific to subtype and is also replicated across many subjects. Indeed, many recent publications utilizing gene pair-based approaches have shown high accuracy and robustness in their validation datasets, reflecting this point (Afsari et al, 2015;Shen et al, 2017;Afsari et al, 2014;Leek, 2009;Kagaris et al, 2018;Patil et al, 2015).…”

TimiGP: Inferring cell-cell interactions and prognostic associations in the tumor immune microenvironment through gene pairs

“…Compared with predictors based on individual gene expressions, gene pair-based prognostic models have better normalizing robustness, predicting accuracy, and translational potential. 81 , 82 , 83 , 84 While recent studies have revealed the advantage of immune-related gene pairs in developing predictive signatures, 35 , 64 it remains statistically and computationally challenging to identify the best combination of gene pair signatures due to the quadratically combinatorial complexity. As we have demonstrated, TimiGP can be used to build effective prognostic models by focusing on marker gene pairs associated with cell-cell interactions.…”

TimiGP: inferring inter-cell functional interactions and clinical values in the tumor immune microenvironment through gene pairs

“…Compared to predictors based on individual gene expressions, gene pair-based prognostic models have better normalizing robustness, predicting accuracy, and translational potential [73][74][75][76] . Despite this, it remains statistically and computationally challenging to identify the best combination of gene pair signatures due to the quadratically combinatorial complexity.…”