Addressing confounding artifacts in reconstruction of gene co-expression networks
Gene co-expression networks capture biological relationships between genes and are important tools in predicting gene function and understanding disease mechanisms. We show that technical and biological artifacts in gene expression data confound commonly used network reconstruction algorithms. We demonstrate theoretically, in simulation, and empirically, that principal component correction of gene expression measurements prior to network inference can reduce false discoveries. Using data from the GTEx project in multiple tissues, we show that this approach reduces false discoveries beyond correcting only for known confounders.
Weighted gene co-expression networks
Gene co-expression networks seek to identify transcriptional patterns indicative of functional interactions and regulatory relationships between genes [1, 2, 3]. These are not yet fully characterized for most species, tissues, and disease-relevant contexts. Therefore, reconstructing co-expression networks from high-throughput measurements is of common interest. However, accurate reconstruction of such networks remains a challenging problem.
Though some specialized methods for the reconstruction of co-expression networks do consider confounding signals within their model [4, 5], routinely used network learning methods [6, 7] do not directly account for technical and unwanted biological effects known to confound gene expression data. Despite this, many studies do not employ any form of data correction or correct only for known confounders prior to network reconstruction (Additional file 1: Table S1). These artifacts influence gene expression measurements, often introducing spurious correlations between genes [8, 9, 10]. These correlations are often inferred as relationships between genes, leading to inaccurate network structure and erroneous conclusions in downstream analyses [4, 5, 8, 11, 12]. Therefore, it is critical to correct gene expression data for unwanted biological and technical variation without eliminating signal of interest before applying standard network learning methods.
Results and discussion
In this study, we provide a framework for data correction leveraging the structure of scale-free networks. We show that for scale-free networks, principal components of a gene expression matrix can consistently identify components that reflect artifacts in the data rather than network relationships. It has been shown that real-world networks including co-expression networks often have scale-free topology, i.e., the node degree distribution of these networks follow a power law [13, 14, 15]. Several studies have employed the assumption of scale-free topology to infer high-dimensional gene co-expression and splicing networks [6, 16].
Using a toy and scale-free simulation, we first showed that confounding can introduce false correlations between sets of genes that can mimic co-expression and can lead to false edge discovery during reconstruction of co-expression networks with graphical lasso—sometimes at the expense of losing true connections (Fig. 1d-f, Additional file 2). We corrected the confounded simulated data using our PC-based approach and reconstructed the network using the residuals. Graphical lasso correctly estimated the network structure obtained from corrected data, which was the same as the true network structure that was obtained from the original simulated data (Fig. 1a-c,g-h, Additional file 2). We also simulated multivariate Gaussian data with 350 samples and 5000 genes from an underlying scale-free network (Additional file 3). Similar to the previous simulation, we found that confounding in data can introduce a lot more false positives in reconstructed co-expression networks. We also showed that networks reconstructed with PC corrected data in this setting were more similar to original simulated data compared to confounded data (Additional file 3). Throughout our analysis, to estimate the number of principal components to be removed, we used a permutation-based scheme  as implemented in the sva package .
To demonstrate the impact of latent confounders and principal component correction on the reconstruction of co-expression networks from real large-scale human gene expression measurements, we applied our method to RNA-Seq data from the Genotype-Tissue Expression (GTEx) project v6p release. We considered data from eight diverse tissues containing between 304 and 430 samples each (Additional file 1: Table S2): Subcutaneous adipose, lung, skeletal muscle, thyroid, whole blood, tibial artery, tibial nerve, and sun-exposed skin. Using the most variable 5000 genes (Additional file 1: Notes 2 and 4), we reconstructed co-expression networks for each tissue with two popular methods: (a) weighted gene co-expression network analysis [6, 23] and (b) graphical lasso [7, 24]. Since the true underlying co-expression network structure is not known, we assessed the networks using gene pairs annotated to function in the same pathways [25, 26] as ground truth edges.
We inferred networks obtained by using (a) uncorrected expression data, the residuals after regressing out (b) RNA integrity number (RIN), (c) exonic rate—a mapping covariate that corresponds to fraction of reads mapped to exons, (d) sample-specific estimate of GC bias, all known to be common confounders in mRNA gene expression data [27, 28, 29], and (e) residuals from multiple regression model using covariates that explained at least 1% of expression variance (adjusted R2 ≥ 0.01, Additional file 1: Table S3–S5) [28, 30, 31, 32, 33].
In graphical lasso networks, we found that networks estimated with principal component corrected data showed fewer false discoveries compared to networks estimated with uncorrected, RIN-corrected or multiple covariates corrected data (Fig. 2d–f, Additional file 1: Figure S2). We observed that in generally improved performance on false discoveries in PC corrected networks over raw data in the whole blood, the skeletal muscle, tibial artery, and tibial nerve. Compared to raw data, jointly correcting the gene expression data for multiple technical covariates that affect expression measurements also improved reconstruction with graphical lasso in some tissues such as the whole blood, thyroid, and tibial artery, while it showed little to no improvement over uncorrected data in the lung, muscle, tibial nerve, and sun-exposed skin (Fig. 2d–f, Additional file 1: Figure S2). However, we observed that across all tissues, PC correction still shows fewer false discoveries compared to multiple technical covariate-based correction. There was no visible improvement in network reconstruction between using uncorrected data and residuals from RIN or exonic rate, thereby suggesting that RIN, exonic rate, or GC bias individually is not a sufficient alternative for the wide range of confounding variation found in gene expression data (Fig. 2, Additional file 1: Figures S2, S4, and S9). We also found that there was no improvement on false negative rates upon PC correction in networks built with WGCNA or graphical lasso (Additional file 1: Figure S14).
With both WGCNA and graphical lasso, networks inferred from principal component corrected data were much sparser than networks from uncorrected and RIN, exonic rate, or GC bias corrected counterparts (Fig. 2g–l). Further, PC corrected networks from graphical lasso also showed higher clustering coefficient and fewer hubs compared to others (Additional file 1: Figures S12 and S13).
Network reconstruction methods are vulnerable to latent confounders present in gene expression data. Co-expression networks obtained from data corrected for effects of RIN, exonic rate, or GC bias individually show little improvement on false discoveries compared to uncorrected data and are not a sufficient surrogate for the diverse sources of confounding variation in gene expression data. With empirical analysis supported by theoretical proof, we show that PC correction is a simple, yet effective approach to address confounding variation for the reconstruction of gene co-expression networks. We do note for particularly dense or connected sub-graphs in the underlying biological system that may not match the scale-free assumption, or when large differences in expression changes are expected (e.g., cancer vs normal), removing principal components may remove biological signal of interest and, as with any data cleaning methodology, should be used with caution. We have implemented our PC correction approach as a function—“sva_network” in sva Bioconductor package which can be used prior to network reconstruction with a range of methods (Vignette: Additional file 4).
Principal component-based correction of gene expression
Evaluation of co-expression networks
To evaluate our correction method and its effect on the reconstruction of co-expression networks, we used two methods to infer the structure of gene co-expression networks: (a) weighted gene co-expression networks (WGCNA)  and (b) graphical lasso  (Additional file 1: Note 2).
Since the underlying network structure is generally unknown, we used genes known to be functional in the same pathways as ground truth to assess these networks.
Shared true positives: We obtained a refined list of real connections described above by restricting to pairs of genes that were present in at least two pathway databases.
AB is supported by the NIH R01MH109905, NIH R01GM120167, and NIH R01GM121459. MCS is supported by the NSF DBI-1350041 and NIH R01HG006677. JTL is supported by the NIH R01GM105705 and NIH R01GM121459.
CR, PP, AB, and JL conceived the study. PP, CR, AJ, MS, AB, and JL designed the experiments. CR performed the theoretical analysis. PP and CR performed the simulation experiments. PP performed empirical analyses. PP, CR, AB, and JL wrote the manuscript with inputs from all co-authors. All authors read and approved the final manuscript.
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The authors declare that they have no competing interests.
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