 Methodology
 Open Access
 Published:
Metaanalytic support vector machine for integrating multiple omics data
BioData Mining volume 10, Article number: 2 (2017)
Abstract
Background
Of late, highthroughput microarray and sequencing data have been extensively used to monitor biomarkers and biological processes related to many diseases. Under this circumstance, the support vector machine (SVM) has been popularly used and been successful for gene selection in many applications. Despite surpassing benefits of the SVMs, single data analysis using small and midsize of data inevitably runs into the problem of low reproducibility and statistical power. To address this problem, we propose a metaanalytic support vector machine (MetaSVM) that can accommodate multiple omics data, making it possible to detect consensus genes associated with diseases across studies.
Results
Experimental studies show that the MetaSVM is superior to the existing metaanalysis method in detecting true signal genes. In real data applications, diverse omics data of breast cancer (TCGA) and mRNA expression data of lung disease (idiopathic pulmonary fibrosis; IPF) were applied. As a result, we identified gene sets consistently associated with the diseases across studies. In particular, the ascertained gene set of TCGA omics data was found to be significantly enriched in the ABC transporters pathways well known as critical for the breast cancer mechanism.
Conclusion
The MetaSVM effectively achieves the purpose of metaanalysis as jointly leveraging multiple omics data, and facilitates identifying potential biomarkers and elucidating the disease process.
Introduction
Over the last decade, the technologies of microarray and massively parallel sequencing generate multiple omics sources from a large cohort at an unprecedented rate. Besides, since the experimental costs have dropped, a huge amount of data sets have been accumulated in public data repositories (e.g., Gene Expression Omnibus (GEO) and Sequence Read Archive (SRA)). And yet low reproducibility has been a chronic concern due to midandsmall size of each individual experimental unit (e.g., 40–100) and low signaltonoise ratios of genomic expression data [24, 26, 27]. In an effort to tackling these challenges, effective data integration methods have been widely spotlighted in biomedical research [2]. The traditional metaanalysis integrates significance levels or effect sizes of similar data sets (similar design or biological hypothesis), and has proven to be effective in discovering significant biomarkers [14, 37]. Multistudy data integration is also known as “horizontal metaanalysis” that combines multiple homogeneous omics data [38]. Moreover, many large consortia such as the Cancer Genome Atlas (TCGA) and Lung Genomics Research Consortium (LGRC) have generated different types of omics data (e.g., mRNA, methylation, CNV and so on) using samples from a single cohort. Datasets are aligned vertically by samples, and thus integration of such multiomics data is called “vertical omics integrative analysis” [38]. Jointly leveraging multilayers of omics data, vertical omics integration facilitates deciphering biological processes, capturing the interplay of multilevel genomic features, and elucidating how a priori knowledge of biological information (e.g., pathway database) functions within the framework of systems biology.
Generally highthroughput microarray and sequencing data have been extensively applied to monitor biomarkers and biological processes related to many diseases [4], to predict complex diseases (e.g., cancer diagnosis, [36]), prognosis [45], and therapeutic outcomes [23]. In particular, the recent classification and prediction tools have notably advanced the translational and clinical applications (e.g. MammaPrint [43]), Oncotype DX [30] and Breast Cancer Index BCI [49]. In this trend, the support vector machine (SVM) has been also popularly applied to many genomic applications and proved as one of the most powerful prediction methods [3, 15, 29] attributed to unmatched flexibility of nonlinear decision boundary. Commonly gene selection (a.k.a. feature reduction) pertaining to outcomes diminishes the dimension of expression data, enabling to shorten the training time and to enhance interpretability. In addition, gene selection removes a large number of irrelevant genes that potentially undermine precise prediction, and notably the idea of feature selection using SVMs can extend to the setting of multiomics data analysis ([18, 25]). As this concern related, many researchers have put tremendous efforts to circumvent low accuracy of the SVMs when analyzing highdimensional genomic data. For instance, Brown et al. [5] introduced a functional gene classification including the usage of various similarity functions (e.g., kernels modeling prior knowledge of genes). Moreover, as SVM takes on the small subset of samples that differentiate between class labels with an exclusion of the remaining samples, it is believed to have the potential to handle large feature spaces and the ability to identify outliers. Guyon et al. [9] also proposed a gene selection method that utilizes the SVM based on Recursive Feature Elimination (RFE) recursively removing insignificant features to increase classification performance. In spite of SVM’s outstanding fortes in many applications, the current SVMs are only focused towards single data analysis, and so inevitably run into the problem of low reproducibility. To address this problem, we propose a metaanalytic framework based on the support vector machine (MetaSVM). The proposed MetaSVM is motivated by the recent metaanalytic method exploiting the metaanalytic logistic regression (Metalogistic; [22]). To our best knowledge, no method has been introduced, which extends the SVMs to combining multiple studies in a metaanalytic fashion. Related to this, we develop a novel implementation strategy in spirit of Newton’s method to estimate parameters of the MetaSVM. It is commonplace that the objective function of SVM is formed with the hinge loss and a range of penalty terms (e.g., L _{1}lasso, group lasso and etcs). Importantly we, however, adopts the sparse group lasso technique (i.e., both L _{1}lasso and group lasso, simultaneously) to capture both common and study specific genetic effects across all studies. The proposed method, on this ground, achieves the identical purpose of rOP [41] and AW [21], metalogistic [22] whose feature selection allows to detect specific effects. In genomic applications, it cannot be emphasized enough that data integration analysis has proved its practical utility and has become commonplace to identify key regulators of cancer. Thus, many have paid attention to credible validation strategies that build on multiple studies [7, 35]. Besides, metaanalysis essentially aids to adjust tissue specific effects possibly distorting the analysis of individual datasets [21]. The optimization strategy to estimate, therefore, focuses on how to maneuver these two terms (L _{1}lasso and group lasso) in the formula. To overcome some of known traditional optimization rules (e.g., linear and quadratic programming), which mostly entails heavy computing tasks, we propose an approximation method to relax computational complexity in favor of concise implementation. The idea is to approximate the hinge loss including but not limited to penalty terms by a quadratic form, and thereby we can apply the classical coordinate descent algorithm to optimize the whole objective function.
The paper is outlined as follows. In Methods section, we introduce the metaanalytic method that builds on the support vector machine (MetaSVM) and its implementation strategy at length. Simulation studies section shows experimental studies to benchmark performance of feature detection under various experimental scenarios. In Applications to real genomic data section, we demonstrate the advantages of MetaSVM in two real data applications using publicly available omics data, and concluding remarks are presented in Concluding remark section. An R package “metaSVM” is publicly available online at author’s github page (https://sites.google.com/site/sunghwanshome/).
Methods
Metaanalytic support vector machine (MetaSVM)
Consider M independent studies, consisting of n ^{(m)} subjects of mth study for 1≤m≤M. Let \(y_{i}^{(m)}\) be a scalar of binary phenotypes and \(x_{i}^{(m)}=\left (x_{i1}^{(m)},\dots,x_{ip}^{(m)}\right)\) be a vector, each containing p common variables of the ith subject for 1≤i≤n ^{(m)} and 1≤m≤M. We consider an objective function of the L _{1} support vector machine using the single mth data set
where λ>0, \(f\left (x_{i}^{(m)};\beta ^{(m)}\right) = \beta _{0}^{(m)} + \sum _{j=1}^{p} x_{ij}^{(m)} \beta _{j}^{(m)} \) for 1≤i≤n ^{(m)} and \(\beta ^{(m)} = \left (\beta _{0}^{(m)}, \dots, \beta _{p}^{(m)} \right) \in \mathbb {R}^{p+1}\). Due to the linearity of \(f\left (x_{i}^{(m)};\beta ^{(m)}\right)\), this is typically known as the linear support vector machine. And our major interest is to estimate the solution of β ^{(m)} that minimizes (1). By extension, in pursuit of integrating the M studies to a unified model, we propose the metaanalytic support vector machine that builds on multiple data via both group lasso and L _{1} lasso (a.k.a sparse group lasso):
where λ _{1},λ _{2}>0, β=(β ^{(1)},…,β ^{(M)}). Here it is interesting to note that the group lasso penalty, \(\sqrt {\sum _{m=1}^{M}{ \big (\beta _{j}^{(m)}}\big)^{2}}\) comes into play to integrate the effect size of the jth variable across M data sets. Of note, the L _{1} lasso penalty encourages the sparsity within a group that potentially circumvents the allin and allout fashion. Thus, this property is in line with metaanalytic feature selection even when heterogeneous studies are present in analysis, since the sparse group lasso allows to accommodate both common effects across all studies and study specific effects simultaneously. Let
be the sparse group lasso estimator of the metaanalytic support vector machine for mth study for 1≤m≤M.
Implementation strategy
For estimating β, the SVM traditionally exploits the linear or quadratic programming wellsuited to SVM’s dual problem. To our best knowledge, no coordinate descenttype optimization has yet been proposed to address the sparse group lasso problem despite the coordinatetype approach’s utility for implementation. The coordinate descent algorithm is one of the most popular algorithms that are built on the convexity assumption. To apply this algorithm to (2), an approximation to the smooth objective function is required on account of the nondifferential property of the hinge loss and the group lasso penalty. With a little of algebraic trick, the group lasso penalty can be made twicedifferentiable. Precisely, we add some sufficiently small constant inside the square root, in the way that the first and second derivative of the L _{1}lasso and group lasso penalty terms can be made at \(\beta _{j}^{(m)}=0\). When it comes to the nondifferential hinge loss, Zhang et al. [48] proposed the successive quadratic algorithm (SQA): a generalization of Newton’s method for unconstrained optimization such that it finds a step away from the current point of iteration by minimizing a quadratic approximation of the problem. Taken together, the objective function (2) can be approximated to
where β ^{(m)∗} is an estimated coefficient vector at the current point for 1≤m≤M. Contrary to (2), \(\tilde {Q}^{\lambda _{1},\lambda _{2}}(\beta)\) is differentiable with respect to β, convex and separable with respect to all of variables so that we can apply the coordinate descent algorithm by means of Newton’s method. Update
and iterate for 1≤j≤p and 1≤m≤M until convergence. More details are provided in Appendix.
Simulation studies
To evaluate the performance of the proposed MetaSVM method in the genomic setting, we simulated expression profiles with arbitrary correlated gene structures and variable effect sizes as follows: Simulate gene correlation structure for P=30 genes, N=20 samples in each study, and M=3. In each study, 10 out of 30 genes belong to C=2 independent clusters.

Randomly sample gene cluster labels of 30 genes (C _{ p }∈{0,1,2} and 1≤p≤P), such that C=2 clusters each containing 5 genes are generated \((\Sigma _{p=1}^{P} 1 (C_{p} = c) = 5\), 1≤c≤C=2) and the remaining 20 genes are unclustered genes (\(\Sigma _{p=1}^{P} 1(C_{p} = 0) = 20\)).

For any cluster c (1≤c≤C) in study m (1≤m≤M), sample \({\Sigma _{c}^{(m)}}^{*} \sim W^{1}(\psi,60)\), where ψ=0.5I _{5×5}+0.5J _{5×5}, W ^{−1} denotes the inverse Wishart distribution, I is the identity matrix and J is the matrix with all the entries being 1. Set vector \(\sigma _{c}^{(m)}\) as the square roots of the diagonal elements in \({\Sigma _{c}^{(m)}}^{*}\). Calculate \(\sigma _{c}^{(m)}\) such that \(\sigma _{c}^{(m)}\Sigma _{c}^{(m)} {\sigma _{c}^{(m)}}^{\top } = {\Sigma _{c}^{(m)}}^{*}\).

Denote by \(p_{1}^{(c)}, \cdots, p_{5}^{(c)}\) as the indices for genes in cluster c. In other words, \(C_{p_{j}^{(c)}} = c\), where 1≤c≤2 and 1≤j≤5. Sample expression of clustered genes by \(\big ({X^{(m)}_{p_{1}^{(c)}n}},\cdots,{X^{(m)}_{p_{5}^{(c)}n}})^{\top } \sim MVN(0, R \Sigma _{c}^{(m)})\), where 1≤n≤N=20, 1≤m≤M and R is an arbitrary constant for adjusting of total variance (R=1 as default). Sample expression for unclustered genes \(X^{(m)}_{pn} \sim N(0, R)\) for 1≤n≤N and 1 ≤m≤M if C _{ p }=0.

To simulate differential expression pattern, sample effect sizes \(\mu _{p}^{(m)}\) from Unif(0.1,0.5) for 1≤p≤10 as differential expression (DE) genes and set \(\mu _{p}^{(m)}=0\) for 11≤p≤P as nonDE genes.

For the first 10 control samples, \(Y_{pn}^{(m)} ={X^{(m)}_{pn}}(1 \leq p \leq P,1 \leq n \leq N/2=10,\) 1≤m≤M). For cases, \(Y_{p(n+10)}^{(m)} ={X^{(m)}_{p(n+10)}} +\mu _{p}^{(m)} (1 \leq p \leq P, 1 \leq n \leq N/2=10,1 \leq m \leq M)\).
All tuning parameters (λ _{1} and λ _{2}) are chosen by crossvalidation, and the simulations were repeated 50 times. Table 1 summarizes the results of all simulation studies. It is noteworthy that the MetaSVM achieves higher Youden index (= sensitivity + specificity −1) compare to the metalogistic regression model across all experimental scenarios (i.e., R=0.1,0.3 and 0.5), and thus this suggests the MetaSVM performs better in identifying the true signal features. Given that the metalogistics model results in low sensitivity, the metalogistic model has a tendency to overly penalize the effect size of features. In contrast, when data are sampled with low variance (R=0.1), specificity of the metalogistic model is shown to be a little higher than that of the MetaSVM (e.g., 1, 0.997 and 0.994 for the Metalogistic, and 0.9843, 0.9837 and 0.9737 for the MetaSVM), and yet the metalogistic model still suffers low sensitivity at the expense of high specificity. Inspired by the simulation design introduced by metaanalysis of rth ordered pvalue (rOP) [41], we also designed simulation schemes such that only a few studies provide major signals that differentiate binary outcomes like real data. To this end, we replaced signal genes of one or two studies with complete random noise (i.e., sampled from N(0,R); no signal genes). This leads to only one or two signal genes, respectively, among three data sets. Under this simulation scenario, the MetaSVM still performs better as in Table 1, presenting higher Youden index than the metalogistic model no matter how many random noises are imposed.
Applications to real genomic data
In this section, we apply the MetaSVM methods to two real examples of idiopathic pulmonary fibrosis expression profiles (IPF; 221 samples in four studies of binary outcome (i.e., case and control)) and breast cancer expression profiles provided by The Cancer Genome Atlas (TCGA) including mRNA, copy number variation (CNV) and epigenetic DNA methylation (http://cancergenome.nih.gov/; 300 samples of estrogen receptor binary outcome (i.e., ER+ and ER)). It should be noticed that we integrate in the first application (IPF) four homogeneous studies in a fashion of horizontal integration, whereas we align in the second application (breast cancer) three genomic data by the common cohort in the context of vertical integration. Integrating multilevelomics data is reasonable, in that interregulation flows in systems biology are present from CNV to mRNA and from DNA methylation to mRNA [16]. Therefore, these interomics features aligned on identical protein coding regions can be jointly estimated in the group lasso. Table 2 outlines the data descriptions, for a total of seven data sets and source references. In the preprocessing stage, genes and DNA methylation probes were matched across homogeneous studies and multiomics data, and centered with scaling. Nonexpressed and/or noninformative genes were filtered according to the rank sum of mean intensities and variances across studies. Importantly noted is that this filtering procedure has been used in a previous metaanalysis work [47] and this filtering step is unbiased since class labels are not involved in the process. This generated 110 common genes in IPF study and 108 common genes and matched methylation probes in TCGA for downstream prediction analysis.
We applied gene set enrichment analysis to TCGA breast cancer data to figure out if our identified gene sets are in line with underlying biological pathways from the KEGG database [12]. It is notable that the identified gene set of the TCGA multiple omics data in Table 3 is significantly enriched in the ABC transporters pathways, which is already wellknown to be correlated to breast cancer mechanisms, particularly related to estrogen receptor and drug resistance [8,28]. To our surprise, the ABC transporters pathway is considerably relevant to breast cancer mechanisms in many ways. For instance, breast cancer resistance protein (BCRP) is an ATPbinding cassette (ABC) transporter known as a molecular cause of multidrug resistance (MDR) in diverse cancer cells [46]. Besides Nakanishi et al. [28] discovered that upregulation of BCRP mRNA expression was shown in estrogen receptor (ER)positive breast cancer. This identified pathway has been consistently verified as critical for cancer outcomes and sensitivity to therapeutic treatments [8,19]. In previous study under the similar design [10], ABCC8 and ABCC11 in Table 3 are believed to be modifiers of progression and response to the chemotherapy of breast cancer.
Generally idiopathic pulmonary fibrosis (IPF) is one of fatal lung diseases with a poor prognosis. Thus, it is quite imperative to monitor potential predictors of outcome. The original studies in Table 2 [17,32] posed a hypothesis on molecular biomarkers associated with IPF, and presented differentially expressed (DE) genes that distinguish IPF and control patients. For instance, Konishi et al. [17] identified in qRTPCR microarray experiments MMP7, AGER and MMP7 are significantly higher and AGER is significantly lower in IPF. Pardo et al. [32] also pointed out that MMP7 is more significantly overexpressed compared with control lungs. Note that MetaSVM is shown to be consistent with known evidence as detecting AGER and MMP7. Our findings in Table 3 also include CCL18. Importantly, it has been repeatedly reported that expression of CCL18 relates to course of pulmonary function parameters in patients with pulmonary fibrosis [33,34]. However, there was a little discrepancy regarding the roles of CCL18 according to the previous studies [31,33]. And yet, since the MetaSVM incorporates multiple data together, we can still give more credence to CCL18 as a molecular biomarker to predict IPF.
Of the 33 identified genes of IPF data (See Table 3 and Additional file 1: Table S1), we further reduce the number of genes for posthoc analysis by exploring significant gene modules, equivalently genegene interaction, via Netbox [6]. NetBox is an analytic software wellsuited to detect connecting genes to a network, identifying statistically significant “linker” genes on the basis of four public data sources: NCINature Pathway Interaction Database [40], Human Protein Reference Database [13], MSKCC Cancer Cell Map (http://www.mskcc.org/), and Reactome [11]. We implemented genegene interaction analysis, and successfully detected four gene modules, each of which constitutes mutually correlated genes. Additional file 1: Figure S1 displays the structure of combined networks based on four distinct gene modules. Focusing on the genes that belong to the four modules, we examine on MMP7 [32,44,50], LTBP1 [20], FHL2 [1], CXCL2 [42], THY1 [39] and AGER [17] to confirm whether or not these are associated with IPF (See Additional file 1: Table S3). MMP7 is traditionally thought of as the predictive signature since MMP7 of IPF patients is among the molecules that are more significantly overexpressed compared with control lungs [32]. More interestingly, Bauer et al. [1] identified a novel set of 12 diseaserelevant translational gene markers including FHL2, MMP7 that are able to separate almost all patients with IPF from control subjects in multiple largescale cohorts. Related to CXCL2, [42] investigated the pathogenesis of pulmonary fibrosis relevant to the imbalance in the expression of these angiogenic and angiostatic CXC chemokines. This study demonstrates in the bleomycin model that the amount of CXCL2 is found positively correlated with measures of fibrosis. When it comes to novel therapeutic targets, profiling DNA methylation changes to fibrosis has been increasingly spotlighted by observing hypomethylation of oncogene promoters. In doing so, Sanders et al. [39] reported that hypermethylation epigenetically decreases THY1 (See Additional file 1: Table S3) in IPF fibroblasts as IPF suppressor genes. Taken together, the MetaSVM is found to be efficient in identifying potential biomarkers that facilitate elucidating the disease process.
Concluding remark
In this article, we introduce a metaanalytic framework using the support vector machine. The objective function of MetaSVM applies the hinge loss and the sparse group lasso, and so we also develop a novel strategy for implementing the sparse group lasso in the context of Newton’s method. More importantly, the proposed MetaSVM shows many advantages in discovering the underlying true signals and in detecting gene sets enriched for cancer disease process validated as biologically significant. Putting all things together, we conclude that the proposed metaSVM is a reasonable choice to effectively achieve the common aims of metaanalysis. This is not that surprising given that the MetaSVM takes advantages of the metaanalytic design that jointly leverages multiple omics data. For future study, we may improve computational speed via lowlevel programming languages (e.g., C/C++ or Fortran) since coordinate descent algorithm sometimes leads to heavy computation due to slow convergence at the exchange of the straightforward algorithm structure. Usage of diverse kernels (e.g., quadratic and radial basis kernels) can be a possible choice to improve performance of feature discovery, and prediction accuracy. Moreover, it is worthwhile to impose interaction terms in the model, making it possible to account for the complex association among genomic features. We leave these ideas for future tasks.
Appendix
Optimization of a penalized univariate quadratic function
Univariate Lasso problem
Consider a quadratic function q defined as
where b>0 and \(c, d \in \mathbb {R}\). Let q ^{λ} be a penalized quadratic function given as
and denote
Note that \( b = q''(z) \quad \forall z \in \mathbb {R} \) and \(c = \text {argmin}_{z \in \mathbb {R}}q(z)\) since c is the solution to q ^{′}(z)=0.
Theorem 1
The minimizer z ^{λ} of q ^{λ} is given by
where the softthresholding operator is defined by
for \(y \in \mathbb {R}\) and λ>0.
Univariate Sparse group lasso problem
Let
where b>0, d≥0 and \(c \in \mathbb {R}\). If d=0, then the univariate sparse group lasso problem becomes the univariate lasso problem. Equivalently,
and we have
Consider the univariate sparse group lasso problem with d>0. Let F _{ s }(z) be the form of the cdf of the logistic distribution with a scale parameter s>0, which is given by
An approximation to \(q^{\lambda _{1}, \lambda _2}\phantom {\dot {i}\!}\) is
When s is sufficiently small, \(\tilde z^{\lambda _{1}, \lambda _{2}}= \text {argmin}_{z \in \mathbb {R}} \tilde q^{\lambda _{1}, \lambda _2}(z)\) is close to
Using the NewtonRaphson method, we can find \( \tilde z^{\lambda _{1}, \lambda _2} \). Note
and
where
Starting from an initial value z ^{(0)}, we iterate
Implementation for the metaanalytic SVM
In order to estimate the solution of β ^{(m)}, we approximate (3) to the univariate quadratic function, and then apply the NewtonRaphson method. To derive the quadratic form, we revisit the successive quadratics algorithm [48]. For each 1≤i≤n ^{(m)} and 1≤m≤M, we have \(\big (y^{(m)}_{i} \big)^2=1\) and
Assume \(\beta ^{(m)^{*}}\) is given, we consider the local quadratic approximation for the second term in (7):
where β ^{(m)∗} is an estimated coefficient vector at the current point. The quadratic form approximated to the entire objective function (3).
Given \(\tilde \beta ^{(m)} = \left (\tilde \beta _{0}^{(m)}, \ldots, \tilde \beta _{p}^{(m)}\right) \in \mathbb {R}^{p+1}\), the function \(\tilde {Q}^{\lambda _{1},\lambda _2}\left (\tilde \beta _{0}^{(m)}, \ldots, \tilde \beta _{j1}^{(m)},\right.\) \(\left.\beta _{j}^{(m)}, \tilde \beta _{j+1}^{(m)}, \ldots, \tilde \beta _{p}^{(m)}\right)\) is an univariate sparse group quadratic function of the form (6) with argument \(z = \beta _{j}^{(m)}\) with suitable b,c,d. We update \(\beta _{j}^{(m)}\) by the minimizer of \(\tilde {Q}^{\lambda _{1},\lambda _2}\left (\tilde \beta _{0}^{(m)}, \ldots, \tilde \beta _{j1}^{(m)}, \beta _{j}^{(m)}, \tilde \beta _{j+1}^{(m)}, \ldots, \tilde \beta _{p}^{(m)}\right)\) for 0≤j≤p and 1≤m≤M. Let
and
where
Observe
and
Combining these, we obtain
The gradient and the Hessian matrix of \(\tilde {Q}^{\lambda _{1}, \lambda _2}\) are, respectively, given as
and
where
\(d_{j} = \sum _{k \neq j} \beta _{k}^{(m)^{2}}\) and a sufficiently small positive constant ε for 1≤j≤p. We propose the following algorithm to solve the metaanalytic SVM via Newton’s method in a fashion of coordinate descent algorithm:
References
 1
Bauer Y, Tedrow J, de Bernard S, BirkerRobaczewska M, Gibson K, et al.A novel genomic signature with translational significance for human idiopathic pulmonary fibrosis. Am J Respir Cell Mol Biol. 2015; 52(2):217–31.
 2
Begum F, Ghosh D, Tseng G, Feingold E. Comprehensive literature review and statistical considerations for gwas metaanalysis. 2012; 40(9):3777–84.
 3
BenHur A, Ong C, Sonnenburg S, Schölkopf B, Rätsch G. Support vector machines and kernels for computational biology. PLoS Comput Biol. 2008; 4(10):000173.
 4
Bhattacharya S, Mariani T. Array of hope: expression profiling identifies disease biomarkers and mechanism. Biochem Soc Trans. 2009; 37(4):855–62.
 5
Brown M, Grundy W, Lin D, Christianini N, Sugnet C, et al.Support vector machine classification of microarray gene expression data. TechnicalReport University of California, Santa Cruz. 1999.
 6
Cerami E, Demir E, Schultz N, Taylor B, Sander C. Automated network analysis identifies core pathways in glioblastoma. PLoS ONE. 2010; 12:e8918.
 7
ElHefnawi M, Soliman B, AbuShahba N, Amer M. An Integrative Metaanalysis of MicroRNAs in Hepatocellular Carcinoma. Genomics Proteomics Bioinformatics. 2013; 11(6):354–67.
 8
Fletcher J, Haber M, Henderson M, Norris M. ABC transporters in cancer: more than just drug efflux pumps. Nat Rev. 2010; 10(2):147–56.
 9
Guyon I, Weston J, Barnhill S. Gene selection for cancer classification using support vector machines. Mach Learn. 2002; 46:389–422.
 10
Hlavac V, Brynychova V, Vaclavikova R, Ehrlichova M, Vrana D, et al. The expression profile of ATPbinding cassette transporter genes in breast carcinoma. Pharmacogenomics. 2013; 14(5):515–29.
 11
JoshiTope G, Gillespie M, Vastrik I, D’Eustachio P, Schmidt E, et al.Reactome: A knowledgebase of biological pathways. Nucleic Acids Res. 2005; 33:428–32.
 12
Kanehisa M, Goto S. Kyoto Encyclopedia of Genes and Genomes (KEGG). Nucleic Acids Res. 2000; 28:27–30.
 13
Keshava T, Goel R, Kandasamy K, Keerthikumar S, Kuar S, et al.Human protein reference database2009 update. Nucleic Acids Res. 2009; 37(Database issue):767–72.
 14
Kim S. MetaKTSP: a metaanalytic top scoring pair method for robust crossstudy validation of omics prediction analysis. Bioinformatics. 2016; 32(13):1966–73.
 15
Kim S. Weighted Kmeans support vector machine for cancer prediction. Springerplus. 2016; 5(1):1162.
 16
Kim S, Oesterreich S, Kim S, Park Y, Tseng G. Integrative clustering of multilevel omics data for disease subtype discovery using sequential double regularization. Biostatistics. 2016. doi:10.1093/biostatistics/kxw039
 17
Konishi K, Gibson K, Lindell K, Richards T, Zhang Y, et al. Gene expression profiles of acute exacerbations of idiopathic pulmonary fibrosis. Am J Respir Crit Care Med. 2009; 180(2):167–75.
 18
Kwon MS, Kim Y, Lee S, Namkung J, Yun T, et al.Integrative analysis of multiomics data for identifying multimarkers for diagnosing pancreatic cancer. BMC Genomics. 2015; 16(Suppl 9):S4.
 19
Leonard G, Fojo T, Bates S. The Role of ABC Transporters in Clinical Practice. The Oncologist. 2003; 8:411–24.
 20
Lepparanta O, Sens C, Salmenkivi K, Kinnula V, KeskiOja J, et al.Regulation of TGFbeta storage and activation in the human idiopathic pulmonary fibrosis lung. Cell Tissue Res. 2012; 3:491–503.
 21
Li J, Tseng G. An adaptively weighted statistic for detecting differential gene expression when combining multiple transcriptomic studies. Ann Appl Stat. 2011; 5(2A):994–1019.
 22
Li Q, Wang S, Huang C, Yu M, Shao J. Metaanalysis based variable selection for gene expression data. Biometrics. 2014; 70:872–80.
 23
Ma X, Wang Z, Ryan P, Isakoff S, Barmettler A, et al.A twogene expression ratio predicts clinical outcome in breast cancer patients treated with tamoxifen. Cancer Cell. 2004; 5:607–16.
 24
Ma S, Sung J, Magis A, Wang Y, Geman D, et al.Measuring the effect of interstudy variability on estimating prediction error. PLoS ONE. 2014; 9(10):110840.
 25
Madhavan S, Gusev Y, Natarajan T, Song L, Bhuvaneshwar K, et al.Genomewide multiomics profiling of colorectal cancer identifies immune determinants strongly associated with relapse. Front Genet. 2013; 4:236.
 26
MAQC Consortium. The microarray quality control (maqc) project shows inter and intraplatform reproducibility of gene expression measurements. Nat Biotechnol. 2006; 24(9):1151–61.
 27
Marchionni L, Afsari B, Geman D, Leek J. A simple and reproducible breast cancer prognostic test. BioMed Central Genomics. 2013; 14:336.
 28
Nakanishi T, Ross D. Breast cancer resistance protein (BCRP/ABCG2): its role in multidrug resistance and regulation of its gene expression. Chin J Cancer. 2012; 31(2):73–99.
 29
Noble W. Support vector machine applications in computational biology, Kernel Methods in Computational Biology. Cambridge: MIT Press; 2004, pp. 71–92.
 30
Paik S, Shak S, Tang G, Kim C, Baker J, et al.A multigene assay to predict recurrence of tamoxifentreated, nodenegative breast cancer. N Engl J Med. 2004; 351(27):2817–26.
 31
Pardo A, Smith K, Abrams J, Coffman R, Bustos M, et al.CCL18/DCCK1/PARC upregulation in hypersensitivity pneumonitis. J Leukoc Biol. 2004; 70:610–6.
 32
Pardo A, Selman M. Role of matrix metaloproteases in idiopathic pulmonary fibrosis. Fibrogenesis Tissue Repair. 2012; 5(Suppl 1):S9.
 33
Prasse A, Pechkovsky D, Toews G, Jungraithmayr W, Kollert F, et al.A vicious circle of alveolar macrophages and fibroblasts perpetuates pulmonary fibrosis via CCL18. Am J Respir Crit Care Med. 2006; 173:781–92.
 34
Prasse A, Pechkovsky D, Toews G, Schafer M, Eggeling S, et al.CCL18 as an indicator of pulmonary fibrotic activity in idiopathic interstitial pneumonias and systemic sclerosis. Arthristis & Rheumatism. 2007; 56(5):1685–93.
 35
Rajamani D, Bhasin M. Identification of key regulators of pancreatic cancer progression through multidimensional systemslevel analysis. Genome Med. 2016; 8:38.
 36
Ramaswamy S, Tamayo P, Rifkin R, Mukherjee S, Yeang C, et al.Multiclass cancer diagnosis using tumor gene expression signatures. Proc Natl Acad Sci. 2001; 98(26):15149–54.
 37
Rhodes D, Barrette T, Rubin M, Ghosh D, Chinnaiyan A. Metaanalysis of microarrays: Interstudy validation of gene expression profiles reveals pathway dysregulation in prostate cancer. Cancer Res. 2002; 62:4427–33.
 38
Richardson S, Tseng G, Sun W. Statistical methods in integrative genomics. Annu Rev Stat Its Appl. 2016; 3(1):181–209.
 39
Sanders Y, Ambalavanan N, Halloran B, Zhang X, Liu H, et al.Altered DNA Methylation Profile in Idiopathic Pulmonary. Fibrosis Am J Respir Crit Care Med. 2012; 186(6):525–35.
 40
Schaefer C, Anthony K, Krupa S, Buchoff J, Day M, Hannay T, Buetow K. PID: The pathway interaction database. Nucleic Acids Res. 2009; 37(Database issue):674–9.
 41
Song C, Tseng G. Hypothesis setting and order statistic for robust genomic metaanalysis. Ann Appl Stat. 2014; 8(2):777–800.
 42
Strieter R, Gomperts B, Keane M. The role of CXC chemokines in pulmonary fibrosis. J Clin Invest. 2007; 117(3):549–56.
 43
Veer L, Dai H, Vijver M, He Y, Hart A, et al.Gene expression profilng predicts clinical outcome of breast cance. Nature. 2002; 415:530–6.
 44
Vij R, Noth I. Peripheral Blood Biomarkers in Idiopathic Pulmonary Fibrosis. Transl Res. 2012; 159(4):218–27.
 45
Vijver M, He Y, Veer L, Dai H, Hart A, et al.A geneexpression signature as a predictor of survival in breast cancer. N Engl J Med. 2002; 347(25):1999–2009.
 46
Wang H, Zhou L, Gupta A, Vethanayagam R, Zhang Y, et al.Regulation of BCRP/ABCG2 expression by progesterone and betaestradiol in human placental BeWo cells. Am J Physiol Endocrinol Metab. 2006; 290(5):E798–807.
 47
Wang X, Lin Y, Song C, Sibille E, Tseng G. Detecting diseaseassociated genes with confounding variable adjustment and the impact on genomic metaanalysis: With application to major depressive disorder. BioMed Central Bioinformatics. 2012; 13:52.
 48
Zhang H, Ahn J, Lin X, Park C. Gene selection using support vector machines with nonconvex penalty. Bioinformatics. 2006; 22(1):88–95.
 49
Zhang Y, Schnabel C, Schroeder B, Jerevall P, Jankowitz R, et al.Breast cancer index identifies earlystage estrogen receptor–positive breast cancer patients at risk for early and latedistant recurrence. Clin Cancer Res. 2013; 19(15):4196–205.
 50
Zuo F, Kaminski N, Eugui E, Allard J, Yakhini Z, et al.Gene expression analysis reveals matrilysin as a key regulator of pulmonary fibrosis in mice and humans. Proc Natl Acad Sci. 2002; 99(9):6292–7.
Acknowledgements
The authors would like to thank the AE and reviewers.
Funding
The authors are supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF2015R1D1A1A01057747 and 2016R1A6A3A01009142).
Availability of data and materials
All of data sets were publicly available at the GEO (http://www.ncbi.nlm.nih.gov/geo/;GSE47460, GSE10667 and GSE2052) and TCGA data portal (http://cancergenome.nih.gov; See Table 2 for details).
Authors’ contributions
SH and JY contributed to method development, study design, paper writing, implementing codes and interpretations. JJ and JH contributed to data preparation and paper writing. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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Not applicable.
Ethics approval and consent to participate
The results of the pancancer and interstitial pulmonary fibrosis (IPF) were based on microarray data downloaded from TCGA Research Network and Gene Expression Omnibus (GEO), which precluded the need for Institutional Review Board (IRB) approval and written informed consents.
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Additional information
An erratum to this article is available at http://dx.doi.org/10.1186/s1304001701286.
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Additional file 1
Table S1. The MetaSVM’s coefficient of lung disease mRNA data. Table S2. The MetaSVM’s coefficient of TCGA breast cancer multilevel omics data. Table S3. Genegene interaction analysis using 33 identified genes of IPF mRNA data. Figure S1. Gene networks that display the relationships among significant genes. The orange nodes are the selected linker genes out of 33 genes in Table 3. The blue nodes indicate linker genes not presented in the original input list, but are significantly connected to members of the input list. (DOCX 187 kb)
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Kim, S., Jhong, JH., Lee, J. et al. Metaanalytic support vector machine for integrating multiple omics data. BioData Mining 10, 2 (2017). https://doi.org/10.1186/s1304001701268
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Keywords
 Support vector machine
 Metaanalysis
 Data integration
 TCGA