Skip to main content

A novel meta-analysis based on data augmentation and elastic data shared lasso regularization for gene expression



Gene expression analysis can provide useful information for analyzing complex biological mechanisms. However, many reported findings are unrepeatable due to small sample sizes relative to a large number of genes and the low signal-to-noise ratios of most gene expression datasets.


Meta-analysis of multi-data sets is an efficient method for tackling the above problem. To improve the performance of meta-analysis, we propose a novel meta-analysis framework. It consists of two parts: (1) a novel data augmentation strategy. Various cross-platform normalization methods exist, which can preserve original biological information of gene expression datasets from different angles and add different “perturbations” to the dataset. Using such perturbation, we provide a feasible means for gene expression data augmentation; (2) elastic data shared lasso (DSL-\({{\varvec{L}}}_{\mathbf{2}}\)). The DSL-\({\mathbf{L}}_{\mathbf{2}}\) method spans the continuum between individual models for each dataset and one model for all datasets. It also overcomes the shortcomings of the data shared lasso method when dealing with highly correlated features. Comprehensive simulation experiment results show that the proposed method has high prediction and gene selection performance. We then apply the proposed method to non-small cell lung cancer (NSCLC) blood gene expression data in order to identify key tumor-related genes. The outcomes of our experiment indicate that the method could be used for identifying a set of robust disease-related gene signatures that may be used for NSCLC early diagnosis or prognosis or even targeting.


We propose a novel and effective meta-analysis method for biological research, extrapolating and integrating information from multiple gene expression datasets.


The wide application of modern high-throughput biomedical instruments has greatly accelerated the speed of data generation in the field of life sciences. For example, the Gene Expression Omnibus (GEO) of the National Center for Biotechnology Information (NCBI) has collected more than 3.4 million samples. How to accurately screen out the gene markers that are closely related to the diagnosis, treatment, and drug development of complex diseases from the gene expression data is one of the essential problems in genomic research [1,2,3,4,5].

There are three main problems in analyzing gene expression data by using biostatistics and machine learning methods. (1) Large p and small n. Gene expression data sets typically contain a large number of genes and a small number of samples [6]. A very few genes are closely related to the target disease, while others are irrelevant. In terms of machine learning, many unrelated genes can introduce noise and may lead to overfitting, further negatively influencing the performance of classifiers [7]; (2) Batch effect. Different gene expression data are generated with different processing structures and data platforms, and the expression values are returned with different numerical scales. Such phenomenon is often referred to as the batch effect [8]; (3) Low reproducibility. Because the signal-to-noise ratio in many gene expression datasets is usually low, the published gene biomarkers are rarely duplicated in other studies [9].

The meta-analysis of multiple gene datasets to improve the statistical performance of genome research is a promising solution to meet the above challenges [10]. The current gene-expression data meta-analysis can be divided into three types: (1) the first type of method performs analysis based on combining results from different studies. For example, p values [11], effect sizes [12, 13], or ranks [14]. These methods tend to gain more power in identifying differentially expressed (DE) genes. But such a method is trivial, and it is easy to lead to false results; (2) the second type of method usually applies a particular cross-platform normalization (CPN) method to remove the batch effect from multiple datasets, subsequently combining multiple datasets into one large data set. Then, the machine learning method can be used to realize the classification and gene selection of the combined dataset. Due to large datasets, such methods often achieve higher result statistical significance than the first type method [15]. However, due to the inherent complexity of biological data, existing CPN methods can only reduce the batch effect of data but can not completely eliminate it. Therefore directly analyzing the integrated data may raise some problems [15, 16]; (3) the third meta-analysis method establishes a unified model on multiple data sets on the basis of no data merging, which is a new research direction of meta-analysis. For example, meta threshold gradient descent regularization [17], meta-lasso [18], meta-nonconvex [19], and data share lasso (DSL) [20]. A discussion of the advantages and disadvantages of the above methods is presented in “Simulation” section. This paper highlights the DSL method because it is more formally concise and reasonable. The DSL method spans the continuum between individual models for each dataset and one model for all datasets. By applying the lasso penalty, the DSL method also achieves gene selection. However, the DSL method does not achieve the grouping effect (strongly correlated genes tend to be included in or omitted from the model altogether [21]) and therefore ignores correlations between the genes and cannot be used to analyze data with dependent structures. If there is a high correlation between a group of genes, the DSL method often only selects one gene representing the whole group. Because genes involved in the same biological pathway are usually highly correlated, group situation is very common in gene expression data [22].

Data augmentation (DA) refers to the appropriate “perturbation” of the original data in order to achieve data set expansion; this is based on certain prior knowledge, and it proceeds on the premise of maintaining specific information [23]. The winning prediction models described in [24,25,26] all use DA strategies to artificially increase the number of training examples. Previous research aimed at systematically understanding the benefits of increasing data shows that DA can act as a regulator to prevent overfitting and enhance the generalization ability of the model [27]. The validity of DA inspires us to consider applying augmentation to gene expression data. However, traditional DA methods, e.g., rotating or scaling, are inadequate for gene expression data because they are unable to yield sufficient biological explanations.

To improve the power of the meta-analysis, in this paper, we proposed a new meta-analysis framework (DA-DSL-\({\mathrm{L}}_{2}\), Fig. 1) based on a new DA strategy and elastic data shared lasso (DSL-\({\mathrm{L}}_{2}\)) method. It consists of two components: (1) a novel data augmentation (DA). Various CPN methods exist that can preserve original biological information of gene expression datasets from different angles and add different “perturbations” to the dataset. Using such perturbation, we can generate a multi-view representation of the datasets; this is a feasible means of gene expression data augmentation. (2) DSL-\({L}_{2}\). The DSL-\({\mathrm{L}}_{2}\) method overcomes the shortcomings of the DSL method when dealing with the presence of highly correlated features. We apply the DA-DSL-\({\mathrm{L}}_{2}\) method to a logistic regression model to fulfill the final model. Then, we perform an analysis of non-small-cell lung cancer (NSCLC) blood-based gene expression data to help identify the gene signatures that can be used for the early diagnosis of NSCLC.

Fig. 1
figure 1

Overview of the proposed DA-DSL-L2 meta-analysis framework. Data1, …, DataM are merged by different cross-platform normalization (CPN) methods, respectively, to achieve data augmentation. We process these augmented data (or multi-views) using the elastic shared lasso method that considers both data homogeneity and heterogeneity to obtain better feature selection performance

Our experimental result shows that the proposed framework is an effective meta-analysis method, which can identify a group of robust genetic markers related to the disease.

The main contributions of the paper are as follows.

  1. (1)

    This study proposes a novel DA strategy that applies to gene expression data. The new strategy will help increase the size of training samples, increase the value density of biological data, improve the effectiveness of machine learning, and enhance the generalizability of molecular marker research.

  2. (2)

    A novel biomarker selection method DSL-\({\mathrm{L}}_{2}\) is proposed. The proposed method improves the performance of DSL methods when dealing with highly correlated data variables. In addition, we discuss the reasons why this method enhances the DSL method theoretically.

  3. (3)

    A refined meta-analysis framework DA-DSL-\({\mathrm{L}}_{2}\) for gene-expression value enhancement is proposed. In this framework, data augmentation of gene expression data, the shared biological information (homogeneity) and the unique effect (heterogeneity) across the multi-views (or multi-datasets), and the group effect for the genes are all well-considered.

  4. (4)

    Because the signal-to-noise ratio of blood gene expression is very low, finding useful information in blood data is difficult. We identified 59 genes in NSCLC blood gene expression data by using the proposed method. These 59 gene markers accurately distinguished lung cancer samples from normal samples. The 59 genes were further verified by literature analysis, pathway analysis, gene alteration analysis, survival prediction analysis, and association analysis. The selected genes could be used for peripheral blood testing for the early diagnosis of NSCLC.

The rest of this paper is organized as follows: We reviewed the related works in “Result” section. In “NSCLC data preparation and augmentation” section We describe our data augmentation strategy for the gene expression data, as well as the novel regularization DSL-\({\mathrm{L}}_{2}\) technique. In “NSCLC model training and performance” section we present a novel algorithm for the DSL-\({\mathrm{L}}_{2}\), and explain how DSL-\({\mathrm{L}}_{2}\) strengthening the DSL theoretically. In “Biological analysis for the selected genes from NSCLC” section we measure the performance of our proposed method through a comprehensive simulation analysis and real mRNA expression level data experiment. A brief discussion and conclusion are provided in “Discussion and conclusion” section.


To test the effectiveness of our proposed method, we conducted a comprehensive simulation test and an evaluation with two large lung cancer gene-expression datasets. The statistical model used here is the logistics regression model.


Four Scenarios are considered in the simulation. Each Scenario consists of three datasets, and each dataset consists of 100 samples with 1000 dimensions. We simulate data from the true model: \(y_{k}\) = [Prob (\(y_{k}\) = 1|\(X_{k}\); \(\beta\)) > 0.5].

In Scenario 1, we assume that the discrepancy among different datasets is small, which can be expressed as \(X_{k} \sim N(\sqrt k - 1,\sqrt k )\), \(k{ = }1,2,3.\)

The \(\beta\) values are simulated from

$$\beta = \left( {\underbrace {{3,3,3,3,3,}}_{5}\underbrace {{0, \ldots ,0}}_{995}} \right),$$

with a grouped variable situation \({x}_{i}=\rho \times {x}_{1}+\left(1-\rho \right)\times {x}_{i}\), i = 2, 3, 4, 5.

Scenario 2 is similar to Scenario 1, except that there are other independent factors also contributing to the corresponding classification variable \(\mathrm{y}\):

$$\beta = \left( {\underbrace {{3,3,3,3,3,2, - 2,2,2, - 2,}}_{10}\underbrace {{0, \ldots ,0}}_{990}} \right)$$

In Scenario 3, we consider that the discrepancy among different datasets is significant: \(X_{k} \sim N\left( {k - 1,\left( {\frac{k}{\sqrt k }} \right)^{2} } \right)\), \(k{ = }1,2,3.\)

$$\beta = \left( {\underbrace {{3,3,3,3,3,1.5,2, - 2,2,2, - 2,}}_{10}\underbrace {3, \ldots ,3,}_{20}\underbrace {{0, \ldots ,0}}_{970}} \right)$$

For which we define two grouped variables:

$$\begin{aligned}{x}_{i}&=\rho \times {x}_{1}+\left(1-\rho \right)\times {x}_{i},\quad\mathrm{ i}=2,3,4,5;\\ {x}_{i}&=\rho \times {x}_{11}+\left(1-\rho \right)\times {x}_{i},\quad \mathrm{ i}=12,\dots ,30; \end{aligned}$$

Scenario 4 is similar to Scenario 3, except that we consider a case where there are three grouped variables:

$$\beta = \left( {\begin{array}{*{20}c} {\underbrace {3, \ldots ,3,}_{30}\underbrace {{ - 2.5,2, - 1.5,1.8, - 2.5,}}_{5}\underbrace {{3, \ldots ,3,}}_{40}\underbrace {{2, \ldots ,2,}}_{25}} \\ {\underbrace {3, \ldots ,3,}_{30}\underbrace {2, \ldots ,2,}_{70}\underbrace {{0, \ldots ,0}}_{800}} \\ \end{array} } \right)$$

The three grouped variables are defined as follows:

$$\begin{aligned} {x}_{i}&=\rho \times {x}_{1}+\left(1-\rho \right)\times {x}_{i},\quad\mathrm{ i}=2,\dots ,30;\\ {x}_{i}&=\rho \times {x}_{36}+\left(1-\rho \right)\times {x}_{i},\quad\mathrm{ i}=37,\dots ,75; \\ {x}_{i}&=\rho \times {x}_{101}+\left(1-\rho \right)\times {x}_{i},\quad\mathrm{ i}=102,\dots ,130;\end{aligned}$$

In this case, there are three groups of correlated genes, and some non-correlated genes. A well-sparse regression approach identifies only the 200 true genes, while setting the coefficients of the other 800 noise genes to zero.

We use tenfold cross-validation (CV) on a multi-dimensions procedure and apply it to the training data in order to select the optimal tuning parameter(s) (which balances the tradeoff between data fit and model complexity). In a tenfold CV, the data is firstly divided into 10 equally (or nearly equally) sized folds (or segments); then, 10 iterations of training and validation are conducted. A different fold of the data is held out for validation in every iteration, while the remaining ninefolds are used for model-building. There are three parameters: \({\lambda }_{1}\), \({\lambda }_{2}\), and \({r}_{d}\). The \({r}_{d}\) parameter is set to \(\frac{1}{\sqrt{D}}\) as recommended by [20]. The (\({\lambda }_{1}\), \({\lambda }_{2}\)) gird that maximizes the cross-validation accuracy performance are chosen as the optimal parameters. The \({\lambda }_{1}\) sequence was generated for the X and Y values in such a way that the largest \({\lambda }_{1}\) value is just sufficient to produce all zero coefficients \(\beta\). \({\lambda }_{2}\) was chose from {0.001:0.01:5} (Start:Step-Size:End). Lasso and Elastic net were performed using the “glmnet” function (Matlab, version 2014b). The other methods were performed using our own Matlab codes. This simulated data experiment and the following real data experiments are calculated based on a personal computer with Ryzen 7 2700X and 64G RAM.

We set the correlation control variable \(\rho\) of genes to 0.3, 0.6, and 0.9, respectively. We ran the experiment 800 times for every method and reported the average 10-CV classification accuracy.

Gene selection is a crucial part of genomic analysis. In our study, the gene selection ability of each approach is measured using Youden’s index (YI). The YI integrates sensitivity and specificity information under situations that emphasize sensitivity and specificity, yielding a value ranging from 0 to 1. A higher YI implies better gene selection performance.

$${\text{YI}} = {\text{Sensitivity}} + {\text{Specificity}}{-}{1}.$$

where Sensitivity \(:=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}}\), Specificity := \(\frac{\mathrm{TN}}{\mathrm{TN}+\mathrm{FP}}\), True Negative (TN) \({:=\left|\overline{\beta }.*\overline{\widehat{\beta } }\right|}_{0}\), False Positive (FP) \({:=\left|\overline{\beta }.*\widehat{\beta }\right|}_{0}\), False Negative (FN) \({:=\left|\beta .*\overline{\widehat{\beta } }\right|}_{0}\) and True Positive (TP) \({:=\left|\beta .*\widehat{\beta }\right|}_{0}\). The \(.*\) is the element-wise product, and \({\left|.\right|}_{0}\) calculates the number of non-zero elements in a vector, \(\overline{\beta }\) and \(\overline{\widehat{\beta } }\) are the logical “not” operators on the vectors \(\beta\) and \(\widehat{\beta }\).

To accomplish DA, we use three classic cross-platform normalization methods (Z-score normalization, COMBAT, and XPN). For example, we use Z-score normalization to merge the three datasets (\(X_{1}\), \(X_{2}\) and \(X_{3}\)) to produce a view of the raw data. Similarly, COMBAT and XPN are used to generate other data views, respectively.

The competing methods can be divided into three groups: (1) Without considering homogeneity. The models training in a single dataset \(X_{1}\) or \(X_{2}\) or \(X_{3}\), respectively, include Lasso, Elastic, HLR (we report the average performance of these models for these three data sets). (2) Without considering heterogeneity. The three datasets are merged into a merged dataset [\(X_{1}\); \(X_{2}\); \(X_{3}\)] by COMBAT. Three models are directly trained on the merged data, including M-Lasso, M-Elastic, and M-HLR. (3) Without considering the grouping effect. Such as Meta-Lasso and DSL. Moreover, one classic integrative analysis method Sparse Group Lasso (SGL) [28] is also involved in the experiment.

Table 1 shows the average classification performance on 10-CV for all the methods for 800 runs. In summary, the DA-DSL-\({\mathrm{L}}_{2}\) method has certain advantages over the other methods regarding classification evaluations. For example, in Scenario 1 with \(\rho\) = 0.3, the mean accuracy attained with the DA-DSL-\({\mathrm{L}}_{2}\) method equals 84.19%, which was the best performance among the methods. In Scenario 3 with \(\rho\) = 0.6, the value achieved by the DA-DSL-\({\mathrm{L}}_{2}\) method equals 79.22%, which is 19.21%, 4.18%, 16.20%, 5.95%, 15.55%, 7.43%, 4.67%, 4.20%, and 3.87% higher than the mean accuracies of Lasso, M-Lasso, Elastic Net, M-Elastic Net, HLR, M-HLR, SGL, Meta-Lasso and DSL, respectively.

Table 1 Classification prediction results of the simulation

Table 2 demonstrates the average capability of the gene section by all the approaches for 800 repetitions. Overall, the DA-DSL-L2 method achieves the best gene selection performance in all cases. For example, in Scenario 3 with \(\rho\) = 0.3, the DA-DSL-L2 achieves the superior gene selection performance, with YI = 84.42%, which is 41.05%, 11.45%, 41.15%, 11.29%, 41.59%, 14.76%, 7.62%, 7.90%, and 5.68% higher than that of Lasso, M-Lasso, Elastic Net, M-Elastic Net, HLR, M-HLR, SGL, Meta-Lasso and DSL, respectively. These outcomes imply that the DA-DSL-L2 method is able to identify fewer noise genes and more meaningful markers.

Table 2 Gene selection results of the simulation

The convergence of these methods is also measured. Take Scenario 2 as an example, with a correlation of 0.6 and platform MATLAB or R, it takes 0.08, 0.09, 0.07, 0.07, 4.98, 13.31, 12.29, 9.7, 0.1895, and 3.22 s for the Lasso, M-Lasso,Elastic net, M-Elastic net, HLR, M-HLR, SGL, Meta-Lasso, DSL and DA-DSL-L2 to converge to their solutions, respectively.

Blood-based gene expression signatures in non–small cell lung cancer

Lung cancer remains the main cause of cancer-related deaths around the world. Global average prognosis remains poor, with a 5-year survival rate of about 15% due to late diagnosis of cancer in incorrigible stages in the majority of patients, a source of frustration in therapeutic regimens for advanced disease. It is urgent to establish a more reliable tool for the detection of Non–Small Cell Lung Cancer (NSCLC) in the early stages of the disease before the onset of symptoms.

NSCLC data preparation and augmentation

To our best knowledge, there are two large (sample size > 150) peripheral whole blood NSCLC gene expression datasets (Table 3). These two datasets are generated from two different platforms, which means that both homogeneity and heterogeneity exist. In this section, we use the proposed method to identify the blood-based gene expression characteristics that can be used for the early diagnosis of NSCLC.

Table 3 Briefing of the NSCLC datasets

Each probe set was mapped to an official gene symbol, and for multiple probe sets corresponding to the same gene, we averaged these probe sets to represent the gene. We took the subset of genes common to all datasets. In all, 11,959 genes were reserved.

We randomly select two-thirds of the samples in GSE12771 and GSE20189 for model training. The remaining third of samples in GSE12771 and GSE20189 are used for model testing runs “test set-1” and “test set-2”.

We use three classic cross-platform normalization methods (Z-score normalization, COMBAT, and XPN) to accomplish data augmentation. For example, we use Z-score normalization to merge two training sets (two-thirds of samples in GSE12771 and GSE20189) to produce a view of the raw data. Similarly, COMBAT and XPN are used to generate other data views, respectively. The final training set consists of 846 samples, including 435 NSCLCs and 411 healthy controls; test set-1 consists of 73 samples, including 31 NSCLCs and 42 healthy controls; test set-2 consists of 49 samples, including 23 NSCLCs and 26 healthy controls.

NSCLC model training and performance

Six strategies are compared with our proposed method: Lasso, Elastic net, HLR, SGL, Meta-Lasso, and DSL.

The tuning regularization parameters of the DA-DSL-\({\mathrm{L}}_{2}\) were tuned by using 5-CV on multi-dimensions in the training dataset. A final classifier has been trained with the determining tuning parameters by using all the training data. The model’s cut-off point is calculated as the point that yields the highest YI value.

As shown in Table 4, the DA-DSL-\({\mathrm{L}}_{2}\) method outperforms all the competitors in terms of training accuracy, with a training error of only 2.23%. By comparison, lasso achieved a 5.09% training error, almost 2.3 times higher than that of our proposed method. Moreover, the DA-DSL-\({\mathrm{L}}_{2}\) method also better than the DSL method (a method that does without achieving grouping effect), which implies that the \({\mathrm{L}}_{2}\) norm technique functions well in gene expression data. The same observation can be seen in the test set-1 and test set-2 results, showing that the proposed method achieves the best classification performance and better efficiency. The test scores predicted by DA-DSL-\({\mathrm{L}}_{2}\) method to be an NSCLC patient for cases compared with healthy controls is significant (P < 0.01, t-test).

Table 4 Discrimination results from all methods

Although the DA-DSL-\({\mathrm{L}}_{2}\) method takes a long time among all the techniques. It is superior in terms of feature selection and classification quality.

Biological analysis for the selected genes from NSCLC

We provide results for the 10 highest-ranked genes identified by all the strategies in Table 5. As explained in the simulation section above, the proposed method exhibits good performance in identifying the critical gene. Thus, we can argue that the genes identified by the DA-DSL-\({\mathrm{L}}_{2}\) method in cancer datasets can help medics attending to cancer patients to deduce the true biomarkers associated with cancer development. For example, EGR1 is linked to cancer suppression due to cell cycle arrest and apoptosis by regulation of cancer suppressor pathways. Patients with low EGR1 expression may be at high risk of disease recurrence, and may have tumors that are resistant to therapy [31]. A recent study reported CD74 gene fusions in patients with lung cancer harboring the kinase domain of the NTRK1 gene that encodes the TRKA receptor. CD74-NTRK1 fusions result in constitutive TRKA kinase development and are oncogenic. Therapy of cells expressing NTRK1 fusions with inhibitors of TRKA kinase activity can restrain autophosphorylation of TRKA and cell growth [32]. The imbalance between VWF secretion and ADAMTS-13 may play an important role in the hypercoagulability form in advanced NSCLC. Nevertheless, the plasma VWF/ADAMTS-13 ratio elevation may serve as the key predictive factor behind mortality in patients with advanced NSCLC [33]. In addition, SIAH proteins play a critical role in many important biological processes. For example, SIAH2 protein expression is significantly enhanced in human lung cancer and may serve as a novel target for lung cancer therapy [34].

Table 5 The highest-ranked selected 10 genes were found by the sparse logistic regression methods from the lung cancer dataset

To further validate the selected genes using the proposed method, we perform alterations and pathways analysis using cBioPortal [31] with the NSCLC TCGA dataset and Reactome [35]. It was found that 59 genes were altered in 865 out of 1229 patients with NCSLC (70%). The results of the 10 highest-ranked gene alterations are illustrated in Fig. 2: it can be seen that the maximum alteration gene is PIK3CA (24% alteration in all patients). ACAP2 and CANNA1R alterations were detected in 17% of patients. These results alone provide promising evidence of the therapeutic value of these genes.

Fig. 2
figure 2

The 10 highest-ranked gene alterations in the TCGA NSCLC cancer (provisional) dataset selected by DA-DSL-\({\mathrm{L}}_{2}\)

We also performed a Kaplan–Meier survival analysis (with the help of the kmplot web resource) for the 10 genes identified by DA-DSL-\({\mathrm{L}}_{2}\) on a union dataset for 1925 patients, the results of which are presented in Fig. 3. Overall, all the genes show a certain prognostic value, for example, MAPK4 (hazard ratio, 1.83; P = 4.4e−10), VT11B (hazard ratio, 1.8; P = 4.1e−09) and, NTRK1 (hazard ratio, 1.43; P = 0.0024). We further validated the 10 genes on the Bittner Lung dataset by Oncomine. As shown in Fig. 4, higher mRNA levels of ACAP2, ECHDC3, EGR1, and CD74 were highly associated with tumor development.

Fig. 3
figure 3

Survival prediction for the top 10 highest-ranked genes selected by DA-DSL-\({\mathrm{L}}_{2}\)

Fig. 4
figure 4

Association between the mRNA expression of ACAP2, ECHDC3, EGR1, and CD74 and tumor grade (grades 1–4) in the Bittner Lung dataset

We then performed a pathway analysis for the genes identified using DA-DSL-\({\mathrm{L}}_{2}\). Fifty-nine biomarkers are enriched in 153 distinct (with P < 0.05) pathways. We summarize the top 20 most significant pathways in Fig. 5.

Fig. 5
figure 5

The pathways analysis. Ratio enrichment indicates the functional significance of a gene module with − log(p value)

Of these significant pathways, some of them are platelet function-related. For example, RUNX1 regulates genes involved in megakaryocyte differentiation and platelet function, platelet degranulation, responses to elevated platelet cytosolic Ca2+, and in platelet activation, signaling, and aggregation. It is known that platelets contribute to tumor development via different mechanisms. Metastasis is the major cause of cancer-related death; however, metastasis is a highly inefficient process. Once they enter the bloodstream, cancer cells come into the vicinity of circulating cells and rapidly bind to platelets [36]. Moreover, platelets may help hide cancer from the immune system by inhibiting the function of T cells [37]. Therefore, blood platelets act as local and systemic responders during tumorigenesis and cancer metastasis, and could therefore serve as useful signature sources for the non-invasive detection of cancer [38]. One of the most significant pathways is the Immune-related pathway of Cytokine Signaling. The microenvironment of the primary tumor site mainly includes tumor-associated macrophages, tumor-associated fibroblasts, myeloid-derived suppressor cells, mast cells, etc. These cells secrete various cytokines and chemokines to promote tumor metastasis [39].

Combining the results from Figs. 2, 3, 4 and 5, the gene signatures selected by DA-DSL-\({\mathrm{L}}_{2}\) provide potential therapeutic markers and pathways in NSCLC.

Colorectal cancer study

Colorectal cancer (CRC) is one of the most common neoplastic diseases worldwide. With a high recurrence rate among all cancers, treatment of CRC only improved a little over the last two decades. Early diagnosis and prompt treatment can significantly reduce mortality and morbidity rates. Here data from three gene expression studies are collected and analyzed (Table 6).

Table 6 Briefing of the colorectal datasets

We primarily follow the data process in the NSCLC study section, such as (1) we took the subset of genes common to all datasets; (2) GSE110223 and GSE110224 are used for model training, and GSE113513 is used for model validation; (3) data augmentation by the three cross-platform normalization methods.

As shown in Table 7, the DA-DSL-\({\mathrm{L}}_{2}\) method outperforms all the competitors in terms of training accuracy, with a training error of only 1.15%. The same observation can be seen in the validation result, showing that the proposed method achieves the best classification performance and better efficiency.

Table 7 Discrimination results from all methods

With the DA-DSL-L2, fifty-one genes, including CCNA2, DLGAP5, RRM2, are identified in the CRC dataset. These selected genes may play an important role in CRC development. For example, the knockdown of CCNA2 could significantly suppress CRC cell growth by impairing cell cycle progression and inducing cell apoptosis [41]. Some articles showed that CCNA2 is a vital sign to judge the poor prognosis of the tumor, as it is also highly expressed in pancreatic cancer, breast cancer, lung cancer, and other tumors [42]. Clinical studies have shown that DLGAP5 was related to the invasion and migration of CRC [43]. The authors also suggested it is an important measure of poor prognosis. When it comes to the expression of RRM2, studies showed that it is related to the depth of invasion, degree of differentiation, disease-free survival, and metastasis of CRC [44].

To further validate the gene selected by DA-DSL-L2, we consider whether the performance improves if a nonlinear classifier such as decision trees is applied to the selected genes (Fig. 6). The result shows promise. The performances of 51 genes are better or equivalent to that of the whole gene set consisting of 12,394 genes.

Fig. 6
figure 6

Decision tree performance comparison between 51 genes selected by DA-DSL- L2 and a whole gene set consisting of 12,394 genes

Discussion and conclusion

Identifying critical disease-related gene biomarkers is one of the greatest challenges in genomics research. Due to cost considerations, most gene expression data sets in genomic research entail small n and large p, and there are problems with generalizing conclusions based on these data. Combining multiple experimental data sets in a meta-analysis is one effective way of solving this problem. This research has suggested a novel meta-analysis framework (DA-DSL-L2). In this framework, data augmentation of gene expression data, the shared biological information (homogeneity) and the unique effect (heterogeneity) across the multi-views (or multi-datasets), and the group effect for the genes are all well considered.

We have demonstrated a comprehensive simulated experiment. The simulation results of our proposed framework are promising in terms of prediction and gene selection. We have applied the proposed method to NSCLC blood gene expression data to identify key tumor-related genes. Finding knowledge in blood data is challenging because the signal-to-noise ratio in blood gene expression is very low. We generated a multi-view representation based on two large blood-based NSCLC datasets to increase the signal-to-noise ratio. The training sample size ranged up to n = 846. We used DSL-\({\mathrm{L}}_{2}\) method to process the data. Our results show that the proposed method achieves a superior classification performance (with only 59 gene signatures) compared with six state-of-the-art methods. Moreover, some of the 59 genes are highly coherent across an independent TCGA dataset. Nevertheless, the 59 genes were enriched over 150 significant pathways, some of which are strongly connected with tumor development. We also validated the proposed method on the CRC datasets. The results show that the suggested method outperforms all the competitors in training accuracy. The same observation can be seen in an external CRC validation dataset. In short, we offer a novel and effective meta-analysis strategy for gene expression study that helps turn raw data from multiple gene-expression datasets into knowledge for cancer diagnostics, prognostic and personalized treatment.

Although we focus on the meta-analysis of gene expression data in this paper, the proposed method can be useful for other data types. For example, the proposed data augmentation (DA) strategy in the framework provides a new idea for DA of other non-image data. The proposed feature selection approach (DSL-L2) can be directly applied to other data types.

We recommend merging three methods—Z-score, COMBAT, and XPN—for DA. However, this combination might not always be necessary. Some novel merge methods can also be considered, such as scBatch [8]. A more comprehensive examination of the combination with other merge methods will be studied in future research. Other techniques can handle the grouping effect, i.e., the network penalty [45,46,47,48,49]. Future directions may also include incorporating an external gene regulatory network to deal with the grouping effect. As described in the algorithm section, we transform the DSL-\({\mathrm{L}}_{2}\) method to a standard Lasso problem. Even though the Lasso problem can be solved by some very efficient method, i.e., glmnet, to solve a big matrix such as a matrix size of over 40,000 * 40,000 in this paper, this is still a computationally heavy and memory expensive procedure. We, therefore, aim to develop a more efficient algorithm for the DA-DSL-\({\mathrm{L}}_{2}\) method in future research. Another weakness of this study is the lack of detailed analysis of the identified genes or pathways.



The analysis of data on high-dimensional gene expression is a useful tool for analyzing complex biological mechanisms [3, 4]. However, many reported results are not reproducible or generalized because of the small sample size for a large number of genes and because the signal-to-noise ratio in many gene expression datasets is usually low [9, 50].

There are many publicly available large gene expression studies concerning meta-analysis, a method of combining multiple datasets or other relevant information to improve the statistical power. The current gene-expression data meta-analysis can be divided into three groups: the first group of the method is to perform analysis based on combining results from different studies. For example, For example, p value [11], effect size [13], rank [14], adaptively Fisher’s method [51]. For an extensive review of these methods, see [15]. However, such methods ignore the correlations between genes. Hughey and Butte [52] proposed a meta-analysis method to resolve this problem based on the elastic net technique. In Hughey and Butte study, a CPN method is required to remove the batch effect amongst the mutil-datasets. However, due to the inherent complexity of biological data, existing CPN methods can only reduce but not completely eliminate the batch effect of data. Thus, directly analyzing the integrated data may cause issues [16]. Without the procedure of CPN, Ma et al. [17] proposed a meta threshold gradient descent regularization method. By considering the joint modeling of multiple genes, the proposed method can account for the joint effects of genes on clinical outcomes. However, such a method performs gene selection in an “all-in-or-all-out” scene; that is, the method considers the important or unimportant genes in all datasets. Data heterogeneity in meta-analyzed data is common, due to the different experiment conditions, process flows, choices of biospecimens, and platforms. Therefore, if a gene is important in one dataset, it may be unimportant in other datasets.

Li et al. [18] proposed the Meta-lasso method to account for data heterogeneity. Through hierarchical decomposition into regression coefficients, this method can not only lend the power of multiple data sets to increase the power of identifying important genes, but also maintain the flexibility of choice between data sets to consider the heterogeneity of data sets. With a similar idea, Zhang et al. [19] proposed Meta-nonconvex to perform meta-analysis based on nonconvex penalties such as SCAD and MCP. However, Meta-lasso or Meta-nonconvex suffers an “all-out” scene; ignoring variables may be significant on some data sets. Gross [20] proposed the DSL technique. This method spans the continuum between individual models for each dataset and one model for all datasets. By applying the lasso penalty, the DSL method also achieves gene selection. However, the DSL method fails to produce a grouping effect and therefore ignores correlations between genes. When dealing with data that contain group structure and when the genes within the group are highly correlated, the DSL method can only select one gene to represent the entire group structure. In genetic research, genes usually co-express biological functions in the form of pathways (or groups). Some works were suggested to resolve the issue of the highly correlated genes. For example, the elastic net [21], an integration of lasso and ridge (or L2 penalty) method, by the L2 penalty in the model, grouping effect can be achieved. Based on the same idea, scholars have successively proposed Elastic SCAD [53], SCAD-\({\mathrm{L}}_{2}\) [54] and HLR [55, 56].

Data augmentation

DA is widely applied by computer vision researchers. Models trained through DA are generally more robust and less overfitting [57, 58]. DA requires appropriate “perturbation” of the original data in order to achieve data set expansion; this is based on certain prior knowledge, and it proceeds on the premise of maintaining specific information [23]. The effectiveness of DA has inspired us to consider applying the data augmentation technique to gene expression data. However, traditional DA methods, e.g., rotating or scaling, are not suitable for gene expression data as they do not yield sufficient biological explanations.

CPN is an important procedure for some gene expression meta-analyses. Such an approach removes differences (or batch effect) between different gene expression datasets while preserving biological information within the data. There are extensive efforts in CPN method development. For example, Z-score normalization [59], is perhaps the simplest way of achieving CPN. More advanced methods have been devised, including Distance-weighted discrimination (DWD) [60]. Each source subset is shifted in the DWD direction, by an appropriate amount, through the subtraction of the DWD direction vector multiplied by each projected mean for each gene. Empirical Bayes (or COMBAT) [61] is a Bayes empirical framework for “borrowing information” across genes and experimental conditions, in the hope that the borrowed information will lead to better estimates or more stable conclusions. XPN [62] is a technique involving search blocks of the gene in multiple datasets with non-heterogeneous genes. PLIDA [63], a method that uses topic models to combine the expression patterns in every dataset before standardizing the topics learned with each data set using per-gene multiplication weights. The WaveICA [64] method uses the time trend of the samples in order of injection, breaks down the original data into multi-scale data with different features, extracts and eliminates the effect batch on the multi-scale data, and obtains clean data. Each CPN method preserves the original biological information of the original dataset from different angles and adds different “perturbations” to the dataset. Using such perturbation, we can generate a multi-view representation of the dataset; this is feasible for gene expression data augmentation.

Data augmentation of the gene expression data

When performing integrative analysis for multiple-gene expression datasets, the batch effect amongst the data usually needs to be eliminated. There exist several proposed methods for removing the batch effect, including DWD [60], disTran [65], Median Rank Score (MRS) [66], Empirical Bayes (ComBat) [61], XPN [62], PLIDA [63], and WaveICA [64]. These CPN methods involve merging data from different aspects and generating different system perturbations. The idea of perturbations is pivotal to DA. In this paper, we propose merging datasets via different merging methods to generate multiple views of the original data. In other words, the gene expression data are augmented via different CPN methods. For example, if there are two datasets with 20 and 30 samples, respectively. We can generate three views of the original data by three CPN methods. The data volume will increase from 50 to 50 * 3 = 150.

Elastic data shared lasso regularization

The original purpose of the DSL was to address problems arising from observations belonging to non-overlapping, pre-specified groups. In this paper, we extend the DSL method to meta-analysis. More formally, we assume we have n observations of the form \(({\varvec{x}}_{{\varvec{i}}} ,y_{i} ,d_{i} )\), whereby \({\varvec{x}}_{{\varvec{i}}} \in {\mathbf{\mathbb{R}}}^{p}\), \(y_{i} \in {\mathbf{\mathbb{R}}}\), and \(d_{i} \in \{ 1,2,...,D\} .\) Here, p denotes the number of genes and D corresponds to the number of datasets (or views). We define X as the matrix that has the \({\varvec{x}}_{{\varvec{i}}}\)’s as rows, \({\varvec{y}} = (y_{1} ,y_{2} ,...,y_{n} )\), and \({\varvec{d}} = (d_{1} ,d_{2} ,...,d_{n} )\). Without loss of generality, the predictors and responses are all normalized and centered. For simplicity, we consider a regression case, in which we argue that \(y_{i}\) is defined as:

$$y_{i} = x_{i}^{T} (\beta + \Delta_{{d_{i} }} ) + \varepsilon_{i} ,$$

whereby the \(\varepsilon_{i}\) are independent noise terms. The standard DSL is presented as follows:

$$(\hat{\beta },\hat{\Delta }_{1} ,...,\hat{\Delta }_{G} ) = {\text{argmin}}\,\frac{1}{2}\sum\limits_{i} {\left( {y_{i} - x_{i}^{T} (\beta + \Delta_{{d_{i} }} )} \right)^{2} + \lambda \left( {\left\| \beta \right\|_{1} + \sum\limits_{d = 1}^{D} {r_{d} } \left\| {\Delta_{d} } \right\|_{1} } \right)}$$

whereby λ is the tuning parameter, \(r_{d}\) is used as the regularization parameter over datasets and controls the amount of sharing between the datasets, β represents a common effect that is shared across datasets, and \(\Delta_{{d_{i} }}\) represents a unique effect for the ith dataset. The common effect here is correspondence to the shared biological information, and the unique effect here is correspondence to the discrepancy among different merging methods. However, the DSL method tends to select only one gene to represent the correlated group; genes that perform a similar function are often correlated. This drawback may lead to deterioration in the performance of the DSL method. To overcome this issue, in this paper, we propose an elastic data shared Lasso (DSL-\({\mathrm{L}}_{2}\)) method, which is encapsulated in the following equation:

$$\begin{aligned} (\hat{\beta },\hat{\Delta }_{1} ,...,\hat{\Delta }_{D} ) &= \arg \min \frac{1}{2}\sum\limits_{i} {\left( {y_{i} - x_{i}^{T} (\beta + \Delta_{{d_{i} }} )} \right)^{2} + \lambda_{1} \left( {\left\| \beta \right\|_{1} + \sum\limits_{d = 1}^{D} {r_{d} } \left\| {\Delta_{d} } \right\|_{1} } \right)}\\& \quad + \lambda_{2} \left( {\left\| \beta \right\| + \sum\limits_{d = 1}^{D} {r_{d} } \left\| {\Delta_{d} } \right\|} \right) \end{aligned}$$

whereby the first part is a linear loss function, and the second part is the lasso method used to produce a sparsity on \(\beta\) and \(\Delta_{d}\); the last part is the \({\mathrm{L}}_{2}\) method or ridge method, which generates a grouping effect on \(\beta\) and \(\Delta_{d}\). The lambda \({\mathrm{L}}_{1}\) and lambda \({\mathrm{L}}_{2}\) are tuning parameters that control the sparsity and grouping effect, respectively.

Finally, we combine DA with DSL-\({\mathrm{L}}_{2}\) method (DA-DSL-\({\mathrm{L}}_{2}\)) for meta-analysis.


In this section, an efficient method is developed to solve the DSL-\({\mathrm{L}}_{2}\) problem. It turns out that solving problem (3) is equivalent to a \({\mathrm{L}}_{1}\)-type optimization problem.

Lemma 1

We define Z, W as

$$\begin{aligned} Z_{N \times ((D + 1) \times P)} & = \left( {\begin{array}{*{20}c} {X_{1} } & {\frac{1}{{r_{1} }}X_{1} } & 0 & {...0} \\ {X_{2} } & 0 & {\frac{1}{{{{r}}_{2} }}X_{2} } & {...0} \\ \vdots & & & \\ {X_{D} } & 0 & 0 & {...\frac{1}{{{{r}}_{D} }}X_{D} } \\ \end{array} } \right), \\ W_{((D + 1) \times P) \times ((D + 1) \times P)} & = \left( {\begin{array}{*{20}c} {\sqrt {\lambda_{2} } {\mathbf{I}}_{P} } & 0 & 0 & {...0} \\ 0 & {\sqrt {\lambda_{2} } \frac{1}{{\sqrt {r_{1} } }}{\mathbf{I}}_{P} } & 0 & {...0} \\ \vdots & & {\sqrt {\lambda_{2} } \frac{1}{{\sqrt {r_{2} } }}{\mathbf{I}}_{P} } & \vdots \\ 0 & 0 & 0 & {...\sqrt {\lambda_{2} } \frac{1}{{\sqrt {r_{D} } }}{\mathbf{I}}_{P} } \\ \end{array} } \right), \\ \end{aligned}$$

where \(X_{k}\) and \(y_{k}\) represent the dataset k (or view k). We also define \(X^{*} { = }(1{ + }\lambda_{2} )^{ - 1/2} \left( {\begin{array}{*{20}c} Z \\ W \\ \end{array} } \right)\), \(\tilde{y} = (y_{1}^{T} ,y_{2}^{T} ,...,y_{D}^{T} )^{T}\), \(\tilde{y}^{*} = \left( {\begin{array}{*{20}c} {\tilde{y}} \\ 0 \\ \end{array} } \right)\), \(\tilde{\beta } = \sqrt {1 + \lambda_{2} } (\beta^{T} ,r_{1} \Delta_{1}^{T} ,...,r_{D} \Delta_{D}^{T} )^{T}\), \(\tilde{\beta }^{*} = \sqrt {1 + \lambda_{2} } \tilde{\beta }\) and \(\gamma { = }\lambda_{1} /\sqrt {1 + \lambda_{2} }\).

Then we have

$$\begin{aligned} \frac{1}{2}\left\| {\tilde{y}^{*} - X^{*} \tilde{\beta }^{*} } \right\|^{2} + \gamma \left\| {\tilde{\beta }^{*} } \right\|_{1} &= \frac{1}{2}\sum\limits_{i} {\left( {y_{i} - x_{i}^{T} (\beta + \Delta_{{d_{i} }} )} \right)^{2} + \lambda_{1} \left( {\left\| \beta \right\|_{1} + \sum\limits_{d = 1}^{D} {r_{d} } \left\| {\Delta_{d} } \right\|_{1} } \right)} \\ &\quad+ \lambda_{2} \left( {\left\| \beta \right\| + \sum\limits_{d = 1}^{D} {r_{d} } \left\| {\Delta_{d} } \right\|} \right) \end{aligned}$$

Let \(\beta^{*}\) be the solver to the above lasso problem, i.e.,

$$\hat{\beta }^{*} = \mathop {\arg \min }\limits_{{\tilde{\beta }^{*} }} \frac{1}{2}\left\| {\tilde{y}^{*} - X^{*} \tilde{\beta }^{*} } \right\|^{2} + \gamma \left\| {\tilde{\beta }^{*} } \right\|_{1} ,$$

then the solution to Eq. (3) becomes

$$\hat{\beta } = \frac{1}{{\sqrt {1 + \lambda_{2} } }}\hat{\beta }^{*} .$$

The proof is just simple algebra, which we omit. Lemma 1 shows that the DSL-\({\mathrm{L}}_{2}\) can perform an automatic gene selection in a way similar to the lasso, and can be solved by many efficient methods, such as the Matlab/R package “glmnet” [67]. A type algorithm to solve lasso is the coordinate descent algorithm (CDA). The algorithm is widely applied for solving optimization models, especially for small n and big p problems. This is because the complexity of the asymptotic time of CDA is just O(npm), where n, p and m represent the numbers of training sample size, iteration, and features, respectively. Typically, n and m are not large.

We now prove the DSL-\({\mathrm{L}}_{2}\) method improves the prediction power of DSL to some extent.

Theorem 1

With the Lemma 1, the DSL-\({\mathrm{L}}_{2}\) estimates \(\widehat{\beta }\) are given by

$$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\beta } = \mathop {\arg \min }\limits_{{\tilde{\beta }^{*} }} \tilde{\beta }^{*{\text{T}}} \left( {\frac{{Z^{{\text{T}}} Z + \lambda_{2} u{\mathbf{I}}}}{{1 + \lambda_{2} }}} \right)\tilde{\beta }^{*} - 2\tilde{y}^{{\text{T}}} Z^{{\text{T}}} \tilde{\beta }^{*} + \lambda_{1} \left| {\tilde{\beta }^{*} } \right|_{1} .$$

where \(u = 1 + \frac{1}{{r_{1} }} + \frac{1}{{r_{2} }} + \cdots + \frac{1}{{r_{D} }}\). The DSL regularization can be rewritten as

$$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\beta } ({\text{DSL}}) = \mathop {\arg \min }\limits_{{\tilde{\beta }^{*} }} \tilde{\beta }^{{\text{*T}}} Z^{{\text{T}}} Z\tilde{\beta }^{*} - 2\tilde{y}^{{\text{T}}} Z^{{\text{T}}} \tilde{\beta }^{*} + \lambda_{1} \left| {\tilde{\beta }^{*} } \right|_{1} .$$

Theorem 1implies the DLS-\({\mathrm{L}}_{2}\) approach is an improved version of the DSL method. Note that \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\Sigma } = Z^{{\text{T}}} Z\) is a sample version of the correlation matrix \(\Sigma\) and

$$\frac{{Z^{{\text{T}}} Z + \lambda_{2} u{\mathbf{I}}}}{{1 + \lambda_{2} }} = (1 - \sigma )\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\Sigma } + \sigma u{\mathbf{I}},$$

where \(\sigma = \lambda_{2} /(1 + \lambda_{2} )\) shrinks \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\Sigma }\) that towards the identity matrix. The prediction accuracy can often be improved by changing \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\Sigma }\) to a more shrunken estimate in the linear discriminate analysis [68, 69]. Thus, the DSL-\({\mathrm{L}}_{2}\) strengthen the DSL method by regularizing \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\Sigma }\) in Eq. (6). The proof of Theorem 1is presented in theAppendix”.

Availability of data and materials

All data used in this manuscript are downloaded at GEO ( with access numbers [GSE12771, GSE20189, GSE110223, GSE110224, and GSE113513].



Gene Expression Omnibus


Cross-platform normalization


Data share lasso


Data augmentation

DA-DSL-\({\mathrm{L}}_{2}\) :

Elastic data shared lasso with a new DA strategy

DSL-\({\mathrm{L}}_{2}\) :

Elastic data shared lasso


Non-small-cell lung cancer


Colorectal cancer


Distance-weighted discrimination


Coordinate descent algorithm


  1. Claussnitzer M, Cho JH, Collins R, Cox NJ, Dermitzakis ET, Hurles ME, et al. A brief history of human disease genetics. Nature. 2020;577:179–89.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  2. Patel N, Bush WS. Modeling transcriptional regulation using gene regulatory networks based on multi-omics data sources. BMC Bioinform. 2021;22:200.

    CAS  Article  Google Scholar 

  3. He M, Huang C, Liu B, Wang Y, Li J. Factor graph-aggregated heterogeneous network embedding for disease-gene association prediction. BMC Bioinform. 2021;22:165.

    Article  Google Scholar 

  4. Flynn E, Chang A, Altman RB. Large-scale labeling and assessment of sex bias in publicly available expression data. BMC Bioinform. 2021;22:168.

    CAS  Article  Google Scholar 

  5. Dong F, He Y, Wang T, Han D, Lu H, Zhao H. Predicting viral exposure response from modeling the changes of co-expression networks using time series gene expression data. BMC Bioinform. 2020;21:370.

    Article  Google Scholar 

  6. Frankell AM, Jammula S, Li X, Contino G, Killcoyne S, Abbas S, et al. The landscape of selection in 551 esophageal adenocarcinomas defines genomic biomarkers for the clinic. Nat Genet. 2019;51:506–16.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  7. Czajkowski M, Kretowski M. Decision tree underfitting in mining of gene expression data. An evolutionary multi-test tree approach. Expert Syst Appl. 2019;137:392–404.

    Article  Google Scholar 

  8. Fei T, Yu T. scBatch: batch-effect correction of RNA-seq data through sample distance matrix adjustment. Bioinformatics. 2020;36:3115–23.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  9. Galvez JM, Castillo D, Herrera LJ, Valenzuela O, Caba O, Prados JC, et al. Towards improving skin cancer diagnosis by integrating microarray and RNA-seq datasets. IEEE J Biomed Health Inform. 2020;24:1.

    Article  Google Scholar 

  10. Jansen IE, Savage JE, Watanabe K, Bryois J, Williams DM, Steinberg S, et al. Genome-wide meta-analysis identifies new loci and functional pathways influencing Alzheimer’s disease risk. Nat Genet. 2019;51:404–13.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  11. Rhodes DR, Barrette TR, Rubin MA, Ghosh D, Chinnaiyan AM. Meta-analysis of microarrays. Cancer Res. 2002;60:28–34.

    Google Scholar 

  12. Choi JK, Yu U, Kim S, Yoo OJ. Combining multiple microarray studies and modeling interstudy variation. Bioinformatics. 2003;19:i84–90.

    Article  PubMed  Google Scholar 

  13. Piras IS, Manchia M, Huentelman MJ, Pinna F, Zai CC, Kennedy JL, et al. Peripheral biomarkers in Schizophrenia: a meta-analysis of microarray gene expression datasets. Int J Neuropsychopharmacol. 2019;22:186–93.

    CAS  PubMed  Article  Google Scholar 

  14. DeConde RP, Hawley S, Falcon S, Clegg N, Knudsen B, Etzioni R. Combining results of microarray experiments: a rank aggregation approach. Stat Appl Genet Mol Biol. 2006;5:1.

    Article  Google Scholar 

  15. Lazar C, Meganck S, Taminau J, Steenhoff D, Coletta A, Molter C, et al. Batch effect removal methods for microarray gene expression data integration: a survey. Brief Bioinform. 2013;14:469–90.

    CAS  Article  PubMed  Google Scholar 

  16. Qi L, Chen L, Li Y, Qin Y, Pan R, Zhao W, et al. Critical limitations of prognostic signatures based on risk scores summarized from gene expression levels: a case study for resected stage I non-small-cell lung cancer. Brief Bioinform. 2016;17:233–42.

    Article  PubMed  Google Scholar 

  17. Ma S, Huang J. Regularized gene selection in cancer microarray meta-analysis. BMC Bioinform. 2009;10:1.

    CAS  Article  Google Scholar 

  18. Li Q, Wang S, Huang C-C, Yu M, Shao J. Meta-analysis based variable selection for gene expression data. Biometrics. 2014;70:872–80.

    Article  PubMed  Google Scholar 

  19. Zhang H, Li S-J, Zhang H, Yang Z-Y, Ren Y-Q, Xia L-Y, et al. Meta-analysis based on nonconvex regularization. Sci Rep. 2020;10:5755.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  20. Gross SM, Tibshirani R. Data shared lasso: a novel tool to discover uplift. Comput Stat Data Anal. 2016;101:226–35.

    PubMed  PubMed Central  Article  Google Scholar 

  21. Zou H, Hastie T. Regularization and variable selection via the elastic net. J R Stat Soc Ser B. 2005;67:301–20.

    Article  Google Scholar 

  22. Segal MR, Dahlquist KD, Conklin BR. Regression approaches for microarray data analysis. J Comput Biol. 2003;10:961–80.

    CAS  PubMed  Article  Google Scholar 

  23. van Dyk DA, Meng X-L. The art of data augmentation. J Comput Graph Stat. 2001;10:1–50.

    Article  Google Scholar 

  24. Krizhevsky A, Sutskever I, Hinton GE. ImageNet classification with deep convolutional neural networks. In: Advances in neural information processing systems (NIPS 2012), vol 25. 2012. p. 1097–105.

  25. Wang J, Sun K, Cheng T, Jiang B, Deng C, Zhao Y, et al. Deep High-resolution representation learning for visual recognition. IEEE Trans Pattern Anal Mach Intell. 2020;43:1.

    Google Scholar 

  26. Szegedy C, Liu W, Jia Y, Sermanet P, Reed S, Anguelov D, et al. Going deeper with convolutions. In: IEEE conference on computer vision and pattern recognition. 2015. p. 1–9.

  27. Cireşan DC, Meier U, Gambardella LM, Schmidhuber J. Deep, big, simple neural nets for handwritten digit recognition. Neural Comput. 2010;22:3207–20.

    Article  PubMed  Google Scholar 

  28. Simon N, Friedman J, Hastie T, Tibshirani R. A sparse-group lasso. J Comput Graph Stat. 2013;22:231–45.

    Article  Google Scholar 

  29. Zander T, Hofmann A, Staratschek-Jox A, Classen S, Debey-Pascher S, Maisel D, et al. Blood-based gene expression signatures in non-small cell lung cancer. Clin Cancer Res. 2011;17:3360–7.

    CAS  PubMed  Article  Google Scholar 

  30. Rotunno M, Hu N, Su H, Wang C, Goldstein AM, Bergen AW, et al. A gene expression signature from peripheral whole blood for stage I lung adenocarcinoma. Cancer Prev Res. 2011;4:1599–608.

    CAS  Article  Google Scholar 

  31. Ferraro B, Bepler G, Sharma S, Cantor A, Haura EB. EGR1 predicts PTEN and survival in patients with non-small-cell lung cancer. J Clin Oncol. 2005;23:1921–6.

    CAS  Article  PubMed  Google Scholar 

  32. Vaishnavi A, Capelletti M, Le AT, Kako S, Butaney M, Ercan D, et al. Oncogenic and drug-sensitive NTRK1 rearrangements in lung cancer. Nat Med. 2013;19:1469–72.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  33. Guo R, Yang J, Liu X, Wu J, Chen Y. Increased von Willebrand factor over decreased ADAMTS-13 activity is associated with poor prognosis in patients with advanced non-small-cell lung cancer. J Clin Lab Anal. 2018;32:e22219.

    CAS  Article  Google Scholar 

  34. Moreno P, Lara-Chica M, Soler-Torronteras R, Caro T, Medina M, Álvarez A, et al. The expression of the ubiquitin ligase SIAH2 (seven in absentia homolog 2) is increased in human lung cancer. PLoS ONE. 2015;10:e0143376.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  35. Jassal B, Matthews L, Viteri G, Gong C, Lorente P, Fabregat A, et al. The reactome pathway knowledgebase. Nucleic Acids Res. 2019;48:D498–503.

    PubMed Central  Google Scholar 

  36. Labelle M, Hynes RO. The initial hours of metastasis: the importance of cooperative host-tumor cell interactions during hematogenous dissemination. Cancer Discov. 2012;2:1091–9.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  37. Rachidi S, Metelli A, Riesenberg B, Wu BX, Nelson MH, Wallace C, et al. Platelets subvert T cell immunity against cancer via GARP-TGFβ axis. Sci Immunol. 2017;2:eaai7911.

    Article  PubMed  PubMed Central  Google Scholar 

  38. Best MG, Sol N, In’t Veld SGJG, Vancura A, Muller M, Niemeijer A-LN, et al. Swarm intelligence-enhanced detection of non-small-cell lung cancer using tumor-educated platelets. Cancer Cell. 2017;32:238-252.e9.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  39. Noy R, Pollard JW. Tumor-associated macrophages: from mechanisms to therapy. Immunity. 2014;41:49–61.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  40. Vlachavas EI, Pilalis E, Papadodima O, Koczan D, Willis S, Klippel S, et al. Radiogenomic analysis of F-18-fluorodeoxyglucose positron emission tomography and gene expression data elucidates the epidemiological complexity of colorectal cancer landscape. Comput Struct Biotechnol. 2019;17:177–85.

    Article  Google Scholar 

  41. Gan Y, Li Y, Li T, Shu G, Yin G. CCNA2 acts as a novel biomarker in regulating the growth and apoptosis of colorectal cancer. Cancer Manag Res. 2018;10:5113.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  42. Brcic L, Heidinger M, Sever AZ, Zacharias M, Jakopovic M, Fediuk M, et al. Prognostic value of cyclin A2 and B1 expression in lung carcinoids. Pathology. 2019;51:481–6.

    CAS  PubMed  Article  Google Scholar 

  43. Branchi V, García SA, Radhakrishnan P, Győrffy B, Hissa B, Schneider M, et al. Prognostic value of DLGAP5 in colorectal cancer. Int J Colorectal Dis. 2019;34:1455–65.

    Article  PubMed  Google Scholar 

  44. Liu X, Zhang H, Lai L, Wang X, Loera S, Xue L, et al. Ribonucleotide reductase small subunit M2 serves as a prognostic biomarker and predicts poor survival of colorectal cancers. Clin Sci. 2013;124:567–79.

    CAS  Article  Google Scholar 

  45. Min W, Liu J, Zhang S. Network-regularized sparse logistic regression models for clinical risk prediction and biomarker discovery. IEEE/ACM Trans Comput Biol Bioinform. 2018;15:944–53.

    PubMed  Article  Google Scholar 

  46. Min W, Liu J, Zhang S. Edge-group sparse PCA for network-guided high dimensional data analysis. Bioinformatics. 2018;34:3479–87.

    CAS  PubMed  Article  Google Scholar 

  47. Huang H-H, Liang Y. A novel Cox proportional hazards model for high-dimensional genomic data in cancer prognosis. IEEE/ACM Trans Comput Biol Bioinform. 2021;18:1821–30.

    CAS  PubMed  Article  Google Scholar 

  48. Huang H, Peng X, Liang Y. SPLSN: an efficient tool for survival analysis and biomarker selection. Int J Intell Syst. 2021;36:5845–65.

    Article  Google Scholar 

  49. Huang HH, Liu XY, Li HM, Liang Y. Molecular pathway identification using a new L1/2 solver and biological network-constrained mode. Int J Data Min Bioinform. 2017;17:189.

    Article  Google Scholar 

  50. Huang H-H, Liang Y. An integrative analysis system of gene expression using self-paced learning and SCAD-Net. Expert Syst Appl. 2019;135:102–12.

    Article  Google Scholar 

  51. Li J, Tseng GC. An adaptively weighted statistic for detecting differential gene expression when combining multiple transcriptomic studies. Ann Appl Stat. 2011;5:994–1019.

    Google Scholar 

  52. Hughey JJ, Butte AJ. Robust meta-analysis of gene expression using the elastic net. Nucleic Acids Res. 2015;43:1–11.

    Article  CAS  Google Scholar 

  53. Becker N, Toedt G, Lichter P, Benner A. Elastic SCAD as a novel penalization method for SVM classification tasks in high-dimensional data. BMC Bioinform. 2011;12:138.

    Article  Google Scholar 

  54. Zeng L, Xie J. Group variable selection via SCAD-L 2. Statistics (Berlin). 2014;48:49–66.

    Article  Google Scholar 

  55. Huang H-H, Liu X-Y, Liang Y. Feature selection and cancer classification via sparse logistic regression with the hybrid L1/2 +2 regularization. PLoS ONE. 2016;11:e0149675.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  56. Huang H-H, Liang Y. Hybrid L1/2 + 2 method for gene selection in the Cox proportional hazards model. Comput Methods Prog Biomed. 2018;164:65–73.

    Article  Google Scholar 

  57. Peng X, Tang Z, Yang F, Feris RS, Metaxas D. Jointly optimize data augmentation and network training: adversarial data augmentation in human pose estimation. In: Proceedings of IEEE conference on computer vision and pattern recognition. 2018. p. 2226–34.

  58. Peng X, Yang Y. Algorithms for interval-valued fuzzy soft sets in stochastic multi-criteria decision making based on regret theory and prospect theory with combined weight. Appl Soft Comput. 2017;54:415–30.

    Article  Google Scholar 

  59. Cheadle C, Vawter MP, Freed WJ, Becker KG. Analysis of microarray data using Z score transformation. J Mol Diagn. 2003;5:73–81.

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  60. Benito M, Parker J, Du Q, Wu J, Xiang D, Perou CM, et al. Adjustment of systematic microarray data biases. Bioinformatics. 2004;20:105–14.

    CAS  PubMed  Article  Google Scholar 

  61. Johnson WE, Li C, Rabinovic A. Adjusting batch effects in microarray expression data using empirical Bayes methods. Biostatistics. 2007;8:118–27.

    PubMed  Article  Google Scholar 

  62. Shabalin AA, Tjelmeland H, Fan C, Perou CM, Nobel AB. Merging two gene-expression studies via cross-platform normalization. Bioinformatics. 2008;24:1154–60.

    CAS  PubMed  Article  Google Scholar 

  63. Deshwar AG, Morris Q. PLIDA: cross-platform gene expression normalization using perturbed topic models. Bioinformatics. 2014;30:956–61.

    CAS  Article  PubMed  Google Scholar 

  64. Deng K, Zhang F, Tan Q, Huang Y, Song W, Rong Z, et al. WaveICA: a novel algorithm to remove batch effects for large-scale untargeted metabolomics data based on wavelet analysis. Anal Chim Acta. 2019;1061:60–9.

    CAS  PubMed  Article  Google Scholar 

  65. Jiang H, Deng Y, Chen H-S, Tao L, Sha Q, Chen J, et al. Joint analysis of two microarray gene-expression data sets to select lung adenocarcinoma marker genes. BMC Bioinform. 2004;5:81.

    Article  Google Scholar 

  66. Warnat P, Eils R, Brors B. Cross-platform analysis of cancer microarray data improves gene expression based classification of phenotypes. BMC Bioinform. 2005;6:265.

    CAS  Article  Google Scholar 

  67. Friedman J, Hastie T, Tibshirani R. Regularization paths for generalized linear models via coordinate descent. J Stat Softw. 2010;33:1–22.

    PubMed  PubMed Central  Article  Google Scholar 

  68. Friedman JH. Regularized discriminant analysis. J Am Stat Assoc. 1989;84:165–75.

    Article  Google Scholar 

  69. Hastie T, Tibshirani R, Friedman J, Franklin J. The elements of statistical learning: data mining, inference and prediction. Math Intell. 2005;27:83–5.

    Google Scholar 

Download references


The authors are very much indebted to the anonymous reviewers, whose constructive comments are valuable for strengthening the presentation of this paper.

About this supplement

This article has been published as part of BMC Bioinformatics Volume 23 Supplement 10, 2022: Application of Bioinformatics in Medical Science. The full contents of the supplement are available online at


This research was supported by the National Natural Science Foundation of China (62102261, 62006155, 6201101081), Macau Science and Technology Development Funds (0056/2020/AFJ, 0158/2019/A3), and Science and Technology Project of Shaoguan City (200811104531028). The publication cost is funded by Shaoguan University. The funding bodies had no role in the design of the study and collection, analysis, and interpretation of data, and in writing the manuscript.

Author information

Authors and Affiliations



HHH, HR, and RM developed the method, performed the analysis, and drafted the article. YL initiated and supervised the project. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Yong Liang.

Ethics declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare that they have no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix: Proof

Appendix: Proof

Proof of Theorem 1

Let \(\hat{\beta }\) be the DSL-L2 solution. By definition and Eq. (5), we have.

$$\begin{aligned} \hat{\beta } & = \mathop {\arg \min }\limits_{{\tilde{\beta }^{*} }} \left| {\tilde{y}^{*} - {{X}}^{*} \frac{{\tilde{\beta }^{*} }}{{\sqrt {1 + \lambda_{2} } }}} \right|^{2} + \frac{{\lambda_{1} }}{{\sqrt {1 + \lambda_{2} } }}\left| {\frac{{\tilde{\beta }^{*} }}{{\sqrt {1 + \lambda_{2} } }}} \right|_{1} \\ & = \mathop {\arg \min }\limits_{{\tilde{\beta }^{*} }} \tilde{\beta }^{{*\text{T}}} \left( {\frac{{{{X}}^{{{*}{\text{T}}}} {{X}}}}{{1 + \lambda_{2} }}} \right)\tilde{\beta }^{*} - 2\frac{{\tilde{y}^{{*{\text{T}}}} {{X}}^{*} }}{{\sqrt {1 + \lambda_{2} } }} + \tilde{y}^{{*{\text{T}}}} \tilde{y}^{*} + \frac{{\lambda_{1} \left| {\tilde{\beta }^{*} } \right|_{1} }}{{1 + \lambda_{2} }}. \\ \end{aligned}$$

Substituting the identities

$$\begin{aligned} {{X}}^{{*{\text{T}}}} {{X}} & = \frac{{Z^{{\text{T}}} Z + \lambda_{2} u{\mathbf{I}}}}{{1 + \lambda_{2} }}, \\ \tilde{y}^{{*{\text{T}}}} {{X}}^{*} & = \frac{{\tilde{y}^{{\text{T}}} Z}}{{\sqrt {1 +\lambda_{2} } }}, \\ \tilde{y}^{{*{\text{T}}}} \tilde{y}^{*} & = \tilde{y}^{{\text{T}}} \tilde{y} \\ \end{aligned}$$

into Eq. (8), we have

$$\begin{aligned} \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\beta } & = \mathop {\arg \min }\limits_{{\tilde{\beta }^{*} }} \frac{1}{{1 + \lambda_{2} }}\left\{ {\tilde{\beta }^{{*{\text{T}}}} \left( {\frac{{Z^{{\text{T}}} Z + \lambda_{2} u{\mathbf{I}}}}{{1 + \lambda_{2} }}} \right)\tilde{\beta }^{*} - 2\tilde{y}^{{\text{T}}} Z^{{\text{T}}} \tilde{\beta }^{*} + \lambda_{1} \left| {\tilde{\beta }^{*} } \right|_{1} } \right\} + \tilde{y}^{{\text{T}}} \tilde{y} \\ & = \mathop {\arg \min }\limits_{{\tilde{\beta }^{*} }} \tilde{\beta }^{{\text{*T}}} \left( {\frac{{Z^{{\text{T}}} Z + \lambda_{2} u{\mathbf{I}}}}{{1 + \lambda_{2} }}} \right)\tilde{\beta }^{*} - 2\tilde{y}^{{\text{T}}} Z^{{\text{T}}} \tilde{\beta }^{*} + \lambda_{1} \left| {\tilde{\beta }^{*} } \right|_{1} . \\ \end{aligned}$$

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit The Creative Commons Public Domain Dedication waiver ( applies to the data made available in this article, unless otherwise stated in a credit line to the data.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Huang, HH., Rao, H., Miao, R. et al. A novel meta-analysis based on data augmentation and elastic data shared lasso regularization for gene expression. BMC Bioinformatics 23 (Suppl 10), 353 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI:


  • Integrative analysis
  • Meta-analysis
  • Regularization
  • Variable selection
  • Gene expression