# Subtyping glioblastoma by combining miRNA and mRNA expression data using compressed sensing-based approach

- Wenlong Tang
^{1}, - Junbo Duan
^{1}, - Ji-Gang Zhang
^{2}and - Yu-Ping Wang
^{1, 2, 3}Email author

**2013**:2

**DOI: **10.1186/1687-4153-2013-2

© Tang et al.; licensee Springer. 2013

**Received: **28 December 2011

**Accepted: **6 December 2012

**Published: **14 January 2013

## Abstract

In the clinical practice, many diseases such as glioblastoma, leukemia, diabetes, and prostates have multiple subtypes*.* Classifying subtypes accurately using genomic data will provide individualized treatments to target-specific disease subtypes. However, it is often difficult to obtain satisfactory classification accuracy using only one type of data, because the subtypes of a disease can exhibit similar patterns in one data type. Fortunately, multiple types of genomic data are often available due to the rapid development of genomic techniques. This raises the question on whether the classification performance can significantly be improved by combining multiple types of genomic data. In this article, we classified four subtypes of glioblastoma multiforme (GBM) with multiple types of genome-wide data (e.g., mRNA and miRNA expression) from The Cancer Genome Atlas (TCGA) project. We proposed a multi-class compressed sensing-based detector (MCSD) for this study. The MCSD was trained with data from TCGA and then applied to subtype GBM patients using an independent testing data. We performed the classification on the same patient subjects with three data types, i.e., miRNA expression data, mRNA (or gene expression) data, and their combinations. The classification accuracy is 69.1% with the miRNA expression data, 52.7% with mRNA expression data, and 90.9% with the combination of both mRNA and miRNA expression data. In addition, some biomarkers identified by the integrated approaches have been confirmed with results from the published literatures. These results indicate that the combined analysis can significantly improve the accuracy of classifying GBM subtypes and identify potential biomarkers for disease diagnosis.

### Keywords

Glioblastoma Data integration Compressed sensing Classification mRNA miRNA## Introduction

Many diseases including cancers have multiple subtypes. For example, leukemia has four main categories: acute lymphoblastic leukemia (ALL), acute myelogenous leukemia, chronic lymphocytic leukemia, and chronic myelogenous leukemia. Each of these categories can be further divided into different subtypes [1]; for example, ALL can be further subtyped into six types [2]. Glioma has four subtypes, including oligodendroglioma, anaplastic oligodendroglioma, anaplastic astrocytoma, and glioblastoma multiforme (GBM) [3]. Prostate cancer has three major subtypes [4]. An accurate and effective classification of those subtypes based on genomic data will result in personalized treatments of the cancer in terms of a particular subtype. In this article, we are interested in the subtyping of GBM, which is a kind of glioma and is the most common form of malignant brain cancer in adults [5]. There is an increasing interest in classifying multiple subtypes of GBM based on its genomic measurements. Most of the existing works are based on gene expression data only. Benjamin et al. [6] classified two types of GBM in adults and found that the genes EGFR and TP53 were important in discriminating the two subtypes. Nutt et al. [7] built a *k*-nearest neighbor model with 20 features to classify 28 glioblastomas and 22 anaplastic oligodendrogliomas and found that the class distinctions were significantly associated with survival outcome (*p* = 0.05). Noushmehr et al. [8] separated a subset of samples in GBM from The Cancer Genome Atlas (TCGA) project, which displayed concerted hypermethylation at a large number of loci. The datasets we used to subtype GBM are also from TCGA. The subtypes of GBM samples in TCGA includes: pro-neural, neural, classical, and mesenchymal [9]. The GBM data we have tested include both miRNA expression and mRNA expression data. The miRNAs, also called microRNAs, are short non-coding RNA molecules that were recently found in all eukaryotic cells except fungi, algae, and marine plants. The human genome may contain over 1,000 miRNAs [10]. Aberrant expressions of miRNAs have been found to be related to many diseases, including cancers [11, 12]. They play an essential role in tissue differentiation during normal development and tumorigenesis [13].

In the last decade, the development of genomic techniques enables the availability of multiple data types on the same patient, such as mRNA or gene expression, SNP, miRNA expression, and copy number variation data. It is well recognized that a more comprehensive analysis result could be obtained based on integrating multiple types of genomic data than using an individual dataset. Soneson et al. [14] investigated the correlation between gene expression and copy number alterations using canonical correlation analysis for leukemia data. A web-based platform, called Magellan, was developed for the integrated analysis of DNA copy number and expression data in ovarian cancer [15], which found significant correlation between gene expression and patient survival. Troyanskaya et al. [16] developed a Bayesian framework to combine heterogeneous data sources to predict gene function with improved accuracy. A kernel-based statistical learning algorithm was also proposed in the combined analysis of multiple genome-wide datasets [17]. In this article, we propose a novel classifier based on the compressed sensing (CS) theory that we have been working with.

The CS technique enables compact storage and rapid transmission of large amounts of information. The technique can be used to extract significant statistical information from high-dimensional datasets [18]. The CS technology has been proven to be a powerful tool in the signal processing and statistics fields. It demonstrates that a compressible signal can be recovered from far fewer samples than that needed by the Nyquist sampling theorem [19]. Our recent work used a CS-based detector (CSD) for subtyping leukemia with gene expression data [20]. The CSD achieved high classification accuracies, with 97.4% evaluated with cross-validation and 94.3% evaluated with an independent dataset. The CSD showed better performance in subtyping two types of leukemia compared to some traditional classifiers such as the support vector machine (SVM), indicating the advantage of the CSD in analyzing high-dimensional genomic data. In this article, we extended the CSD to multiple data types and proposed a detector called MCSD. In particular, we applied the MCSD to the subtyping of four types of GBM by combining miRNA expression and mRNA expression data. We present a novel combined analysis method based on the CS and demonstrate that the classification performance can significantly be improved in subtyping four types of GBM, with both miRNA expression and mRNA expression data.

## Methods and materials

### Data collection

**GBM subtypes and their corresponding samples used for the training and the testing**

Glioblastoma subtypes | Training (total 60) | Testing (total 55) |
---|---|---|

Pro-neural | 15 | 17 |

Neural | 15 | 3 |

Classical | 15 | 17 |

Mesenchymal | 15 | 18 |

For multiple types of genomic data (e.g., miRNA expression data, mRNA expression data, etc.), we used x_{1i} to denote the data vector for the *i* th sample in data 1 (e.g., miRNA expression), x_{2i} to denote the data vector for the *i* th sample in data 2 (e.g., mRNA expression), and x_{
ni
} to denote the data vector for the *i* th sample in data *n*. The combined data for the *i* th sample is ${x}_{i}={\left({x}_{1}\begin{array}{c}\hfill T\hfill \\ \hfill i\hfill \end{array},{x}_{2}\begin{array}{c}\hfill T\hfill \\ \hfill i\hfill \end{array},\dots ,{x}_{n}\begin{array}{c}\hfill T\hfill \\ \hfill i\hfill \end{array}\right)}^{T}$, which is arranged in a cascaded manner.

### MCSD

#### Bayesian classifier

*n*classes, we define the actual class (“ground truth”) to which it belongs as

*g*; the class to which it is assigned (“decision”) as

*d*. The

*n*classes are defined as:

*π*

_{1,}

*π*

_{2},…,

*π*

_{ n }. Let

*U*

_{ πi }(y

*,g*) be the utility of assigning y, actually from

*π*

_{ g }, to

*π*

_{ i }. The “utility” is negative relevant to the Bayes Risk (BR) [22], which is the minimum classification error. Thus, we make:

*U =*1-BR. The two-class one-dimensional BR (shaded area in Figure 1) can be calculated by

*y*

_{0}is the decision boundary,

*P*

_{1}

*P*

_{2}are the prior probabilities and

*P*

_{1}(

*y*),

*P*

_{2}(

*y*) are the conditional probability density functions of the two classes, respectively (shown in Figure 1).

*n*classes and

*N*dimensions. Then Equation (1) can be rewritten as

where *P*_{
j
} is the prior probability of a given subject belonging to the class *π*_{
j
}, *j* = 1,…,*n*; *P*_{
j
}(*y*) is the conditional probability density function of the class *π*_{
j
}, and *Ω*_{
i
} is the Bayesian decision region for class *π*_{
i
}[23].

where *P*(*d* = *π*_{
i
}|*g* = *π*_{
j
}) denotes the probability of assigning a given observation y, actually belonging to *π*_{
j
}, to *π*_{
i.
}*δ*_{
ij
} is the Kronecker’s delta.

*d = π*

_{ i }iff

*U*

_{i|j}to express the utility of assigning a given observation y, actually belonging to

*π*

_{ j }, to

*π*

_{ i }. The inequality (4) can be written as

*P*

_{ y }(y|

*g*=

*π*

_{ k }),

*k*= 1,…,

*n*, is the probability density function for the signal observations. According to Inequality (5), we decide

*d = π*

_{ i }iff

*π*

_{1},

*π*

_{2},…,

*π*

_{ n }have the same prior probability, i.e., $P\left(g={\pi}_{k}\right)=\frac{1}{n}$. The detector (8) can be rewritten as

The calculation of the utility is shown in the Additional file 1.

### Dimension reduction using CS

*,*called compress matrix

*.*The generation of the compress matrix can be formulated as a sparse representation problem as in Equation (10)

*M*is the dimension of the sample after the projection, y

_{ i }is the

*i*th column in the compressed signal,

*c*is the total number of columns in the compressed signal, $\mathit{S}=\left\{{\mathit{s}}_{i}\right\}\in {\mathbb{R}}^{N\times c}$ is the original signal, and

*N*is the dimension of the original signal and

*N >> M*. The matrix $\mathit{\Phi}\in {\mathbb{R}}^{M\times N}$ is a sparse matrix, with most of the entries ‘0’s. The compress matrix Φ projects the original sample S to a much smaller dimensional signal Y. The original sample may contain redundancy; through this projection, the original sample can significantly be compressed and compactly represented, which usually lead to better classification performance. Suppose we have

*n*groups, with

*c*

_{1}training samples in group 1,

*c*

_{2}training samples in group 2, and so forth,

*c*

_{ n }training samples in group

*n*, and

*c*=

*c*

_{1}+

*c*

_{2}+ ··· +

*c*

_{ n }for $\mathit{S}=\left[{\mathit{s}}_{1,}{\mathit{s}}_{2},\dots ,{\mathit{s}}_{c}\right]\in {\mathbb{R}}^{N\times c}$ and $\mathit{Y}=\left[{\mathit{y}}_{1,}{\mathit{y}}_{2},\dots ,{\mathit{y}}_{c}\right]\in {\mathbb{R}}^{M\times c}$. The transpose of Equation (10) is

*j*th column of Φ

^{ T }, and ${\left({\mathit{Y}}^{T}\right)}_{\mathrm{j}}\in {\mathbb{R}}^{c\times 1}$ denote the

*j*th column of Y

^{ T }, where

*j*= 1, 2,…,

*M*. Then Equation (11) can be rewritten as

*l*-1 norm minimization algorithm such as Homotopy method, or the least angle regression method [24]. The

*l*-1 norm optimization problem reads

where ‖(Φ^{
T
})_{
j
}‖_{1} is the *l*-1 norm of the vector (Φ^{
T
})_{
j
}, i.e., the sum of the absolute values of entries in vector (Φ^{
T
})_{
j
}. Obviously, the compress matrix Φ projects the original signal ${\mathit{s}}_{i}\in {\mathbb{R}}^{N\times 1}$ to a much smaller dimensional signal $\mathit{\Phi}{\mathit{s}}_{i}\in {\mathbb{R}}^{M\times 1}$. Instead of dealing with the original signal, we only use $\mathit{\Phi}{\mathit{s}}_{i}\in {\mathbb{R}}^{M\times 1}$ and $\mathit{\Phi}{\mathit{\Phi}}^{T}\in {\mathbb{R}}^{M\times M}$ in the subtyping procedure, leading to a fast classification.

### Determination of feature vector

*MeanStd, StdStd*), the standard deviation of the means of all the groups (

*StdMean*), and the mean and standard deviation of Pearson’s linear correlation coefficient (

*MeanCorr, StdCorr*) between the samples and their class label vector. Therefore, for the

*i*th sample, we have a five-dimensional feature vector as follows:

where *i* = 1,2,…,*N*, and *N* is the number of samples. Each element in the vector V_{
i
} has been normalized by its overall maximum value so that its value is between 0 and 1, i.e., V_{
i
} ∈ [0, 1]. A number of *M* informative features were selected by setting the threshold values of V_{
i
}. If a feature is informative or significant, we expect that the values from different patients within the same subtype are similar while the differences among different subtypes are relatively large. In addition, it is easy to understand that, if the correlation between the feature vector and the class label is high, the feature vector can serve as a significant biomarker to distinguish the subtypes. According to the above analysis, matrix Y in Equation (10) is built by those features with low *MeanStd, StdStd, StdCorr* while high *StdMean, MeanCorr*, which are significant for the classification.

### Classifier based on CS

where $\widehat{\mathit{y}}\in {\mathbb{R}}^{N}$ is a given observation; $\mathit{s}\in {\mathbb{R}}^{N}$ is the mean of a sample; and σ is the standard deviation of the data.

where $\widehat{\mathit{y}}\in {\mathbb{R}}^{M}$ is a compressed observation; $\mathit{s}\in {\mathbb{R}}^{N}$ is a known signal and Φ is the compress matrix. The MCSD used in this study is constructed by substituting Equation (15) into Equation (9) for maximum likelihood estimation.

- 1.
Inputs: training dataset and testing dataset

- 2.
Normalize the rows of the training and the testing datasets to the range of [0,1]

- 3.
Select informative features according to the feature selection criteria

- 4.
Calculate compress matrix $\mathit{\Phi}\in {\mathbb{R}}^{M\times N}$ by the training dataset by Equation (14)

- 5.
Identify the class of the compressed testing data by Equation (9), where the probability density function is given by Equation (15).

There are many other classifiers such as SVM that can be used. But our purpose here is to show that dimension reduction with the CS can improve subsequent classification and the often used Bayesian classifier is chosen.

## Results

We subtyped four types of GBM with multiple genomic data types (e.g., miRNA expression, mRNA expression, and their combinations) from TCGA. The MCSD was first trained by the training data with known class labels, and was then employed to detect subtypes in another independent testing dataset. The classification accuracy by the MCSD was compared with that without using MCSD. The classification performance between using the combined data types and using a single type of data was also compared.

**Comparison of classification accuracy between MCSD and non-compressed detector using combined and single data type**

MCSD | Non-compressed accuracy (%) | ||
---|---|---|---|

Accuracy (%) | Number of features | ||

Combined analysis | 90.9 | 121 | 32.7 |

miRNA | 69.1 | 54 | 41.8 |

Gene expression | 52.7 | 432 | 32.7 |

We also tested if the classification performance of the MCSD was better than non-compressed detector in the combined analysis of both miRNA expression and mRNA expression data as shown in Table 2. The subtyping accuracy by the non-compressed detector was 32.7%. The classification accuracy by the MCSD showed a significant improvement over the non-compressed detector. The accuracy was 90.9% (121 informative features selected or 145 informative features selected). The 121 features selected are shown in Additional file 2 with the probes and the corresponding symbols.

## Conclusion and discussion

In this study, we applied the proposed MCSD to subtype four types of GBM: pro-neural, neural, classical, and mesenchymal with multiple genetic data from TCGA. High classification accuracy was achieved by using CS-based technique (i.e., MCSD) along with the combination of multiple datasets. The results from combining two types of genomic data were compared with those from single type of data. Moreover, the performance of the classification with and without MCSD technique had also been compared. The comparisons showed that the CS-based combined analysis of multiple types of genetic data could significantly improve the accuracy of detecting GBM subtypes.

Combining different types of genomic data allows us to interpret the information in the datasets comprehensively. The information from miRNA and mRNA are complementary to each other; so a combined analysis can give a better result than single data type analysis. miRNAs are a recently discovered class of small non-coding RNAs that regulate gene expression [25], which can be combined with mRNA data for better disease subtyping. However, if no dimension reduction with CS was applied, we found from Table 2 that the classification accuracy from combined analysis was comparable to that from the single mRNA expression because of the redundancy added. The classification performance was significantly improved after we used CS method, indicating that CS may reduce redundancy [26] in the combined datasets and thus improve the classification accuracy.

Informative features/biomarkers selected in this study have also been validated to be associated with GBM and have been reported in the literatures. In the combined data analysis, the 121 features/probes selected (shown in Additional file 2), the 3 miRNA expression probes and 118 mRNA expression probes are listed. Two of the selected miRNAs probes that represent the same miRNA, “hsa-miR-9” (sequence “TCATACAGCTAGATAACCAA”), have been validated to have stemness potential and chemoresistance to GBM cells [27–29], and known to be specifically expressed during brain neurogenesis. In the listed mRNA expression probes, the four probes of “CD44” and the three probes of “ASCL1” are selected. Both of the genes have been validated as biomarkers in subtyping GBM in multiple genomic studies [9, 30–32]. It demonstrates the significance of “CD44” and “ASCL1” in discriminating different subtypes of GBM. The three probes from “THBS1” are also selected in the 121 probes list. “THBS1” is a subunit of a disulfide-linked homotrimeric protein. This protein has been shown to play roles in platelet aggregation, angiogenesis, and tumorigenesis [33]. “THBS1” is also a major activator of “TGFB1” and the “TGFB1” expression is associated with GBM [34]. Moreover, it has been found that “TbRII”, a receptor of “TGFB1”, has a strong relationship with human malignant glioblastoma cells [35]. There are biomarkers listed in Additional file 2 that have not been reported yet. However, they may be potential biomarkers for GBM, deserving further study.

We also performed Gene Ontology (GO) analyses to determine that these genes were enriched in specific GO terms (biological processes). The GO term “antigen processing” and presentation “lymphocyte mediated immunity” (*p* = 1.78 × 10^{–6}), and several GO terms related to wounding healing [e.g. “response to wounding” (*p* = 1.26 × 10^{–8}); “wound healing” (*p* = 2.44 × 10^{–6})], and cell adhesion [e.g. “biological adhesion” (*p* = 6.53 × 10^{–7}); “cell adhesion” (*p* = 6.41 × 10^{–7})] showed highly significant enrichment for our selected genes. These results were expected. Taking “lymphocyte mediated immunity”-related GO categories as an example, lymphocyte-mediated cellular responses play a critical role in the body’s ability to generate an antitumor immune response, and activation status of lymphocytes is an important determinant of sensitivity to tumor-mediated apoptosis [36]. In addition, according to previous studies, the miRNAs we identified are related to glioblastoma. For example, it was found that “has-miR-9” inhibit differentiation of glioblastoma stem cells, and the calmodulin-binding transcription activator 1 (CAMTA1) as “has-miR-9” target is a tumor suppressor in glioblastoma [37].

To test the stability of the classification results, the samples in training and testing were randomly rearranged ten more times. The number of samples from each subtype in training and testing was maintained the same as in the description in the section “Data collection”. The overall classification rate has an average value of 87.1% with a standard deviation of 4.5%, indicating that the results are rather robust.

In summary, we have developed a CS-based technique for combining multiple genomic data to subtype glioblastoma more accurately. The biomarkers identified with our approaches have also been validated or reported in some existing literatures, indicating that the integrated approach can provide comprehensive information for better disease diagnosis.

## Declarations

### Acknowledgments

This study was supported by the NIH grant R21 LM010042, NSF Advances in Biological informatics (ABI) grant and The Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning. The authors deeply appreciate the anonymous referees for their valuable suggestions.

## Authors’ Affiliations

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