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# Integrating fMRI and SNP data for biomarker identification for schizophrenia with a sparse representation based variable selection method

- Hongbao Cao
^{1}, - Junbo Duan
^{2, 3}, - Dongdong Lin
^{2}, - Vince Calhoun
^{4, 5}and - Yu-Ping Wang
^{2, 3}Email author

**6 (Suppl 3)**:S2

https://doi.org/10.1186/1755-8794-6-S3-S2

© Cao et al.; licensee BioMed Central Ltd. 2013

**Published:**11 November 2013

## Abstract

### Background

In recent years, both single-nucleotide polymorphism (SNP) array and functional magnetic resonance imaging (fMRI) have been widely used for the study of schizophrenia (SCZ). In addition, a few studies have been reported integrating both SNPs data and fMRI data for comprehensive analysis.

### Methods

In this study, a novel sparse representation based variable selection (SRVS) method has been proposed and tested on a simulation data set to demonstrate its multi-resolution properties. Then the SRVS method was applied to an integrative analysis of two different SCZ data sets, a Single-nucleotide polymorphism (SNP) data set and a functional resonance imaging (fMRI) data set, including 92 cases and 116 controls. Biomarkers for the disease were identified and validated with a multivariate classification approach followed by a leave one out (LOO) cross-validation. Then we compared the results with that of a previously reported sparse representation based feature selection method.

### Results

Results showed that biomarkers from our proposed SRVS method gave significantly higher classification accuracy in discriminating SCZ patients from healthy controls than that of the previous reported sparse representation method. Furthermore, using biomarkers from both data sets led to better classification accuracy than using single type of biomarkers, which suggests the advantage of integrative analysis of different types of data.

### Conclusions

The proposed SRVS algorithm is effective in identifying significant biomarkers for complicated disease as SCZ. Integrating different types of data (e.g. SNP and fMRI data) may identify complementary biomarkers benefitting the diagnosis accuracy of the disease.

## Keywords

- Sparse Representation
- fMRI Data
- High Classification Accuracy
- Restricted Isometry Property
- Sparse Model

## Background

Schizophrenia (SCZ) is one of the most disabling and emotionally devastating illnesses. The global median lifetime morbid risk for schizophrenia is 7.2/1,000 persons [1]. Genetic factors play an important role in the development of schizophrenia. To date, over 1000 genes have been reported to associate with SCZ (http://www.szgene.org/default.asp) and many SNPs have been identified as biomarkers for the disease [2–4]. For example, Kordi-Tamandani et al. showed that that promoter methylation of the CTLA4 gene can increase the risk of SCZ disease [2]. Shayevitz et al. confirmed the gene NOTCH4 as a candidate gene for schizophrenia with genome-wide association studies (GWAS) [3]. Chen et al. stated that three SNPs spanning the MYO5B gene are significantly associated with SCZ: rs4939921, rs1557355 and rs4939924 [4]. Besides genomic data, fMRI is another widely used data modality in SCZ studies [5][6]. To date, many methods have been proposed to integrate multi-types of data in SCZ disease study [7–11]. For example, Chen et al. proposed parallel independent component analysis (paraICA) to identify genomic risk components associated with brain function abnormalities and detected significant biomarkers from both fMRI data and SNP data that are strongly correlated [7]. Parallel ICA is an effective method for the joint analysis of multiple modalities including interconnections between them [8]. Utilizing this method, Meda et al. detected three fMRI components significantly correlated with two distinct gene components in SCZ study [11]. In this study, a novel sparse representation based variable selection (SRVS) method was proposed and applied to an integrative analysis of two types of data: fMRI and SNP, aiming to obtain comprehensive analysis.

Sparse representation including compressive sensing has been widely used in signal/image processing and computational mathematics [12–18]. Candes et al. showed that stable signal can be approximately recovered from incomplete and inaccurate measurements [14]. Wright et al. proposed a sparse representation based clustering (SRC) for face recognition, demonstrating high classification accuracy [15]. In our recent works [16–18], we developed novel classification and feature selection algorithms based on sparse representation theory. We applied those methods to gene expression data analysis [16], to chromosome image classification [18], and to joint analysis of different data modalities (e.g. SNP data and gene expression data) [17], and achieved improved classification accuracies as well as better feature selections.

In applications of sparse representation, The availability of a limited number of samples is an important issue (e.g., feature selection and signal recovery) [19][20][21]. According to compressive sensing theory (e.g., the restricted isometry property (RIP) condition [23][24] for signal recovery), the number of available samples should not be less than the number of signals to be selected/recovered. However, the number of features/variables in genomic data (e.g. SNP data) or medical imaging data (e.g. fMRI data) are usually significantly big than the number of samples. In those cases, the traditional methods for compressive sampling cannot effectively analyse the data.

In a recent work, Li et al. [21] developed a voxel selection algorithm for fMRI data analysis. The method was based on sparse representation and is designed to get a sparse solution when sufficient samples exist. However, it may not handle the small sample problem described above.

In this study, a novel sparse representation based variable selection (SRVS) algorithm was proposed to select relevant biomarkers from big data sets having small sample sizes. The analysis was obtained by using a window based approach, whose size determines the resolution of the variable selection. We first tested the SRVS algorithm on a simulated data set (size of 100 × 1e^{6}, with 50 cases and 50 controls), demonstrating the multi-resolution characteristic of the method. Then the algorithm was applied to an integrative analysis of two real data sets: a SNP data set (size of 208 × 759075) and a fMRI data set (size of 208 × 153594). Using the proposed SRVS algorithm, biomarkers for SCZ were identified and validated.

## Methods

### fMRI and SNP data collection

A total of 208 subjects, after signing informed consent, were recruited in the study, including 96 SCZ cases (age: 34 ± 11, 74 males) and 112 healthy controls (age: 32 ± 11, 68 males). Both SNP and fMRI data were collected from each of those 208 subjects. The healthy controls have no history of psychiatric disorders and were free of any medical. SCZ cases met the DSM-IV diagnostic criteria for schizophrenia. After pre-processing, 153594 fMRI voxels and 759075 SNP loci were obtained for the following biomarker selections. Please refer to [22] for detailed description of data collection and pre-processing.

### Generalized sparse model

where $y\in {R}^{n\times 1}$ is the phenotype vector of the subjects; matrix ${X}_{1}\in {R}^{n\times {p}_{1}}$ and ${X}_{2}\in {R}^{n\times {p}_{2}}$ represent data sets of different modalities having normalized column vectors (e.g., ${\left|\right|*\left|\right|}_{2}=1$); $X=\left[{\alpha}_{1}{X}_{1},{\alpha}_{2}{X}_{2}\right]\in {R}^{n\times p}$; ${\alpha}_{1}+{\alpha}_{2}=1$, and ${\alpha}_{1},{\alpha}_{2}>0$ are the weight factors for ${X}_{1}$ and ${X}_{2}$ respectively. The measurement error $\epsilon \in {R}^{n\times 1}$. We aim to reconstruct the unknown sparse vector $\delta =\left[\begin{array}{c}\hfill {\delta}_{1}\hfill \\ \hfill {\delta}_{2}\hfill \end{array}\right]\in {R}^{p\times 1}$ based on $\phantom{\rule{0.25em}{0ex}}y$ and $\phantom{\rule{0.25em}{0ex}}X$, where ${\delta}_{1}\in {R}^{{p}_{1}\times 1}$, ${\delta}_{2}\in {R}^{{p}_{2}\times 1}$, and ${p}_{1}+{p}_{2}=p$.

It can be proven that when $p>35n$, the matrix $X\in {R}^{n\times \mathsf{\text{p}}}$ has the difficulty to satisfy the restricted isometry property (RIP) condition [24] for signal recovery. In this work, $p=759075+153594=912669$ and $n=208$. Thus $p\gg 35n=7280$. To overcome this problem, we propose the SRVS algorithm described as follows.

### SRVS algorithm

where ${\left|\right|*\left|\right|}_{2}$ represents ${L}_{p}$ norm; $p\in \left[0,1\right]$. The SRVS Algorithm given below is used to solve the ${L}_{p}$ minimization problem and select the phenotype relevant column vectors out of $\phantom{\rule{0.25em}{0ex}}X$.

#### Spare representation base variable selection (SRVS) algorithm (http://hongbaocao.weebly.com/software-for-download.html)

1. Initialize ${\delta}^{\left(0\right)}=0$;

2. For the $\phantom{\rule{0.25em}{0ex}}l$ th step, randomly select ${X}_{l}\in {R}^{n\times k}$ from $X=\left\{{x}_{1},\phantom{\rule{0.3em}{0ex}}.\phantom{\rule{0.3em}{0ex}}.\phantom{\rule{0.3em}{0ex}}.\phantom{\rule{0.3em}{0ex}},\phantom{\rule{0.3em}{0ex}}{x}_{p}\right\}\in {R}^{n\times p}$; Mark the indexes of the columns in ${X}_{l}$ as ${I}_{l}\in {R}^{1\times k}$;

4. Update ${\delta}^{\left(l\right)}\in {R}^{p\times 1}$ with ${\delta}_{l}$: ${\delta}^{\left(l\right)}\left({I}_{l}\right)={\delta}^{\left(l-1\right)}\left({I}_{l}\right)+{\delta}_{l}$; where ${\delta}^{\left(l\right)}\left({I}_{l}\right)$ and ${\delta}^{\left(l-1\right)}\left({I}_{l}\right)$ denote the ${I}_{l}$ th entries in ${\delta}^{\left(l\right)}$ and ${\delta}^{\left(l-1\right)}$ respectively;

5. If $\left|\right|{\delta}^{\left(l\right)}/l-{\delta}^{\left(l-1\right)}/{\left(l-1\right)\left|\right|}_{2}>\alpha $, update $l=l+1$; go to Step 2.

6. Set $\delta ={\delta}^{\left(l\right)}/l$. The non-zero entries in $\phantom{\rule{0.25em}{0ex}}\delta $ correspond to the columns in $\phantom{\rule{0.25em}{0ex}}X$ to be selected.

In Step 3, we sought to solve a ${L}_{0}$ minimization problem using the OMP algorithm [19]. The OMP has been widely used for signal recovery and approximation [18], [26–30].

It can be proven that, by using the SRVS algorithm, one can identify the significant variables with high probabilities. In addition, the SRVS algorithm can be shown convergent for any given $\phantom{\rule{0.25em}{0ex}}k$ and $\phantom{\rule{0.25em}{0ex}}\epsilon $, generating an effective solution for the sparse model specified by Eq. (2). In the following section, we discuss the sparsity control issue to determine the number of variables to be selected.

### Sparsity control using $\phantom{\rule{0.25em}{0ex}}k$

### Further sparsity control using $\phantom{\rule{0.25em}{0ex}}\epsilon $

### Validation

To validate the variable selected using our proposed SRVS algorithm, we compared our selected SNPs and fMRI voxels with that of previous studies. In addition, we used the selected SNPs and fMRI voxels to identify SCZ patients from healthy controls with the sparse representation based classifier (SRC) [15][18]. Then a leave one out (LOO) cross-validation approach was carried out to evaluate the identification accuracy. We compared the classification results with that of Li et al.'s method [21]. Furthermore, we compared the results of using variables selected from one type of data and that of both types of data. We also studied the influences of selecting different number of variables.

## Result

We applied our SRVS method with the sparse model given by Eq. (1) to an integrative analysis of SNP and fMRI data sets. The results were compared with that of Li et al.'s method under different weighting factors. We also discussed the sparsity control issues using $\phantom{\rule{0.25em}{0ex}}k$ and $\phantom{\rule{0.25em}{0ex}}\epsilon $.

### Variable selection with different weight factors

In each of the 16 trials given by Figure 3, we selected the top 200 biomarkers by our proposed SRVS method and by Li et al.'s method [21]. As shown in Figure 3, the weight factor has similar effects on the variable selection of the two methods. It was interesting to see that even though the number of SNPs was much larger than that of fMRI voxels (759075 vs. 153594), similar number of variables were selected from both data sets when weight factor ${\alpha}_{1}$ for SNP data set was around 0.5 (0.46 for SRVS method with ${L}_{0}$ norms, and 0.47 for Li et al.'s method). This suggests that the two data sets may contain similar information for the SCZ case/control study.

### Comparison with Li et al.'s method

The comparison with the reported first 45 SCZ genes (http://www.szgene.org/default.asp). The Index is the order of the specific gene in the top 45 reported genes list.

SRVS (${L}_{0}$) | Li et al.'s method | ||||
---|---|---|---|---|---|

Index | Genes | SNPs | Index | Genes | SNPs |

6 | PDE4B | rs10846559 | 1 | PRSS16 | rs13399561 |

26 | NRG1 | rs12097254 | 11 | DAOA | rs16869700 |

35 | PLXNA2 | rs4811326 | 17 | RPP21 | rs1836942 |

37 | OPCML | rs3026883 | 37 | OPCML | rs1745939 |

To further compare the two methods at different sparsity level, we studied more top variables in each of the 16 trials. To reach this purpose, we set $\epsilon =0.3{y}_{2}$ and $k=0.05$ for SRVS method. For Li's method [21], the number of subjects selected in each run was one tenth of total number of subjects; and we set the threshold $\phantom{\rule{0.25em}{0ex}}\theta $ = 0.01(please refer to [21] for the meaning of $\phantom{\rule{0.25em}{0ex}}\theta $). As a consequence, 500 to 800 variables (SNPs and fMRI voxels) were selected in each trial. In this case, our proposed method selected 20 reported genes. For Li et al.'s method, 14 reported genes were located, and 11 of the top 45 genes were identified by both methods [22]. However, the genes identified by the two methods have <10% overlaps. For the top 50 genes selected by the two methods, there was only one gene, *CSMD1*, was identified by both methods. We listed the top 50 genes and the corresponding SNPs chosen by the two methods in Additional file 2.

Main brain regions of selected voxels using SRVS method

Brain region | Left(L)/Rigth(R) aal | Selected voxels number |
---|---|---|

Precuneus | L/R | 51 |

Precentral Gyrus | L/R | 35 |

Sub-Gyral | L/R | 32 |

Middle Frontal Gyrus | L/R | 26 |

Middle Temporal Gyrus | L | 20 |

Cuneus | R | 17 |

Culmen | L/R | 16 |

Paracentral Lobule | L | 16 |

Lentiform Nucleus | L/R | 13 |

Superior Temporal Gyrus | L/R | 13 |

Declive | L/R | 13 |

Cingulate Gyrus | * | 13 |

Postcentral Gyrus | R | 9 |

Medial Frontal Gyrus | R | 7 |

Superior Frontal Gyrus | R | 7 |

Anterior Cingulate | R | 7 |

### Multivariate classification

*p*-value > 0.1).

From Figure 6 (a) we showed that the highest classification accuracy was achieved at the weight factor ${\alpha}_{1}=0.5$, where around equal sized SNPs and fMRI voxels were selected by the SRVS method. At the two ends (${\alpha}_{1}=0.3\phantom{\rule{0.3em}{0ex}}\mathsf{\text{or}}\phantom{\rule{0.3em}{0ex}}0.6$), the classification accuracies were relatively lower. This suggests that using biomarkers from both types of data may lead to better identification accuracy.

## Discussion

In this study, we introduced a novel sparse representation based variable selection (SRVS) method, and applied it to an integrative analysis of SNP data and fMRI data. In the case of medical imaging data (e.g. fMRI data) or genomic data (e.g. SNP data), the number of samples tend to be much less than the number of variables (e.g. fMRI voxles; SNP loci). As a consequence, many of those variables are correlated and cannot be identified by traditional sparse signal recovery methods. The proposed SRVS method can identify significant variables with high probability, regardless of the coherence conditions required for exact signal recovery in compressive sensing. For example, significant fMRI voxels functionally correlated (within neighbour brain regions) were identified simultaneously by using our proposed SRVS algorithms (see Figure 5 (a)). This manifests the capability of out proposed SRVS method in handling big data set with small sample sizes.

In addition, the proposed SRVS method can be generalized to integrate multiple data modalities for joint analysis and achieve comprehensive diagnosis. As can be seen from Figure 6 (a), the highest classification accuracy was achieved using approximately equal sized variables from both data sets, suggesting that using biomarkers from both types of data may lead to higher diagnosis accuracy.

Another advantage of the SRVS method is its multiple detection resolutions. By choosing different values of widow length $\phantom{\rule{0.25em}{0ex}}k$ one can select different number of variables at different significance level. Furthermore, the error term $\phantom{\rule{0.25em}{0ex}}\epsilon $ can be used for further sparsity control of the solution $\phantom{\rule{0.25em}{0ex}}\delta $, selecting the most important variables. This multi-resolution characteristic of SRVS provides a flexible variable selection approach for big data sets.

When compared to the previous SCZ studies, our method effectively identified more reported SCZ genes than Li et al.'s method. Furthermore, most of the brain regions identified using our proposed SRVS method are previously reported as SCZ associated brain regions. When using the selected variable to identify SCZ patients from controls, our method generated significantly higher classification ratio than Li et al.'s method (Figure 5 (b), $p-\mathsf{\text{value}}\phantom{\rule{0.3em}{0ex}}<{\mathsf{\text{1}}}^{\mathsf{\text{e}}-\mathsf{\text{11}}}$). Those results demonstrated the effectiveness of our method.

## Conclusions

Our proposed SRVS is effective in variable selection for complex disease as SCZ. The biomarkers selected generate better identification accuracy than that of Li et al.'s method. When combining information from fMRI data and SNP data for integrative analysis, higher identification accuracy can be achieved, demonstrating the advantage of the combined analysis.

## Declarations

### Acknowledgements

This work is partially supported by the NIH and NSF.

This work is based on "Bio marker identification for diagnosis of schizophrenia with integrated analysis of fMRI and SNPs ", by Hongbao Cao which appeared in Bioinformatics and Biomedicine (BIBM), 2012 IEEE International Conference on. ^{©} 2012 IEEE [22].

**Declarations**

The publication costs for this article were funded by the corresponding author.

This article has been published as part of *BMC Medical Genomics* Volume 6 Supplement 3, 2013: Selected articles from the IEEE International Conference on Bioinformatics and Biomedicine 2012: Medical Genomics. The full contents of the supplement are available online at http://www.biomedcentral.com/bmcmedgenomics/supplements/6/S3.

## Authors’ Affiliations

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