Multi-Kernel LS-SVM Based Bio-Clinical Data Integration: Applications to Ovarian Cancer

TL;DR

This paper presents a multi-kernel LS-SVM approach for integrating diverse bio-clinical data to improve prediction and stratification in ovarian cancer, demonstrating enhanced accuracy over single data type analyses.

Contribution

It introduces a novel multi-kernel pipeline for integrating molecular and clinical data, improving patient stratification and prediction in ovarian cancer.

Findings

Higher log-rank statistics with integrated data

Improved clinical status prediction accuracy

Effective patient clustering based on multi-omics data

Abstract

The medical research facilitates to acquire a diverse type of data from the same individual for particular cancer. Recent studies show that utilizing such diverse data results in more accurate predictions. The major challenge faced is how to utilize such diverse data sets in an effective way. In this paper, we introduce a multiple kernel based pipeline for integrative analysis of high-throughput molecular data (somatic mutation, copy number alteration, DNA methylation and mRNA) and clinical data. We apply the pipeline on Ovarian cancer data from TCGA. After multiple kernels have been generated from the weighted sum of individual kernels, it is used to stratify patients and predict clinical outcomes. We examine the survival time, vital status, and neoplasm cancer status of each subtype to verify how well they cluster. We have also examined the power of molecular and clinical data in predicting dichotomized overall survival data and to classify the tumor grade for the cancer samples. It was observed that the integration of various data types yields higher log-rank statistics value. We were also able to predict clinical status with higher accuracy as compared to using individual data types.

Tables

Table 1. Table 1: Numbers of samples and features of data types for OV cancer.

Data Type	Platform	$\#$Genes altered in
	Union of considered genes	312 patient
Methylation	Illumina Human Meth.	13772	13772
CNA	Agilent 1M	16383	16070
mRNA expression	AgilentG4502A	18361	16070
Mutation	WUSM	9039	9039

Table 2. Table 2: Patient stratification using molecular data

Cluster	Size	Avg. age	Vital status		neoplasm cancer status
			Deceased	Living	With tumor	Tumor free	Missing
1	33	61.24	13 (39.39)	20 (60.61)	18 (54.54)	11 (33.33)	4 (12.12)
2	48	56.96	27 (56.25)	21 (43.75)	27 (56.25)	10 (20.83)	11 (22.92)
3	50	60.34	31 (62.0)	19 (38.0)	37 (74.0)	10 (20.0)	3 (6.0)
4	47	62.47	34 (72.34)	13 (27.66)	36 (76.59)	6 (12.77)	5 (10.64)
5	53	59.87	31 (58.49)	22 (41.51)	30 (56.60)	17 (32.08)	6 (11.32)

Table 3. Table 3: Patient stratification using clinical data

Cluster	Size	Avg. age	Vital status		neoplasm cancer status
			Deceased	Living	With tumor	Tumor free	Missing
1	50	49.28	30 (60.0)	20 (40.0)	30 (60.0)	14 (28.0)	6 (12.0)
2	64	71.22	38 (59.37)	26 (40.63)	39 (60.94)	17 (26.56)	8 (12.5)
3	45	68.24	27 (60.0)	18 (40.0)	30 (66.67)	9 (20.0)	6 (13.33)
4	72	52.61	51 (70.83)	31 (43.05)	49 (68.06)	14 (19.44)	9 (12.5)

Table 4. Table 4: Patient stratification with linear kernel weights using molecular data and clinical data

Cluster	Size	Avg. age	Vital status		neoplasm cancer status
			Deceased	Living	With tumor	Tumor free	Missing
1	46	55.07	0 (0.0)	46 (100)	15 (32.61)	25 (54.35)	6 (13.04)
2	30	59.23	0 (0.0)	30 (100)	12 (40.0)	15 (50.0)	3 (10.0)
3	108	60.74	108 (100)	0 (0.0)	91 (84.26)	4 (3.70)	13 (12.04)
4	24	63.29	24 (100)	0 (0.0)	22 (91.67)	0 (0.0)	2 (8.33)
5	23	64.87	4 (17.39)	19 (82.61)	8 (34.78)	10 (43.48)	5 (21.74)

Table 5. Table 5: Patient stratification with optimized kernel weights using molecular data and clinical data

Cluster	Size	Avg. age	Vital status		Neoplasm cancer status
			Deceased	Living	With tumor	Tumor free	Missing
1	15	59.53	1 (6.67)	14 (93.33)	4 (26.67)	10 (66.67)	1 (6.67)
2	19	63	19 (100)	0 (0.0)	17 (89.47)	0 (0.0)	2 (10.53)
3	37	67.38	37 (100)	0 (0.0)	33 (89.19)	0 (0.0)	4 (10.81)
4	52	56.60	52 (100)	0 (0.0)	41 (78.85)	3 (5.76)	8 (15.38)
5	81	58.09	0 (0.0)	81 (100)	29 (35.80)	40 (49.38)	12 (14.81)
6	27	61.11	27 (100)	0 (0.0)	24 (88.89)	1 (3.70)	2 (7.41)

Table 6. Table 6: Patient survival risk prediction with individual data types.

Data types	TP	FP	TN	FN	Spec.	Sens.	Acc.
CNA	0.6904	0.3095	0.7368	0.2632	74.36	68.29	71.25
Mutation	0.6667	0.3333	0.7105	0.2895	71.79	65.85	68.75
Methylation	0.6905	0.3095	0.7105	0.2895	72.5	67.5	70
mRNA	0.6428	0.3571	0.6842	0.3158	69.23	63.41	66.25
Clinical	0.7143	0.2857	0.73684	0.2632	75.0	70.0	72.5
CNA+Mutation+mRNA Methylation	0.7381	0.2619	0.7368	0.2632	75.61	71.79	73.75

Table 7. Table 7: Pateint survival risk prediction with individual data types and clinical.

Data types	TP	FP	TN	FN	Spec.	Sens.	Acc.
CNA+clinical	0.7143	0.2857	0.7368	0.2632	75	70	72.5
Mutation+clinical	0.6667	0.3333	0.7368	0.2632	73.68	66.67	70
Methylation+clinical	0.7143	0.2857	0.7105	0.2895	73.17	69.23	71.25
mRNA+clinical	0.6429	0.3571	0.7368	0.2632	72.97	65.12	68.75
CNA+Mutation+Methylation +mRNA+Clinical	0.7619	0.2381	0.7632	0.2368	78.05	74.36	76.25

Equations

$$k_{linear}({\mathbf{x}}_i,{\mathbf{x}}_j)=<{\mathbf{x}}_i\cdot {\mathbf{x}}_j>.$$

$$k_{RBF}({\mathbf{x}}_i,{\mathbf{x}}_j)=exp(-||{\mathbf{x}}_i-{\mathbf{x}}_j|{|}^2/2{\sigma }^2),$$

$$K_{\beta }({\mathbf{x}}_i,{\mathbf{x}}_j)=\sum _{s=1}^S{\beta }_s{k}_s(\varphi ({\mathbf{x}}_i^s),\varphi ({\mathbf{x}}_j^s))$$

$$\text{subjected to }{\beta }_s\ge 0\text{ and }\sum _{s=1}^S{\beta }_s=1,$$

$$\underset{\mathbf{w},b,err}{\min }(\frac{1}{2}{\mathbf{w}}^T\mathbf{w}+\gamma \sum _{i=1}^{N}er{r}_i^2)$$

$$\text{subjected to }{y}_i[{\mathbf{w}}^T\varphi ({\mathbf{x}}_i)+b]=1-er{r}_i^2\text{ for }i=1,2,\dots ,N$$

$$\underset{\beta ,\mathbf{w},b,err}{\min }(\frac{1}{2}\sum _{s=1}^S\beta {\mathbf{w}}^T\mathbf{w}+\gamma \sum _{i=1}^{N}er{r}_i^2)$$

$$\begin{array}{rl}\text{w.r.t. }& w_k\in {\Re }^{D_k},err\in {\Re }^N\end{array}$$

$$\begin{array}{r}\text{subjected to }\{\begin{array}{l}{y}_i(\sum _{s=1}^S{\beta }_s{\mathbf{w}}_s^T{\varphi }_k({\mathbf{x}}_i)+b)=1-er{r}_i^2,\\ er{r}_i\ge 0\text{ for }i=1,2,\dots ,N,\\ \sum _{s=1}^S{\beta }_s=1,{\beta }_s\ge 0\text{ for }s=1,2,\dots ,S.\end{array}\end{array}$$

$$\min \delta -\sum _{s=1}^S{\alpha }_i$$

$$\delta \in \Re ,\alpha \in {\Re }^N$$

$$\begin{array}{r}\text{subjected to }\{\begin{array}{l}0\le \alpha \le 1\gamma ,\sum _{i=1}^S{\alpha }_i{y}_i=0\\ \frac{1}{2}\sum _{i,j=1}^S{\alpha }_i{\alpha }_j{y}_i{y}_j{k}_k(x_i,x_j)\le \delta ,\forall =1,\dots ,K\end{array}\end{array}$$

$$D(\{{\pi }_c{\}}_{c=1}^k)=\sum _{c=1}^k\sum _{{\mathbf{x}}_i\in {\pi }_c}||\varphi ({\mathbf{x}}_i)-{\mathbf{m}}_c|{|}^2$$

$$||\varphi ({\mathbf{x}}_i)-{\mathbf{m}}_c||$$

Full text

Multi-Kernel LS-SVM Based Integration Bio-Clinical Data Analysis and Application to Ovarian Cancer

Jaya Thomas1,2, Lee Sael1,2*

1 Department of Computer Science, SUNY Korea, Incheon, Republic of Korea

2 Department of Computer Science, Stony Brook University, Stony Brook, NY, USA

Abstract

The medical research facilitates to acquire a diverse type of data from the same individual for a particular cancer. Recent studies show that utilizing such diverse data results in more accurate predictions. The major challenge faced is how to utilize such diverse data sets in an effective way. In this paper, we introduce a multiple kernel based pipeline for integrative analysis of high-throughput molecular data (somatic mutation, copy number alteration, DNA methylation and mRNA) and clinical data. We apply the pipeline on Ovarian cancer data from TCGA. After multiple kernels have been generated from the weighted sum of individual kernels, it is used to stratify patients and predict clinical outcomes. We examine the survival time, vital status, and neoplasm cancer status of each subtype to verify how well they cluster. We have also examined the power of molecular and clinical data in predicting dichotomized overall survival data and to classify the tumor grade for the cancer samples. It was observed that the integration of various data types yields higher log-rank statistics value. We were also able to predict clinical status with higher accuracy as compared to using individual data types.

1 Introduction

Cancer is a disease with extreme complexity which alters the function of combinations of genes. It is believed to be an outcome of accumulated genetic changes [1]. Among various types of cancer, ovarian cancer is the fifth most common cancers diagnosed in females [25] with overall five-year survival rate only around 44$\%$[4]. The Cancer Genome Atlas (TCGA)[34] reports diverse genomic information with paired clinical information for more than 500 cases of ovarian serous cystadenocarcinoma. The genomic information includes copy number alteration (CNA), somatic mutation, gene expression, and DNA methylation. Understanding the genetic changes in cancer patients through this rich information allows for better diagnostics and treatment of cancer, including ovarian cancer.

Integrative analysis of multiple perspectives of a patient helps in both patient stratification and clinical outcome prediction. Patient stratification and clinical outcome predictions both help the researchers in understanding and exploring the genomic characteristics in a relationship with their current phenotypes and thus to recognizing opportunities for clinical improvement. In the case of cancer data analysis, including ovarian cancer data, an improved stratification and clinical prediction can be achieved by integrative analysis of the multiple bio-clinical data. However, due to the complex relationship between the multiple data types, the integrative analysis is still a challenging task.

There are several works related to clinical outcome predictions. Wang et al. [39] have used gene expression data to predict distant metastasis of lymph-node-negative primary breast cancer. They identified a 76-gene signature consisting of 60 genes for patients positive for estrogen receptors (ER) and 16 genes for ER-negative patients. Teschendorff et al. [33] proposed a gene expression classifier for ER positive breast cancer. Zhang et al. [45] used copy number alterations in combination with gene expression to identify the genomic loci and their mapped genes, having a high correlation with distant metastasis capability of human breast cancer. Deneberg et al. [8] used gene specific and global methylation patterns predict outcome in patients with acute myeloid leukemia. They also concluded in their work that global and gene specific methylation patterns are independently associated with the clinical outcome in AML patients. Nair et al. [21] reported a comprehensive review on the clinical outcome prediction by the miRNA expression for numerous types of cancer. These approaches only integrated a smaller number of data types and failed to integrate with other levels of genomic data.

On the other hand, for the patient stratification, biomarkers, genetic profiles, research data along with clinical information are used to find a subgroup of the patients thereby making easier to detect and interpret relationships as well as predict outcomes in a specific subgroup. Kim et al.[14] considers somatic mutation profile and exploited k-means clustering to identify the tumor subtypes. The sparsity of the mutation data was handled by applying Jaccard and Euclidean distance measures. Further, the Cox proportional hazards regression model was used to find the similarity between the derived subtypes and the patient survival time. In their recent work [15], a compressed somatic mutation profile was suggested for fast comparison. The profile utilized Gene-Ontology and non-negative matrix factorization for condensing the mutation profile. To verify their work, stratification was performed on various cancer types. Hofree et al. [11] has used genome-scale somatic mutation profiles in combination with a gene interaction network to carry out subgrouping of patients. Recently, Wang et al.[38] proposed a modified consensus clustering to carry out patient stratification for breast cancer patients. The approach considered both numerical and categorical data for mRNA and miRNA data set.

Analysis of one or few data types may not be sufficient for accurate predict or stratification. Thus, efforts to integrate the molecular data were carried out. Thomas et al.[36] work presents two general class of heterogeneous data integration, i.e., Multiple Kernel learning and Bayesian network, are detailed and discussed in the bioinformatics domain. Also, many problem-specific integrative approaches have been proposed to associate the molecular data with the clinical outcome. These include a software package implemented in R [19] to show the effect of DNA methylation and copy number alterations in gene expression of several known oncogenes for two cancer type glioblastoma multiforme and ovarian. Kim et al. [13] proposed a graph based integrated framework using CNA, methylation, miRNA, and gene expression data to carry out a molecular based classification of clinical outcomes. In this approach, a single graph was constructed by determining the optimum linear combination coefficient from the multiple graphs obtained at different genomic level. Sohn et al. [29] modeled the influence of multi-layered genomic features on gene expression traits by modeling an integrative statistical framework based on a sparse regression. The results showed that using CNA, miRNA, and methylation on gene expression in the predictive power for gene expression level is improved over a single data type based analysis. Schafer et al. ([26] approach integrated copy number and gene expression by a modified correlation coefficient and an explorative Wilcoxon test to find DNA regions of abnormalities. The recent work also includes model based prediction of clinical outcomes. Mankoo et al. [20] have applied multivariate Cox Lasso model and median time-to-event prediction algorithm on data set integrated from the four genomic data types (CNA, methylation, miRNA, and gene expression data). Yuan et al. [43] evaluated the predictive power of patient survival and binary clinical outcome using clinical data in combination with one molecular data: somatic copy number alteration, DNA methylation, and mRNA, miRNA and protein expression. They showed a slight improvement in some cases when clinical information was combined with one of the molecular. Although this paper showed the predictive power of clinical data in combination with a molecular data, all available molecular data was not used integratively.

An integrative analysis method that can cover heterogeneity of data types in molecular data and clinical data can beneficial in predicting the prognostics of patients via stratifying the patients in the different risk groups. Multiple kernel learning is well known for addressing various data heterogeneity. Moreover, Kernel methods, including multiple kernels, are well-suited for handling non-linearity of high dimensional data by mapping data to feature space [5].

In this paper, we make the following contributions:

• •

Combines clinical data with multiple molecular data. We examine how adding more molecular information increases the prediction performance in stratifying ovarian cancer patients, and predicting tumor grade and patient survival time.

• •

Propose a multiple kernel based pipeline model (Fig. 1) to integrate multiple heterogeneous data types. The proposed model allows to analyze heterogeneous data i.e., combines data with diverse background distributions, relations, dimensions, and formats to enhance the statistical significance and thus, obtain more refined information.

• •

Propose the data pre-processing using patient-centered gene set analysis. It allows to handle the large heterogeneous tumor data by grouping them into much smaller set of pathways and biologic processes.

2 Material and methods

2.1 Datasets and Raw Mutation Scores

Data are initially selected and downloaded 312 samples that contained all four genomic data types, i.e., copy number alternation, methylation, mRNA expression and the mutation information, from TCGA data portal [32] via TCGA assembler [46] and TCGA Firehose [6]. The summary of the genomic data types and number of associated genes for each data type in the 312 samples are shown in Table 2.1. Clinical information of the 312 samples is also downloaded from TCGA. The clinical data includes the survival time (days to death), age, tumor stage, tumor grade, vital status and neoplasm cancer status.