Investigating the utility of clinical outcome-guided mutual information network in network-based Cox regression
- Hyun-hwan Jeong^{1},
- So Yeon Kim^{1},
- Kyubum Wee^{1} and
- Kyung-Ah Sohn^{1}Email author
https://doi.org/10.1186/1752-0509-9-S1-S8
© Jeong et al.; licensee BioMed Central Ltd. 2015
Published: 21 January 2015
Abstract
Background
Network-based approaches have recently gained considerable popularity in high- dimensional regression settings. For example, the Cox regression model is widely used in expression analysis to predict the survival of patients. However, as the number of genes becomes substantially larger than the number of samples, the traditional Cox or L_{2}-regularized Cox models are still prone to noise and produce unreliable estimations of regression coefficients. A recent approach called the network-based Cox (Net-Cox) model attempts to resolve this issue by incorporating prior gene network information into the Cox regression. The Net-Cox model has shown to outperform the models that do not use this network information.
Results
In this study, we demonstrate an alternative network construction method for the outcome-guided gene interaction network, and we investigate its utility in survival analysis using Net-Cox regression as compared with conventional networks, such as co-expression or static networks obtained from the existing knowledgebase. Our network edges consist of gene pairs that are significantly associated with the clinical outcome. We measure the strength of this association using mutual information between the gene pair and the clinical outcome. We applied this approach to ovarian cancer patients' data in The Cancer Genome Atlas (TCGA) and compared the predictive performance of the proposed approach with those that use other types of networks.
Conclusions
We found that the alternative outcome-guided mutual information network further improved the prediction power of the network-based Cox regression. We expect that a modification of the network regularization term in the Net-Cox model could further improve its prediction power because the properties of our network edges are not optimally reflected in its current form.
Keywords
Background
The Cox regression model [1] has been commonly used in survival analysis to detect important features and to predict patient survival. Due to the advance of sequencing technology, the number of genes or features in these analyses is becoming substantially larger than the number of samples. Although several variant models, such as L_{1} −regularization [2] or L_{2} −regularization in Hilbert space [3], have been proposed to resolve this issue, those variant models are still prone to noise and over-fitting [4]. Recently, network-based approaches have gained considerable popularity for expression quantitative trait loci (eQTL) studies and clinical outcome predictions in high-dimensional regression settings. These approaches incorporate prior network information of either the features [5] or outcomes [6], or both [7, 8]. For survival analysis, Zhang et al. [9] recently proposed a variant of the L_{2} −regularized Cox model called the Net-Cox model, which is a network-regularized Cox regression model. The typical types of networks used in such approaches are either coexpression networks, which are constructed by computing the correlation between every pair of variables, or static networks, such as the protein-protein interaction (PPI) network, which can be obtained from the existing knowledgebase. In the Net-Cox model, co-expression and functional linkage networks were incorporated in the survival analysis, and the results showed enhanced performance when compared with the conventional methods, which do not use the network information.
A potential limitation of these conventional networks is that the edges only reflect the information of within-features or within-outcomes relations, and do not consider the association between features and outcomes, which may be useful in improving the predictive power. In this study, we show that the outcome-guided mutual information network improves the performance of survival analysis in the Net-Cox regression [9]. We demonstrate the utility of this outcome-guided gene network with the analysis of a TCGA ovarian cancer dataset and compare its performance with those of survival analyses that use other types of networks.
Methods
Background on survival analysis using Cox regression
Regularized Cox regression in high-dimensional setting
in which λβ′Γβ is the penalty term and Γ = (1 - α) L + αI conveys prior network information between genes. Here, L = I − S, where I is the identity matrix and S is a normalized Laplacian matrix, which comes from the gene network.
The parameter α ∈ (0,1] controls the contribution of network information to the model. When α is small, more network information is incorporated into the penalty term than when α is large. We note that when α = 1, the network-based cox regression model reduces to the L_{2} −Cox model that does not use any network information.
The typical network used for this type of network-based approach is the coexpression network, in which the edge weights correspond to the correlation between expression vectors of two genes [6]. In [9], a functional linkage network was constructed from the existing knowledgebase. We note that both types of networks do not reflect information about the relation between the features and the outcomes inferred from a given dataset. Therefore, we consider an alternative approach of constructing and utilizing outcome-guided mutual information network in survival analysis. The detailed procedures are explained in the following sections.
Gene interaction networks associated with clinical outcome
Note that genomic feature values, such as gene expressions or clinical outcome values, are often numeric. To compute the mutual information, we discretize the genomic feature values using a histogram-based technique as in [14]. In the case of survival data, a simple thresholding scheme converts the outcome variable of the survival month to a binary variable. In the case of the TCGA dataset used in this study, we split the patients into short-term living (≤ 3 years) and long-term living (> 3 years). Patients who are reported as living and have an overall survival time less than 3 years are filtered out of this study.
where P is the set of all genes, Y denotes the binary survival status of patients, and I(g_{ i }, g_{ j }; Y) is the mutual information of the gene pair (g_{ i }, g_{ j } ) and Y. We adopt this thresholding scheme and test the performance of different parameter values. In order to apply the network to the Net-Cox model, we also normalize G_{ σ }and create a normalized Laplacian matrix $\mathsf{\text{S}}={\mathsf{\text{R}}}^{-\frac{1}{2}}{G}_{\sigma}{C}^{-\frac{1}{2}}$, where ${\mathsf{\text{R}}}_{ii}={\displaystyle {\sum}_{j}}{G}_{{\sigma}_{ij}}$ and ${\mathsf{\text{C}}}_{ii}={\sum}_{j}{G}_{{\sigma}_{ij}}^{\prime}$ both of which are diagonal matrices.
Dataset
We use genomic profiles and clinical outcome data from patients with ovarian serous cystadenocarcinoma in TCGA. Genomic profiles of copy number alterations (CNAs), messenger RNA (mRNA), and methylation (METH) are used in the experiments. We remove genes or patients with missing values and extract genes that are common to all three profiles. As a result, our data matrix consists of expressions and alterations of 10,022 genes and 340 patients for each of the three profiles.
Evaluation measure
We compare the performance of the Net-Cox model using the proposed mutual information networks with those of models using a gene co-expression and gene functional linkage network as seen in [9]. In order to create a baseline, an analysis of the L_{2} − Cox model, which does not use any network information, is performed. This is the same as setting α = 1 in the Net-Cox model.
With each run of the Net-Cox analysis, the prognostic indices $PI={X}^{\prime}\widehat{\beta}$ are calculated as prediction markers, where X is the test data not used in training, and the regression coefficient $\widehat{\beta}$ is estimated from given training data, network information, and the parameters. We evaluate the prediction performance using a time-dependent area under the curve (AUC) [15].
in which c is the cut-off point, t is the survival time, f(X) are the prognostic indices, $f\left(X\right)={\mathsf{\text{X}}}^{\prime}\beta $and δ(t) is the event indicator at time t [16]. Upon examination of sensitivity[c, t|f(X)] and 1 - specificity[c, t|f(X)], we can define ROC[t|f(X)] as receiving operating characteristic (ROC) curves at any time t and AUC[t|f (X) ] as the area under the ROC curves at any time t. The larger AUC[t|f(X)] is, the better our prediction model performs at time t.
In addition, we evaluate the performance, using a validation set and the log-rank test [17], to analyze whether the patients are properly classified: high-risk or low-risk. We rank patients in descending order by their prognostic indices (PI) and divide them into a high-risk group containing the top 40% of patients and a low-risk group containing the bottom 40%. We then test the validity of this group assignment by using the log-rank test and the true survival information.
Cross validation
We select the optimal parameters, λ and α, that respectively control the degree of sparsity and the amount of network constraint in the Net-Cox model using a 5-fold cross validation process. We reserve 20% of all the samples in this study for validation (the validation set) and use the remaining 80% (the training set) for cross validation in order to optimize the parameters and check the cross-validation error. In the case of mutual information networks, we also choose the optimal σ using cross-validation. The average time-dependent AUC is used as an evaluation measure for each genomic profile and the different kinds of networks.
We trained each model five times using a 5-fold cross validation process on the training set. At each run, we estimate the regression coefficient $\widehat{\beta}$ and the mutual information network (or co-expression network) on four folds of the training data. The estimated coefficient $\widehat{\beta}$ and the remaining fold, consisting of 20% of the training data, are then used to calculate the prognostic indices PI = X′β, which are, in turn, used to rank the patients according to their expected survival time, or month.
To examine how the mutual information network filtered by significance level σ contributes to the performance of the Net-Cox model, we experiment with the complete mutual information network and those networks filtered by σ, where σ = [0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3] for each profile. This corresponds to eight mutual information networks on each profile, including the complete network. We vary the parameters λ = [10^{−4},10^{−3}, 10^{−2}, 10^{−1}] and α = [0.1, 0.3, 0.5, 0.7, 0.9, 1]. As a result, we choose the optimal (λ, α) pair with the best performance, in terms of the time-dependent ROC curves, for each network and each profile.
Enrichment analysis
In order to assess the biological significance of the results, we performed a gene list enrichment analysis for the 100 genes with the largest regression coefficients for each profile using ToppGene http://toppgene.cchmc.org[18]. The enrichment analysis is based on Gene Ontology [19] and Pathway and Disease [20]. The terms that have adjusted p-values under 0.05 when using the Benjamini-Hochberg correction [21] are considered biologically significant. We also ran the enrichment test on the genes in the network consisting of the 100 edges with the largest mutual information values for each profile.
Results and discussion
Optimal parameter selection using cross validation
Optimal parameters and averaged time-dependent AUCs of each network using 5-fold cross validation on training data
Profile | Network | σ | λ | α | Mean (time AUC) |
---|---|---|---|---|---|
CNA | Mutual Information | 0.30 | 10^{−3} | 0.1 | 0.5875 |
Correlation | - | 10^{−3} | 0.9 | 0.5817 | |
Functional Linkage | - | 10^{−3} | 0.3 | 0.5786 | |
L_{2} − Cox | - | 10^{−3} | 1.0 | 0.5810 | |
mRNA | Mutual Information | 0.10 | 10^{−4} | 0.1 | 0.6317 |
Correlation | - | 10^{−4} | 0.9 | 0.6280 | |
Functional Linkage | - | 10^{−4} | 0.3 | 0.6242 | |
L_{2} − Cox | - | 10^{−4} | 1.0 | 0.6288 | |
METH | Mutual Information | 0.30 | 10^{−4} | 0.5 | 0.5912 |
Correlation | - | 10^{−4} | 0.7 | 0.5894 | |
Functional Linkage | - | 10^{−4} | 0.3 | 0.5860 | |
L_{2} − Cox | - | 10^{−4} | 1.0 | 0.5899 |
Performance comparison on validation set
Signature genes for each profile
We find that the identified genes are associated with ovarian cancer in many previous studies. The gene with the largest coefficient in the CNA profile was URI1, prefoldin-like chaperone (URI1), which is reported to be an oncogene that amplified in ovarian cancer cells [22]. Dual-Specificity Tyrosine-(Y)-Phosphorylation Regulated Kinase 1B (DYRK1B), which is over-expressed in a wide spectrum of ovarian cancer cell lines and human specimens [23], was the fourth highest gene. The largest coefficient gene from the mRNA profile, Oviductal Glycoprotein 1 (OVGP1), is reported to be a more accreted detection marker than other markers of ovarian epithelial cancers [24]. Over-expression of the Elafin/Peptidase Inhibitor 3 (PI3) gene from the mRNA profile is associated with poor overall survival [25]. We found no reported associations of the top five genes in the methylation profile with ovarian cancer from previous studies.
Significantly enriched terms (using ToppGene) in the 100 genes that have the largest regression coefficients for each profile
Profile | Category | ID | Name | p-value | Adjusted p-value | Count | Total |
---|---|---|---|---|---|---|---|
CNA | GO:BP | GO:0048706 | embryonic skeletal system development | 5.99E-06 | 1.25E-02 | 7 | 129 |
GO:BP | GO:0048704 | embryonic skeletal system morphogenesis | 1.43E-05 | 1.50E-02 | 6 | 98 | |
GO:BP | GO:0009952 | anterior/posterior pattern specification | 2.17E-05 | 1.52E-02 | 8 | 217 | |
Disease | ctd:D010051 | Ovarian Neoplasms | 5.24E-04 | 2.84E-02 | 4 | 78 | |
Disease | ctd:D002277 | Carcinoma | 7.42E-03 | 3.66E-02 | 4 | 161 | |
GO:BP | GO:0031442 | positive regulation of mRNA 3'-end processing | 7.94E-05 | 4.15E-02 | 3 | 16 | |
GO:BP | GO:0031440 | regulation of mRNA 3'-end processing | 1.15E-04 | 4.80E-02 | 3 | 18 | |
mRNA | GO:MF | GO:0004568 | chitinase activity | 4.80E-06 | 1.78E-03 | 3 | 7 |
GO:BP | GO:0006032 | chitin catabolic process | 4.83E-06 | 4.94E-03 | 3 | 7 | |
GO:BP | GO:0006030 | chitin metabolic process | 4.83E-06 | 4.94E-03 | 3 | 7 | |
GO:BP | GO:1901072 | glucosamine-containing compound catabolic process | 7.70E-06 | 5.24E-03 | 3 | 8 | |
GO:MF | GO:0086080 | protein binding involved in heterotypic cell-cell adhesion | 8.12E-05 | 1.50E-02 | 2 | 3 | |
GO:MF | GO:0098631 | protein binding involved in cell adhesion | 1.62E-04 | 1.50E-02 | 2 | 4 | |
GO:MF | GO:0098632 | protein binding involved in cell-cell adhesion | 1.62E-04 | 1.50E-02 | 2 | 4 | |
GO:BP | GO:0046348 | amino sugar catabolic process | 3.86E-05 | 1.97E-02 | 3 | 13 | |
GO:MF | GO:0008061 | chitin binding | 2.69E-04 | 1.99E-02 | 2 | 5 | |
GO:MF | GO:0030492 | hemoglobin binding | 7.45E-04 | 4.61E-02 | 2 | 8 | |
METH | GO:CC | GO:0030424 | axon | 9.91E-06 | 1.95E-03 | 11 | 409 |
GO:CC | GO:0043025 | neuronal cell body | 2.06E-04 | 1.57E-02 | 10 | 478 | |
GO:CC | GO:0043195 | terminal bouton | 3.15E-04 | 1.57E-02 | 4 | 62 | |
GO:CC | GO:0036477 | somatodendritic compartment | 3.19E-04 | 1.57E-02 | 12 | 705 | |
GO:CC | GO:0043005 | neuron projection | 4.07E-04 | 1.61E-02 | 14 | 945 | |
GO:CC | GO:0044297 | cell body | 5.10E-04 | 1.68E-02 | 10 | 536 | |
GO:CC | GO:0032983 | kainate selective glutamate receptor complex | 7.48E-04 | 2.11E-02 | 2 | 8 | |
GO:MF | GO:0004952 | dopamine neurotransmitter receptor activity | 2.80E-04 | 4.01E-02 | 2 | 5 | |
GO:MF | GO:0001965 | G-protein alpha-subunit binding | 3.95E-04 | 4.01E-02 | 3 | 27 | |
GO:MF | GO:0015075 | ion transmembrane transporter activity | 4.14E-04 | 4.01E-02 | 13 | 819 | |
GO:MF | GO:0022857 | transmembrane transporter activity | 5.21E-04 | 4.01E-02 | 14 | 951 | |
GO:MF | GO:0015026 | coreceptor activity | 5.98E-04 | 4.01E-02 | 3 | 31 | |
GO:MF | GO:0022891 | substrate-specific transmembrane transporter activity | 7.68E-04 | 4.29E-02 | 13 | 875 | |
GO:MF | GO:0022892 | substrate-specific transporter activity | 9.57E-04 | 4.58E-02 | 14 | 1012 |
Network analysis
Network properties of mutual information sub-network for each profile
Properties | CNA | mRNA | METH |
---|---|---|---|
Nodes | 78 | 154 | 149 |
Connected components | 7 | 54 | 50 |
Network centralization | 0.312 | 0.058 | 0.052 |
Characteristic path length | 2.117 | 2.187 | 2.164 |
Average number of neighbors | 2.564 | 1.299 | 1.342 |
Network density | 0.033 | 0.008 | 0.009 |
Network heterogeneity | 1.383 | 0.828 | 0.809 |
R ^{ 2 } of node degree distribution | 0.672 | 0.922 | 0.909 |
Significantly enriched terms (using ToppGene) in the sub-network consisting of the gene pairs that have the 100 largest mutual information values.
Profile | Category | ID | Name | p-value | Adjusted p-value | Count | Total |
---|---|---|---|---|---|---|---|
CNA | Disease | ctd:D006949 | Hyperlipidemias | 1.76E-05 | 2.24E-03 | 3 | 13 |
Disease | ctd:D009765 | Obesity | 1.98E-03 | 1.21E-02 | 4 | 132 | |
Disease | ctd:D007333 | Insulin Resistance | 8.96E-03 | 2.42E-02 | 2 | 35 | |
Disease | ctd:D009369 | Neoplasms | 1.05E-02 | 2.78E-02 | 2 | 38 | |
mRNA | Disease | ctd:D002277 | Carcinoma | 1.19E-04 | 1.23E-02 | 8 | 161 |
Disease | ctd:D009364 | Neoplasm Recurrence, Local | 1.25E-02 | 4.96E-02 | 3 | 52 | |
METH | GO:MF | GO:0008528 | G-protein coupled peptide receptor activity | 4.15E-05 | 1.21E-02 | 7 | 120 |
GO:MF | GO:0001653 | peptide receptor activity | 4.86E-05 | 1.21E-02 | 7 | 123 | |
GO:MF | GO:0004942 | anaphylatoxin receptor activity | 1.78E-04 | 1.78E-02 | 2 | 3 | |
GO:MF | GO:0004948 | calcitonin receptor activity | 1.78E-04 | 1.78E-02 | 2 | 3 | |
GO:MF | GO:0004800 | thyroxine 5'-deiodinase activity | 1.78E-04 | 1.78E-02 | 2 | 3 |
Conclusions
In this study, we investigated the utility of an alternative network construction approach based on mutual information in network-based Cox regression. Our results show that the mutual information based network can further improve prediction performance in survival analyses. Moreover, the permutation testing scheme used to discard insignificant pairs improved the prediction performance.
Overall, the performance gain of this alternative approach over existing methods was rather marginal. It seems due to a mismatch between the high mutual information value and the small value of the penalty term $\left(\psi \left(\beta \right)\right)=\frac{1}{2}{\sum}_{i,j}^{p}{S}_{i,j}{\left({\beta}_{i}-{\beta}_{j}\right)}^{2})$ in the Net-Cox model--it does not necessarily mean that the gene pairs containing high mutual information with respect to survival should have similar marginal effects because the mutual information measure is more concerned with the interaction effect. Even with this discrepancy, results based on the mutual information network are still promising. In future studies, the regularization term could be modified to better reflect the information contained in the mutual information network and, hence, further improve the performance. Another direction would be to apply this network scheme to network-based approaches in other domains.
Declarations
Acknowledgements
This research was supported by the Basic Science Research Program through the National Research Foundation (NRF) of Korea funded by the Ministry of Science, ICT, and Future Planning (MSIP) (No. 2010-0028631), and by the Ministry of Education (2012R1A1A2042792).
Declarations
The publication costs of this article were funded by Ajou University, S. Korea.
This article has been published as part of BMC Systems Biology Volume 9 Supplement 1, 2015: Selected articles from the Thirteenth Asia Pacific Bioinformatics Conference (APBC 2015): Systems Biology. The full contents of the supplement are available online at http://www.biomedcentral.com/bmcsystbiol/supplements/9/S1
Authors’ Affiliations
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