Abstract
Recently, with the rapid progress of high-throughput sequencing
technology, diverse genomic data are easy to be obtained. To
effectively exploit the value of those data, integrative methods are
urgently needed. In this paper, based on SNF (Similarity Network
Diffusion) [[28]1], we proposed a new integrative method named ndmaSNF
(network diffusion model assisted SNF), which can be used for cancer
subtype discovery with the advantage of making use of somatic mutation
data and other discrete data. Firstly, we incorporate network diffusion
model on mutation data to make it smoothed and adaptive. Then, the
mutation data along with other data types are utilized in the SNF
framework by constructing patient-by-patient similarity networks for
each data type. Finally, a fused patient network containing all the
information from different input data types is obtained by using a
nonlinear iterative method. The fused network can be used for cancer
subtype discovery through the clustering algorithm. Experimental
results on four cancer datasets showed that our ndmaSNF method can find
subtypes with significant differences in the survival profile and other
clinical features.
Keywords: cancer subtyping, integrative method, network diffusion,
somatic mutation data
INTRODUCTION
Cancer is believed to be a complicated and heterogeneous disease since
that it is driven by different combinations of mutated genes rather
than the individual gene, and those mutations vary among tumor samples.
Great efforts have been made by several large-scale projects such as
The Cancer Genome Atlas (TCGA) [[29]2], International Cancer Genome
Consortium (ICGC) [[30]3], and Cancer Cell Line Encyclopedia (CCLE)
[[31]4], etc., which generated a sea of multiple genomic platform data.
Therefore, integrative methods are urgently needed to simultaneously
employ those molecular data for identification of tumor subsets with
different clinical and biological meaning.
Until now, many successful researches on such integrative framework for
cancer subtype identification have been published. For instance, Liu et
al. [[32]5] brought forward a method using regularized non-negative
matrix factorization for gene expression analysis. Liu et al. [[33]6]
also came up with an approach for integrated analysis via
block-constraint robust principal component analysis. Gu et al. [[34]7,
[35]8] came up with approaches which had made progress in
classification and regression. Shen et al. [[36]9] proposed a joint
latent variable model named iCluster which can realize data integration
and dimensionality reduction simultaneously. Clustering result can be
obtained by applying a standard K-means algorithm on the joint latent
variable. Though pioneering and effective, iCluster to a great extent
relies on the step of feature preselection. Wang et al. [[37]1]
introduced a distinct integrative approach called SNF which contains a
few steps. First, for each data type, a sample-by-sample similarity
network is constructed using the Euclidean distance and a scaled
exponential similarity kernel, then these similarity networks are fused
into one single network by a nonlinear iterative method. At last, this
fused network is clustered by spectral clustering to receive several
tumor groups. In SNF, diverse data such as DNA methylation, mRNA
expression and miRNA expression data were used for identification of
meaningful cancer subtypes. However, those data types are with
continuous value for which the Euclidean metric is suitable. Obviously,
it turns out to be helpless with discrete profile such as somatic
mutation data. Indeed, for discrete data they do propose to use
chi-squared distance (Supplementary Note-Chi-squared distance) to
calculate the similarity between the patients, nevertheless by which we
cannot get a satisfactory result.
There are intrinsic differences between mutation data and other data
types with quantitative value: (i) mutation data has binary value so it
is not suitable for Euclidean measurement; (ii) high-dimensionality
makes typical binary similarity measures hard to be used; (iii) its
sparseness (fewer than 100 genes mutated in nearly ten thousand genes)
makes it heterogeneous such that clinically identical patients rare to
share more than a single mutation. So it makes traditional
distance-based similarity measurement impossible to be used. Actually,
somatic mutation data has important value since it provides information
about relationships between genes and biochemical pathways and
comprehensive insight into tumor progress [[38]10]. To deal with this
problem, Hofree et al. [[39]11] brought forward a method named NBS
(network-based stratification) which integrated somatic mutation data
with gene networks using network diffusion model and performed
clustering in a consensus clustering framework to make result robust.
It shows that somatic mutation data is a promising source for cancer
subtype identification. However, NBS did not use any other levels of
information data such as epigenome, transcriptome, etc.
In this paper, we proposed a method named ndmaSNF (network diffusion
model assisted SNF) based on the integrative framework of SNF [[40]1]
for cancer subtype identifying using somatic mutation profile and other
data from different platforms simultaneously. Figure [41]1 shows the
schematic overview of our method. We roughly divided the data sources
into two categories: continuous data and discrete data (Figure [42]1A).
For discrete data (e.g. mutation status), we made it fit the framework
of SNF by using network diffusion model (Figure [43]1B) along with gene
interaction network. Then the discrete data was smoothed and could be
used well via SNF framework together with those continuous data (Figure
[44]1C). By combining similarity matrices from those two different
kinds of data, a fused patient-by-patient similarity matrix was
obtained through the nonlinear combination method used in SNF framework
(Figure [45]1D). On this fused matrix, clustering result can be
acquired by applying a clustering algorithm such as spectral
clustering. We extensively applied ndmaSNF on several human cancer data
sets consisted of various kinds of data types, and received
biologically and clinically relevant cohorts of patients, with better P
value and silhouette value compared to SNF. The clustering result
broadly met the PAM50 classification indicated clinical value for
treatment.
Figure 1. The flow chart of ndmaSNF.
[46]Figure 1
[47]Open in a new tab
(A) Dividing data into two main categories. (B) Pre-process for data
types with discrete value via network diffusion model incorporating
gene interaction network. (C) “Smoothed” mutation data. (D) All of
these patient similarity matrices derived from various data types were
combined into one fused patient similarity matrix through integrative
framework of SNF.
Moreover, existing methods generally identify network modules common to
all tumors which may ignore the heterogeneity between various subtypes.
In this study, we first use ndmaSNF on various data sources to gain
cancer subtypes, and for each cancer subtype, we use DriverNet [[48]12]
to get potential driver genes. We then did pathway enrichment analysis
on those genes per subtype. And the top 60 potential driver genes
attained from DriverNet were used for subtype-specific network module
discovery via software GenRev [[49]13]. The experimental results
indicated that our ndmaSNF has the ability to find distinct cancer
subtypes relevant to different clinical outcomes and network modules.
RESULTS
Performance comparison
We evaluated the performance of our method ndmaSNF by comparing it with
two state-of-the-art methods, i.e. SNF [[50]1] and LRAcluster [[51]14]
via silhouette value and P value as metrics on four cancer datasets
(BIC: breast invasive carcinoma; KRCCC: kidney renal clear cell
carcinoma; LSCC: lung squamous cell carcinoma; COAD: colon
adenocarcinoma). The experimental results are listed in Tables [52]1
and [53]2 (For P value, the lower the better; for silhouette value, the
higher the better).
Table 1. Comparison of ndmaSNF with other methods on four cancer datasets
using P value.
LSCC KRCCC BIC COAD
SNF without mutation data 1.16E-03 8.76E-04 5.74E-06 3.38E-04
SNF 9.86E-04 1.45E-03 1.59E-06 3.56E-04
LRAcluster 4.30E-02 3.24E-02 5.70E-02 9.90E-03
ndmaSNF 2.83E-04 3.43E-04 2.46E-08 1.40E-04
[54]Open in a new tab
Table 2. Comparison of ndmaSNF with other methods on four cancer datasets
using silhouette value.
LSCC KRCCC BIC COAD
SNF without mutation data 0.46 0.34 0.43 0.50
SNF 0.46 0.33 0.34 0.51
LRAcluster 0.50 0.32 0.46 0.35
ndmaSNF 0.52 0.39 0.45 0.43
[55]Open in a new tab
In Table [56]1, the terms in second row (SNF without mutation data)
mean that we used 3 continuous data types (DNA methylation, mRNA
expression, miRNA expression). And the terms in other rows (SNF,
LRAcluster and ndmaSNF) are the results with 4 data types including
mutation data. By comparing the second row (SNF without mutation data)
and the fifth row (ndmaSNF), we can see that somatic mutation profile
is a promising data source for identification of cancer subtypes.
However, the promising value of the mutation data was not reflected by
using original SNF as the third row (SNF) shows. By comparing the
second row and the third row, we can see that SNF didn’t exploit the
mutation data well, and even may had a bad influence compared with
result without mutation data (KRCCC, COAD). LRAcluster [[57]14] is
another integrative method with fast properties to find the shared
principal subspace across multiple data types. However, it even didn’t
perform well compared with original SNF. Due to its fastness, we think
that LRAcluster has an advantage in large-scale data analysis such as
pan-cancer analysis instead.
In terms of silhouette value, the promotion of our method compared with
other methods was slight (Table [58]2). And for COAD cancer data set,
performance of our method even decreased slightly, we attributed the
result to the fact that COAD has at least one subtype with few
patients, it makes the silhouette value very sensitive and unstable.
However, we can at least conclude that the involvement of the mutation
data did not destroy the combination of the original 3 data types (DNA
methylation, mRNA expression, miRNA expression) used in SNF [[59]1].
A case study: breast invasive carcinoma
To further validate that our ndmaSNF can identify subtypes with
biological and clinical differences, we then did in-depth research on
breast invasive carcinoma. Breast invasive carcinoma (BIC) is a common
breast cancer, growing into normal and healthy tissues.
We totally identified 5 subtypes of BIC with log-rank P value of
2.46E-08. To show the extent of those subtypes discovered by our method
corresponded to the established PAM50 classification, we gathered
statistics of the distribution of PAM50 per subtype. C1-C5 in Figure
[60]2A represents subtypes identified by our method. We can see that C3
and C4 are considerably fit the result of PAM50 classification:
Basal-like for C3 and Luminal A for C4. And C1 is mostly consisted of
Basal-like cases, C2 is mostly composed of luminal B cases. C5 is
mostly comprised by Basal-like cases and Her2-enriched cases. Luminal A
subtype is more likely to have a good prognosis while Basal-like
subtype is aggressive and have a poorer prognosis, this can be
reflected in Kaplan-Meier plot which shows an obvious significant
survival difference in Figure [61]2B. C3 has significantly shorter
overall survival durations than those with C4. Although C1 and C3 are
both Basal-like subtypes, they have a difference in survival
probability (P = 0.036) which can be seen in Figure [62]2A. C1 is more
aggressive than C3 as the survival curves shows.
Figure 2.
[63]Figure 2
[64]Open in a new tab
(A) Distribution of PAM50 samples in the identified subtypes. (B)
Kaplan-Meier survival curves of 5 subtypes identified.
In Figure [65]3A, we can see that C1 and C3 are mainly triple negative
while C2 and C4 are largely ER positive, PR positive and HER2 negative,
however, the situation of C5 is somewhat complicated. Basal-like
subtype breast cancer is usually triple negative, this verified the
fact that C1 and C3 are mostly consisted of Basal-like cases in Figure
[66]2A.
Figure 3.
Figure 3
[67]Open in a new tab
(A) Clinical features with ER/PR/HER2 per subtype. (B) Comparison of
the mutation frequencies among the identified subtypes.
Furthermore, we turned to mutation frequencies for more validation.
Thus, we focus on the genes with high mutation frequency and can find
evident differences between each cluster (Figure [68]3B): ZNF670,
SNMYD3, CNST, and TFB2M for cluster 1; CCND1, MAP3K1 and ERBB2 for
cluster2; TP53, CTSS, NLRP3, SH3BP5L for cluster 3; PIK3CA, GATA3 for
cluster 4 and TP53, PIK3CA, ERBB2 and CCND1 for cluster 5. It shows
that each subtype identified has a different combination of genes
highly mutated and corresponded to various biological processes.
Driver gene analysis per subtype identified in breast invasive carcinoma
To further study by what gene combination each subtype is driven, and
whether those driver genes combination are different corresponded to
different biological pathway, we applied DriverNet [[69]12] to find
important genes by using gene expression data, mutation data and
gene-by-gene network.
In table [70]3, Note that TP53 showed great importance in all subtypes,
however, a total combination of top driver genes is distinct in each
subtype. To clearly show the difference, we used the top 60 driver
genes identified from each subtype to do further study including
pathway enrichment analysis and network module identification. The aim
is to find out what biological process and important pathway those
driver genes from different subtypes participated in.
Table 3. Top 10 driver gene per subtype attained by DriverNet [[71]5].
C1 C2 C3 C4 C5
TP53 TP53 TP53 TP53 TP53
CSNK2A1 MYC MYC PIK3CA ERBB2
EP300 CCND1 CDKN2A MYC MYC
PRKCA PAK1 RB1 IGF1R PIK3R1
UBQLN4 CSNK2A1 STAT5A MAP2K4 SMAD3
SHC1 ERBB2 MCL1 LRP2 ACTL6A
MYC IGF1R IGF1R GATA3 TTN
CCDC85B MAPT TUBG1 MCL1 U2AF2
RELA RELA IKBKB CDH1 SMAD2
PAK1 PIK3R1 BRCA1 TTN CDKN2A
[72]Open in a new tab
We did a KEGG pathway enrichment analysis per subtype and selected
pathways related to breast cancer. From Figure [73]4, we can see
differences between subtypes at the enrichment level. It is not
surprising to see that all subtypes have an apparent enrichment in
hsa05200: Pathways in cancer. Also, Apoptosis, a programmed cell death
mechanism, is commonly enriched in C2, C3 and C5.
Figure 4. Pathway enrichment analysis for the top 60 driver genes per
subtype.
[74]Figure 4
[75]Open in a new tab
C1 is typically enriched in Wnt and ErbB signaling pathway. The Wnt
signaling pathway is one of a group of signal transduction pathways
made of proteins that pass signals into a cell through cell surface
receptors. Wnt signaling is identified for its role in carcinogenesis.
This pathway's clinical importance is demonstrated by mutations that
lead to various diseases, including breast cancer [[76]15].
Furthermore, excessive ErbB signaling is associated with the
development of a wide variety of types of solid tumor [[77]16].
C2 is typically enriched in MAPK signaling pathway. The MAPK is a chain
of proteins in the cell that communicates a signal from a receptor on
the surface of the cell to the DNA in the nucleus of the cell. When one
of the proteins in the pathway is mutated, it can become stuck in the
“on” or “off” position, which is a necessary step in the development of
many cancers. Components of the MAPK/ERK pathway were discovered when
they were found in cancer cells. Drugs that reverse the “on” or “off”
switch are being investigated as cancer treatments [[78]17].
C3 is typically enriched in p53 signaling pathway. In breast cancer,
p53 mutation is associated with more aggressive disease and worse
overall survival. Molecular pathological analysis of the structure and
expression of constituents of the p53 pathway is likely to have value
in diagnosis, in prognostic assessment and in treatment of breast
cancer [[79]18].
C4 is typically enriched in Cell cycle and Adherens junction. The cell
cycle is the series of events that takes place in a cell leading to its
division and duplication. Regulation of the cell cycle involves
processes crucial to the survival of a cell, including the detection
and repair of genetic damage as well as the prevention of uncontrolled
cell division. Adherens junctions, the most common type of
intercellular adhesions, are important for maintaining tissue
architecture and cell polarity and can limit cell movement and
proliferation.
C5 is typically enriched in many pathways represented in C1-C4 such as
Cell cycle, p53 signaling pathway, Adherens junction, ErbB signaling
pathway and Apoptosis. This also can be reflected in Figure [80]2A: C5
is a mixture of different PAM50 subtypes.
Network module identification and analysis per subtype identified in breast
invasive carcinoma
To get a more clear understanding of the combination of different
driver genes, we seek for their significance at network module level.
Therefore, we used them as seed genes to find network module per
subtype.
For subtype C1, we used top 60 driver genes as seed genes and 42 genes
connected to each other on gene interaction network by utilizing GenRev
[[81]13]. We totally found 10 network modules and 5 of which are
connected to each other and have more than 4 genes with the division
modularity of 0.53. Those 5 modules comprised the largest sub-network
(Figure [82]5). The densest module is TP53 module which contains many
important genes related to breast cancer. TP53 is a well-known tumor
suppressor gene associated with various cancers including breast
invasive carcinoma. Its mutation status and gene-expression based
groups are important survival markers of breast cancer, and these
molecular markers may provide prognostic information that complements
clinical variables [[83]19]. TP53 module also contained SMARCA4, which
can inhibit the cells’ ability to migrate and invade. So it attaches an
importance to pathogenesis of breast cancer as a prognostic marker
together with a possibly selective therapeutic target [[84]20]. HDAC2
is another important gene related to breast cancer that is inclined to
strongly express in aggressive breast cancer tumor subgroups [[85]21].
We also discovered a SMAD4 module. Current research shows that SMAD4
plays a key role in both tumor suppression and progression of breast
cancer cells [[86]22]. Another critical gene included in this module is
EP300, it encodes the transcriptional cofactor p300, which is highly
expressed in diverse human cancers. Specially, the over expression of
p300 in breast cancer predicts tumor recurrence and adverse prognosis
[[87]23]. The remaining three modules contain some other important
genes such as PIK3CA, TYK2 and APOA1, respectively. PIK3CA is a
well-known oncogene in human cancers. Accumulating evidence suggests
that mutation of PIK3CA is an early event in breast cancer and is more
likely to play a role in breast tumor initiation than in invasive
progression [[88]24]. The role of TYK2 is confirmed by biological
experiments in suppressing the growth and metastasis of breast cancer
[[89]25]. For APOA1, it is one of the most significant genes correlated
with the proteomic profile that are closely related to breast cancer
and may be involved in robust detection of disease progression
[[90]26].
Figure 5. Network modules discovered in subtype 1.
[91]Figure 5
[92]Open in a new tab
The green nodes represent genes we input, and the yellow nodes
represent linker genes connecting those genes we input.
For subtype C2, after inputting top 60 driver genes as seeds, 41 genes
were retained and we wholly got 8 modules with the division modularity
of 0.50. The most densely connected sub-network is shown in Figure
[93]6. The ESR1 module contained some important genes such as ESR1.
Recent studies suggest that activating mutations in ESR1 are a key
mechanism in acquired endocrine resistance in breast cancer therapy
[[94]27]. The PIK3CA module contained some important genes such as
STAT3 and PIK3R1. Current findings show that activated STAT3 signaling
contributes to breast cancer progression and resistance to chemotherapy
by inducing expression of the antiapoptotic protein, Survivin in part
[[95]28]. PIK3CA mutations and PIK3R1 underexpression show opposite
effects on patient outcome and could become useful prognostic and
predictive factors in breast cancer [[96]29]. We also identified a
CDC42 module including important genes such as CDC42 and PAK1. Growth
and motility inhibition of breast cancer cells by epidermal growth
factor receptor degradation is correlated with inactivation of CDC42
[[97]30]. And study shows associations between PAK1 expression and
subcellular localization in tumor cells and tamoxifen resistance
[[98]31].
Figure 6. Network modules discovered in subtype 2.
[99]Figure 6
[100]Open in a new tab
We also did network module analysis for C3, C4 and C5, the results are
given in [101]Supplementary Materials (Supplementary Results-network
module analysis for C3, C4 and C5).
DISCUSSION
Integrative methods are urgently needed to exploit multiple genomic
platform data simultaneously and get insight into human neoplasia, such
as identification of cancer subtypes. In our work, we proposed a method
named ndmaSNF by extending SNF, an integrative framework, to make full
use of somatic mutation data. By using a network diffusion model, the
somatic mutation data was “smoothed” and its value can be exploited to
a large extent. The experimental results on several cancer data sets
indicated that our method outperformed in identification of patients
cohort with biological and clinical meaning. For example, we totally
find 5 subtypes C1-C5 in BIC with different biological and clinical
features. C3 is mostly consisted of Basal-like cases whereas C4 is
mostly composed of luminal A cases. And the prognosis of C4 is better
than C3. Interestingly, C5 is a mixture of different PAM50 subtypes and
is typically enriched in many pathways represented in C1-C4. According
to those subtypes, we did a deeper analysis including pathway
enrichment analysis and network module identification. The results
showed that our method could capture biological and clinical features
effectively. Our research also demonstrated the value of the mutation
data in giving insight into tumorigenesis. In the future, we will use
some other discrete data such as copy number variations to make our
method more compatible.
MATERIALS AND METHODS
Datasets
The data (DNA methylation, mRNA expression, miRNA expression) we used
in this paper including four cancer data sets from TCGA website
([102]https://cancergenome.nih.gov/), which have been processed and
provided by Wang et al. [[103]1]. And the mutation data of those four
cancer data sets were obtained from UCSC data portal
([104]http://genome.ucsc.edu/). We restricted our analysis to the 85
TCGA LSCC cases, 75 TCGA COAD cases, 101 TCGA KRCCC cases and 105 TCGA
BIC cases, for which all DNA methylation, mRNA expression, miRNA
expression and somatic mutation data were available. We used PPI
(protein-protein interaction) network data obtained from NBS [[105]11]
after processing, with 11491 genes as gene interaction network.
SNF integrative framework
Suppose we have n samples (X[1], X[2] … X[n]) which possess several
data sources on multi-scale level (e.g. mutation data, expression
data). We want to use these data simultaneously for identification of
cancer subtype. The SNF framework can be described as follows.
First, for each data type, an nn patient similarity matrix W was
constructed with its entry W(i, j) demonstrating the similarity between
X[i] patient and patient X[j]. The specific formula to calculate W is
as follows:
[MATH:
W(i,j)=exp(−<
/mo>ρ2(xi,xj<
/msub>)μεi,j<
mo>) :MATH]
(1)
Here
[MATH:
ρ(Xi
,Xj) :MATH]
represents the Euclidean distance between patient X[i] and patient
X[j]. And μ is an empirical hyper parameter which is recommended to be
set in the range of [0.3, 0.8]. Furthermore, ε[i, j] is defined as
follows:
[MATH:
εi,j=mean<
mo>(ρ(xi,Ni))+mean(ρ(xj,Nj))+ρ<
mo>(xi,xj)3 :MATH]
(2)
Here
[MATH:
mean(ρ(Xi,Ni))<
/mo> :MATH]
is the average of the sum of the distances between X[i] and each of its
neighbors. Obviously, the Euclidean distance measure is suitable for
continuous variables. For discrete data, the chi-square distance is
proposed (Supplementary Note-Chi-squared distance). There are two
derivatives of matrix W, namely, matrix P and matrix S. Matrix P
carries the full information about the similarity of each patient to
all others obtained by performing normalization on W:
[MATH:
P(i,j)={W(i,j)<
mn>2∑k≠iW(i,k)
,j≠i 1/2
,j=i :MATH]
(3)
Matrix S only encodes the similarity to the K most similar patients for
each patient via K nearest neighbors (KNN):
[MATH:
S(i,j)={W(i,j)<
mstyle
displaystyle="true">∑k∈NiW(<
mrow>i,k),j∈Ni<
/mi> 0,otherwise
:MATH]
(4)
where N[i] represents a set of X[i]’s neighbors including X[i]. By
using P as the global structure and S capturing local structure, a
nonlinear iterative procedure is proposed:
[MATH:
P(v)
=S(v)×(
∑k≠vP(k)m−1)×(S(
v))T,v=1,2,.
..,m :MATH]
(5)
where P^(V) represents P calculated from the v-th data profile. This
procedure updates every P^(V) each time by m parallel interchanging
diffusion processes. After t steps, the fused matrix P^(C) can be
learned by taking average of all P^(V).
Network diffusion model
We proposed to apply network diffusion model [[106]32] incorporating
gene interaction network on mutation profile and other discrete data.
By using this method, the discrete data was “smoothed” and carries the
information about similarity of tumor sample at the pathway level
rather than the individual gene level, thus making SNF integrative
framework work suitably and effectively on discrete data.
We first mapped patient mutation profile onto a gene interaction
network. Then network diffusion model was applied to diffuse the effect
of each mutated gene over this network for each patient according to
the function:
[MATH: Ft+1=
αFtA+(1−α)F0 :MATH]
(6)
F[0]is the binary patient-by-gene mutation data (Figure [107]7A), and A
is a degree-normalized adjacency matrix of the gene interaction network
(Figure [108]7B).α is used to adjust the distance that the mutation
signal can propagate in the network. It is a tuning parameter in the
optimal range of [0.5, 0.8]. The diffusion function run iteratively
until F[t+1] converges
[MATH:
(Ft+<
mn>1−Ft<
1×10−
6) :MATH]
. The result F[t+1] obtained is a “smoothed” mutation profile with
quantitative value indicating the influence of each mutation per
patient through network diffusion (Figure [109]7C). In this way, not
only genes that are mutated will get high influence scores, but also
genes that are close to the mutated genes in the network. According to
this “smoothed” matrix, we seek for patient similarity as mutational
consistency at pathway level rather than individual gene level. The
benefit is 2-fold: (i) by “smoothing”, the sparseness is reduced, so
the traditional distance measurement is feasible. (ii) in network
diffusion model, mutation consistency is searched at pathway level
rather than individual gene level, thus it will give a more
comprehensive insight into similarity between patients. Since tumor
process is driven by a combination of mutated genes, those genes’
influence is propagated through gene interaction network, so the tumor
similarity at pathway level is more biologically significant and can
improve the identification of cancer subtype.
Figure 7. Simple presentation on network diffusion model.
[110]Figure 7
[111]Open in a new tab
(A) Somatic mutation data. (B) Gene interaction network. (C) “Smoothed”
mutation data via network diffusion model.
Evaluation metrics
To compare the performance of our method with established methods, we
chose two metrics as evaluation index. First, we used P value for
log-rank test of survival analysis by using survival time. P value
measures the degree of significant difference between survival data of
different subtypes. The lower the P value is, the more obvious the
difference between subtypes is. For survival analysis, we took the same
method used in SNF [[112]1], thus we used the number of days to the
last follow-up and vital status. However, for COAD, due to many missing
values, these are combined with the number of days of last known
living.
We also used silhouette value [[113]33] to measure the quality of the
clustering result. The silhouette value ranges from -1 to 1, where a
high value indicates that the patient is well matched to its own
cluster and poorly matched to other clusters. Then the mean value of
silhouette value for all the patients was used as a measure of the
compactness within clusters and the separation among clusters.
SUPPLEMENTARY MATERIALS FIGURES
[114]oncotarget-08-89021-s001.pdf^ (1.8MB, pdf)
Footnotes
CONFLICTS OF INTEREST
The authors declare that they have no competing interests.
FUNDING
This study was supported by the National Natural Science Foundation of
China (No. 61672037), the Key project of Anhui Provincial Education
Department (No. KJ2017ZD01), and the Anhui Provincial Natural Science
Foundation (Nos. 1508085QF135 and 1608085MF136).
REFERENCES