Abstract
Background
Prediction of drug-disease interactions is promising for either drug
repositioning or disease treatment fields. The discovery of novel
drug-disease interactions, on one hand can help to find novel
indictions for the approved drugs; on the other hand can provide new
therapeutic approaches for the diseases. Recently, computational
methods for finding drug-disease interactions have attracted lots of
attention because of their far more higher efficiency and lower cost
than the traditional wet experiment methods. However, they still face
several challenges, such as the organization of the heterogeneous data,
the performance of the model, and so on.
Methods
In this work, we present to hierarchically integrate the heterogeneous
data into three layers. The drug-drug and disease-disease similarities
are first calculated separately in each layer, and then the
similarities from three layers are linearly fused into comprehensive
drug similarities and disease similarities, which can then be used to
measure the similarities between two drug-disease pairs. We construct a
novel weighted drug-disease pair network, where a node is a
drug-disease pair with known or unknown treatment relation, an edge
represents the node-node relation which is weighted with the similarity
score between two pairs. Now that similar drug-disease pairs are
supposed to show similar treatment patterns, we can find the optimal
graph cut of the network. The drug-disease pair with unknown relation
can then be considered to have similar treatment relation with that
within the same cut. Therefore, we develop a semi-supervised graph cut
algorithm, SSGC, to find the optimal graph cut, based on which we can
identify the potential drug-disease treatment interactions.
Results
By comparing with three representative network-based methods, SSGC
achieves the highest performances, in terms of both AUC score and the
identification rates of true drug-disease pairs. The experiments with
different integration strategies also demonstrate that considering
several sources of data can improve the performances of the predictors.
Further case studies on four diseases, the top-ranked drug-disease
associations have been confirmed by KEGG, CTD database and the
literature, illustrating the usefulness of SSGC.
Conclusions
The proposed comprehensive similarity scores from multi-views and
multiple layers and the graph-cut based algorithm can greatly improve
the prediction performances of drug-disease associations.
Keywords: Drug-disease interaction, Integration strategy, Similarity,
Graph cut, Guilt-by-association
Background
On one hand, traditional drug development is a time-consuming and
costly process with low success rate [[29]1–[30]3]. To speed up the
process and reduce the risks and costs, drug repositioning has becoming
a promising alternative for de novo drug discovery [[31]1, [32]4,
[33]5]. However, to reposition a drug might also be a haphazard process
with a bit of luck, for examples, repositioning sildenafil (brand name:
Viagra) from the treatment of angina to erectile dysfunction [[34]6],
repositioning minoxidil from the treatment of hypertension to hair loss
[[35]7], and so on. Thus, there are urgent needs to develop effective
computational methods for drug reposition. On the other hand, the
commonly used drugs for some diseases may suffer from the problems of
severe side-effects or resistance, for example, the drug for
Parkinson’s disease, L-dopa, has severe side effects such as dyskinesia
[[36]8]. It is necessary to find better pharmacological treatments of
some diseases. Predicting drug-disease interactions is devoted to above
two issues.
There are lots of methods proposed to predict the potential
drug-disease relations. Some methods are based on gene expression
profile data under the hypothesis that if the drug and disease have
opposite expression signatures, then the drug is possible to treat that
disease [[37]9]. For instance, Sirota et al. integrated gene expression
measurements from 100 diseases and 164 drug compounds, and predicted
potential indications for these drugs, such as lung adenocarcinoma as
the potential indications of cimetidine [[38]10]; Jahchan et al.
proposed a systematic approach to query gene expression profiles so as
to identify antidepressant drugs to treat small cell cancer [[39]11].
The vast amount of information of drugs and diseases in literature and
databases make it possible to mine or infer the potential associations
between drugs and diseases based on literature mining and semantic
inference. Suppose that B is reported to be one of the characteristics
of disease C in some literature, and drug A is reported to affect B in
other literature, then it has a potential interaction between drug A
and disease C [[40]12, [41]13]. For example, Ahlers et al. found the
potential link between the antipsychotic agents and cancer based on
MEDLINE citations [[42]14]. Since high-throughput experiments have
accumulated massive data on diseases and drugs, more and more methods
focus on building prediction models via machine learning strategies.
For example, Gottlieb et al. proposed a logistic regression based
method by integrating different information on drugs and diseases
[[43]15]; Chen et al. regarded the prediction of drug-disease
associations as a recommendation problem, and adopted two
recommendation algorithms to infer drug-disease interactions [[44]16];
Liang et al. developed a Laplacian regularized sparse subspace learning
(LRSSL) based method to predict drug-disease interactions by
integrating drug chemical structure, drug target domain and target
annotation information [[45]17].
In recent years, the network-based prediction, which first builds a
network based on the existed data and then builds the prediction model,
is very promising and a few methods have been proposed, such as
network-based guilt-by-association (GBA) method [[46]4], network-based
inference (NBI) method [[47]18], random walk and network propagation
based algorithm [[48]19], and so on. Recently, Wang et al. proposed to
build heterogeneous graph model HGBI for the prediction of drug-target
interactions [[49]20], and to build three-layer heterogeneous graph
model (TL-HGBI) for the prediction of drug-disease interactions
[[50]21]. Even so, they did not take full advantages of the diverse
information from genes, drugs, diseases, and their associations yet.
Since organizing heterogeneous data in a good way may contribute to the
discovery of drug-disease relations [[51]21, [52]22] and help to build
accurate prediction models, in this work we first present a framework
to integrate multiple sources/levels of data into base layer, gene
layer and treatment layer. Each layer is expected to reflect one aspect
of the drug-disease associations. Then we construct a novel weighted
graph where a node is a drug-disease pair and an edge represents the
node-node relation with the similarity score between two pairs as its
weight. According to the observed data, some drug-disease pairs have
known treatment relationships whereas others have not. Based on the
weighted graph, we propose a semi-supervised graph cut (SSGC) algorithm
to predict the drug-disease interactions that have been observed in the
data yet. The overall framework is shown in Fig. [53]1.
Fig. 1.
Fig. 1
[54]Open in a new tab
The framework of this work. Firstly, multi-sources of data, such as
drug substructures, disease phenotypes, protein-protein interactions
(PPI), gene profiles and network profiles, are well organized into
three layers. Secondly, those information are utilized to calculate
similarity scores as well as drug-disease treatment priori. Thirdly,
the similarity matrices and the priori are integrated to construct
drug-disease pair graph. Finally, SSGC algorithm is applied to predict
drug-disease treatment relations
Methods
Data collection
We have collected drugs, genes, diseases, and the interactions
information from several data sources. With these data, we attempt to
investigate whether there is a treatment relation within any unknown
drug-disease pair.
From DrugBank ([55]https://www.drugbank.ca) [[56]23], we obtained the
chemical structures of 1186 drugs, 1141 genes, and 4594 drug-gene
associations (the polypeptides and drugs whose targets are not in human
cells are not included).
From DGIdb ([57]http://dgidb.genome.wustl.edu) [[58]24], MINT
([59]http://mint.bio.uniroma2.it) [[60]25] and UniProt
([61]http://www.uniprot.org) [[62]26], we have collected 6988 genes,
and 42162 gene-gene associations. Among the genes, 1141 genes are
associated with drugs (in DrugBank), and 700 genes are associated with
diseases.
From OMIM ([63]https://omim.org) [[64]27] and Gottlieb’s data set
[[65]15], we downloaded 449 diseases and 700 related genes that form
1365 disease-gene associations. Furthermore, 1827 treatment relations
between 302 of the 449 diseases and 551 drugs [[66]15] were also
collected.
To facilitate the data integration, we organized the heterogeneous data
into three layers. The base layer provides information on drug
substructures and disease phenotypes; the gene layer provides genes and
gene-gene associations information; and the treatment layer provides
drug-disease interactions information (left part of Fig. [67]1).
For convenience, we suppose there are m drugs (m=1186), n diseases
(n=449), l druggable genes (l=6988), and q drug-disease pairs (q=m×n)
hereinafter. Moreover, we denote the k-order identity matrix as I [k],
matrix element multiplication and division as ⊗ and ⊘ respectively, and
the shorthand for the Euclidean norm as ∥∙∥.
Similarity calculation in the base layer
Our approach is mainly inspired by the assumption that similar drugs
might treat similar diseases. Hence, similarity calculation is the key
issue of our approach. Different with other methods, we first computed
drug-drug and disease-disease similarities from three different
aspects, corresponding to the drug structures/disease phenotypes,
functional information of genes, and drug-disease treatment
relationships respectively; And then we integrated three similarities
into the comprehensive drug (disease) similarity.
In the base layer, we calculate the drug-drug and disease-disease
similarities respectively according to drug chemical substructures and
disease phenotype information.
Structural similarity between drugs
The SMILES (simplified molecular-input line-entry system) strings
[[68]28] for all drug structures are obtained from the DrugBank
database, based on which the 2D fingerprints of the drugs are
calculated via Openbabel tool [[69]29]. Using the fingerprints
information, we can calculate the Tanimoto score (the size of the
intersection divided by the size of the union) [[70]30] and use it as
the structural similarity for each drug pair. Obviously, the drug-drug
structural similarity matrix, denoted as S [bc], is an m×m symmetrical
matrix with diagonal elements being ones.
Phenotype similarity between diseases
The normalized phenotype similarity scores (ranging from 0 to 1)
between diseases are obtained directly from MimMiner
([71]http://www.cmbi.ru.nl/MimMiner/suppl.html) [[72]31] which are
constructed based on MeSH terms [[73]32]. The n×n disease-disease
phenotype similarity matrix, S [bd], is also an symmetrical matrix with
diagonal elements ones.
Similarity calculation in the gene layer
Since diseases (drugs) associated with the same genes or genes in the
same pathways are likely to have similar functional mechanism, we can
measure the functional similarities of the disease (drug) pairs
according to the associated genes’ information.
Gene-gene association measurement
Based on the gene-gene interaction network, we first measure all gene
pairs distances by using all-pairs shortest path algorithm. Suppose the
result gene-gene distance matrix is D [g]. For genes i and
[MATH:
i′<
/mrow> :MATH]
, we then calculate their association according to the following
Perlman’s formula [[74]33]:
[MATH:
Sgi,i′=ae−bDgi,i′ :MATH]
where S [g] is the l×l association matrix which is obviously
symmetrical and with diagonal elements ones; a and b are two scalars
that are respectively set to 0.3 and 1.0 by experience.
Profile similarity between drugs or diseases
We first get the profile for each drug or disease according to the
drug-gene or disease-gene interaction information. The profile is
represented as an l-dimensional vector in which every element
corresponds to one gene and is encoded as either 1 or 0 indicating
whether the gene associates with the drug or disease. Suppose the
profiles of drugs i and
[MATH:
i′<
/mrow> :MATH]
are c [i] and
[MATH:
ci′ :MATH]
, the profiles of disease j and
[MATH:
j′<
/mrow> :MATH]
are d [j] and
[MATH:
dj′ :MATH]
. We then separately calculate the profile similarities according to
the following two fomulas:
[MATH: Sgci,i′=ciTS<
/mi>gc<
mrow>i′<
/mo>ciTSg<
/msub>cici′TSgci′
:MATH]
[MATH: Sgdj,j′=djTS<
/mi>gd<
mrow>j′<
/mo>djTSg<
/msub>djdj′TSgdj′
:MATH]
where S [gc] is the m×m drug profile similarity matrix, and S [gd] is
the n×n disease profile similarity matrix. Obviously they are
symmetrical and with elements ones on the main diagonal.
Similarity calculation in the treatment layer
If two drugs (diseases) share some diseases (drugs), they might be
similar. Therefore, the known drug-disease associations can also be
utilized to calculate the drug-drug (disease-disease) similarities.
According to the drug-disease associations, we first build a
drug-disease bipartite graph, and then compute the drug-drug
(disease-disease) distances by using the all-pairs shortest path
algorithm. The distances can easily be converted into the similarity
scores according to the Perlman formula [[75]33]:
[MATH: Stc′i,i′=ae−bDtci,i′;Std′j,j′=ae−bDtdj,j′ :MATH]
where D [tc] is the 551 × 551 dimensional drug distance matrix; D [td]
is the 302 × 302 dimensional disease distance matrix. Accordingly,
[MATH: Stc′ :MATH]
is the 551 × 551 dimensional drug similarity matrix;
[MATH: Std′ :MATH]
is the 302 × 302 dimensional disease similarity matrix. We set the
scalars a and b to 0.9 and 1 by experience, and set the self-similarity
of a drug (disease) to one.
It is noticeable that we have collected 1186 drugs and 449 diseases in
all, yet we can only calculated the similarities for 551 drugs and 302
diseases in the treatment layer according to the information from
Gottlieb’s data set. Therefore, we adopt the same method as in [[76]34]
to project those drugs (diseases) that do not occur in Gottlieb’s data
set into a unified network similarity space. By this way, we can get
all drug-drug (disease-disease) similarities from
[MATH: Stc′Std′ :MATH]
. We denote the final similarity matrice in treatment layer as S [tc]
(m×m dimension) and S [td] (n×n dimension) respectively.
Integrating similarities from three layers
Similarity measurements respectively from three layers can be
integrated via various approaches. For simplification, we just adopt
the linear combination strategy in this work. More sophisticated
strategies will be considered in the future. Concretely, the
comprehensive drug-drug (disease-disease) similarity matrix S [c] (S
[d]) are obtained as follows.
[MATH: Sc
=αc
Sbc+
βcSgc+
γcStc
:MATH]
1
[MATH: Sd
=αd
Sbd+
βdSgd+
γdStd
:MATH]
2
where α [c],β [c],γ [c], α [d],β [d] and γ [d] are combination weights
satisfying that α [c]+β [c]+γ [c]=1 and α [d]+β [d]+γ [d]=1.
To determine the values of α [c],β [c],γ [c], α [d],β [d] and γ [d], a
simple way to integrate the similarities is to assign equal weights to
each layer. However this integration strategy has a weak point: the
information from the layer with much smaller scores might be neglected
due to the integration, and vice verse. A more rational way is to make
each layer has equal contribution to the final results. In this work,
we adopted the latter strategy to integrate the similarities from three
layers.
Novel weighted drug-disease pair graph
There are m∗n drug-disease pairs in all based on m drugs and n
diseases, where some pairs have known treatment relationships according
to the observed data whereas others have not. The aim of this work is
to determine whether an unknown drug-disease pair has a treatment
relationship or not. We propose to construct a novel weighted completed
graph G=(V,E) for this purpose, where V={(i,j)|d r u g i∈[1,m],d i s e
a s e j∈[1,n]}.
[MATH: E=est|s≠<
/mo>t,s=(i,j)∈1,q
,t=i′,j′<
/mrow>∈1,q :MATH]
. In fact, s=(i−1)×n+j,
[MATH: t=i′−1×n+j′
:MATH]
. For every edge e [st], we assign a weight to it as the similarity
score between two nodes that is calculated as follows:
[MATH:
W(s,t)=<
mfenced close="" open="{"
separators="">Sci,i′Sdj,j′,s≠t<
/mtr>0,s=t
:MATH]
3
where W is the q×q weight matrix that is symmetrical and with the
diagonal elements zeros.
Obviously, In all q drug-disease pair nodes in the graph, some
drug-disease pairs have known treatment relationships whereas others
are unknown which need to be predicted.
Let f=(f [1],f [2],⋯,f [s],⋯,f [q])^T, f [s]∈{0,1} indicates whether
the drug-disease pair (i,j) has a treatment relationship or not. Then
the problem of predicting the drug-disease treatment relationships
could be addressed by determining the value of f. In this work, we
consider this problem as a graph cut problem [[77]35], and cluster all
drug-disease pair nodes into two groups (treatment and non-treatment)
by cutting the graph into several sub-graphs so that pairs within the
same sub-graph belong to the same group.
Semi-supervised graph cut approach
Suppose the treatment label matrix obtained from the data be Y (m×n). Y
[ij] is 1 if drug i can treat disease j, otherwise 0. If drug i relates
to genes or pathways that also associated with disease j, then the drug
would potentially treat the disease. We take this priori knowledge into
consideration by introducing a priori matrix P (m×n), where the element
P [ij] is calculated as the following:
[MATH: Pij=c
iTSgdj<
msubsup>ciT<
/mrow>Sgci<
/msqrt>djTSgdj<
/mrow>,<
mrow>Yij=0
0,Yij=1
:MATH]
4
Equation ([78]4) illustrates that we only consider the priori values of
unknown drug-disease pairs.
Let ∧[L](Labeled) and ∧[U](Unlabeled) are two q×q diagonal matrices
indicating the treatment states of drug-disease pairs observed from the
data set; p=(p [1],p [2],⋯,p [s],⋯,p [q])^T(p [s]=P [ij]); y=(y [1],y
[2],⋯,y [s],⋯,y [q])^T(y [s]=Y [ij]). Obviously, y is the diagonal
vector of matrix ∧[L]; ∧[U]=I [q]−∧[L]; and
[MATH:
∧Lk
=∧L :MATH]
,
[MATH:
∧Uk
=∧U :MATH]
; ∧[L] y=y, ∧[U] p=p.
We define a loss function L o s s(f) to be minimized as follows:
[MATH: Loss(f)=14∑s,t<
/mrow>Wst(fs−
ft)<
mrow>2+μ2∥∧Lf−y∥2
+ξ2
∥∧Uf<
/mi>−p∥2 :MATH]
5
Where μ and ξ are two parameters. Obviously, in order to minimize L o s
s(f), f should meet the requirements that similar drug-disease pairs
should have similar treatment relationships; the derived treatment
relationships should be in accord with the known observed facts and
also should be inclined to consistent with the priori knowledge. In
this work, we set μ>ξ>0 with the consideration that violating the
observed facts would receive greater penalty than out of the priori
knowledge. Obviously, the f with the minimal L o s s(f) corresponds to
the optimal graph cut.
Let A be a q×q diagonal matrix with diagonal vector a=(a [1],a [2],⋯,a
[s],⋯,a [q]), where
[MATH:
as=∑tWst=∑i′<
mrow>Sci,i′∑j′<
/msup>Sdj,j′−1 :MATH]
. Then we have
[MATH:
14∑s,tWst(fs−
ft)<
mrow>2=12fT(A−W)
f :MATH]
6
Suppose L=A−W, obviously L is the Laplace matrix of G, and the
normalized matrix [[79]36] is
[MATH: L¯=A−1/2LA−1/2<
/mrow>=Iq−A−1
/2WA
−1/2
:MATH]
. Let S=A ^−1/2 W A ^−1/2, then we have
[MATH: L¯=Iq−S :MATH]
.
Hence, Eq. ([80]5) turns into the following equation:
[MATH: Loss(f)=12fTL¯f+μ
2∥∧<
/mrow>Lf−y∥2+
ξ2∥<
mrow>∧Uf−p∥2
:MATH]
7
According to the original definition of f, every element f [s]∈{0,1},
which makes the problem of minimizing L o s s(f) be NP-hard. We
therefore relax the constraint and let f [s]∈[0,1] hereinafter.
Correspondingly, we can get the derivative of L o s s(f):
[MATH: ∇Loss(f)=(Iq
+μ∧L+ξ∧U)f−Sf−(μy+ξp) :MATH]
8
To minimize L o s s(f), ∇L o s s(f) is expected to be 0. According to
the gradient descent algorithm, ∇L o s s(f)=0 equals that Eq. ([81]9)
is convergent (α is a learning rate).
[MATH:
f(k+1)=f(k)−α∇Loss(f)|f=f(k)=α(μ−ξ)<
msub>∧U+Sf(k)+(1−α)y^ :MATH]
9
Fortunately, Eq. ([82]9) is convergent when setting α=1/(1+μ),
[MATH: y^=y
+ξμp :MATH]
and
[MATH:
f(0)=y^ :MATH]
according to [[83]37]. It is expected to minimize L o s s(f) by
repeating the iterative process until Eq. ([84]9) converges. However,
we find that the memory consumption is too large when running the
iteration because of the extreme large matrix S (for example, if
n=10^3,m=10^3, then the dimension of S is 10^12).
Now that directly calculating Sf in Eq. ([85]9) is space expensive, we
provide a method to calculate it without explicit storage consumption.
Let F and
[MATH: A^
:MATH]
are two n×m auxiliary matrices respectively with elements as
[MATH:
Fij=fs=<
mrow>f(i−1)×n+jA^i,j=<
mrow>as
=a(
i−1)×n+<
/mo>j
:MATH]
Let
[MATH: A~=A^⊗A^ :MATH]
, then we have
[MATH:
(A−
1f)s<
/msub>=(F⊘A~)ij :MATH]
and
[MATH: A−1<
/mn>+Sfs<
mo>=A−1<
/mn>/2(I<
/mrow>q+W)A−1/2<
/mrow>fs<
/msub>=∑t(Iq+W)stft
asat<
/msqrt>=
1A^ij∑i′,
j′<
/mrow>Sci,i′Fi<
/mrow>′j′Sdj′,jA^i′j′=1A^ijSc(i,∗)F⊘A^Sd(
∗,j)
:MATH]
where S [c](i,∗) represents the i-th row of matrix S [c] and S [d](∗,j)
indicates the j-th column of matrix S [d]. Therefore, we have
[MATH: (Sf)s
=ScF⊘A^Sd⊘
A^−F
⊘A~ij
:MATH]
10
Equation ([86]10) implies that we can compute Sf with a space
complexity Θ(max(n ^2,m ^2)), rather than Θ((n m)^2), which enables the
iteration process to go through on the desktops.
To sum up, the framework to find the optimal graph cut is listed in
Algorithm 1.
graphic file with name 12920_2017_311_Figa_HTML.gif
Results
Redundancy check of the data set
We desire to check the redundancy of the data set, since high redundant
data set could lead to worse generalization. The redundancy is measured
by similarity score distribution of drugs and diseases. Figure [87]2
[88]a shows the similarity scores distribution of drugs. Obviously, the
number of drug pairs with high similarity score is small (only 0.12% of
the drug pairs have similarity scores larger than 0.5) and the majority
similarity scores are around zeros. Figure [89]2 [90]b demonstrates the
similarity scores distribution of diseases, and the case is similar.
Only 0.23% of the disease pairs have similarity scores larger than 0.5,
and the majority of the scores are around zeros. Therefore, we can
conclude that the majority similarity scores of both drug pairs and
disease pairs are small and the redundancy of data set is negligible.
Fig. 2.
Fig. 2
[91]Open in a new tab
Similarity scores distribution. a Similarity scores distribution of
drugs. b Similarity scores distribution of diseases. The right most
bars of both (a) and (b) indicate self similarity scores
Rationality validation by guilt-by-association assumption
As multiple sources of information has been collected and organized
into three layers based on the inherent relationships, we wish to
illustrate the rationality and validity of the collected information as
well as the way to organize them by guilt-by-association (GBA)
principle. The basic assumption of GBA is that similar drugs are
inclined to be associated with similar diseases and vice versa, which
implies two aspects: the drugs treating the same disease share
structure/network properties and the diseases treated by the same drug
also share phenotype/network properties. Therefore, similarity scores
of drugs (diseases) which share some diseases (drugs) should be
apparently greater than those which don’t share any diseases (drugs).
Obviously, the validation results (Table [92]1) on the data support the
GBA assumption. At the same time, the GBA ratios increase along with
the layers, it is reasonable that the higher layer integrates more
information.
Table 1.
GBA analysis
Base layer Gene layer Treatment layer
avg-same avg-diff ratio avg-same avg-diff ratio avg-same avg-diff ratio
Drug 0.25 0.17 1.47 0.29 0.12 2.41 0.33 0.06 5.50
Disease 0.23 0.10 2.30 0.40 0.13 3.08 0.32 0.05 6.40
[93]Open in a new tab
avg-same: represent the overall average similarity scores of
drugs/diseases which share some diseases/drugs. avg-diff: represent the
overall average similarity scores of drugs/diseases which don’t share
any diseases/drugs. ratio = avg-same / avg-diff
Setting of thresholds and combinations weights
Previous studies imply that small similarity scores are usually noise
data which provide little information and sometimes even have adverse
effect to the prediction performance [[94]20, [95]21]. Therefore, we
chose thresholds to cut off the small similarity scores. However,
taking the thresholds together, there are 12 parameters in Eqs. ([96]1)
and ([97]2) in all, which makes it impractical to search all the
parameter space to get the optimal parameter settings. For feasibility,
we set the parameters based on two principles: (1) each layer has close
GBA ratio; and (2) each layer has nearly equal contribution to the
ultimate similarity matrices.
Thresholds setting based on GBA assumption
We want to let each layer have similar GBA ratio. Since the treatment
layer achieves the highest GBA ratios (Table [98]1), we set the
similarities thresholds for S [tc],S [td] to zeros and then accordingly
choose the thresholds for other two layers so that three layers have
similar GBA ratios. As a result, the thresholds of S [bc],S [gc],S [bd]
and S [gd] are set to 0.1, 0.01, 0.14 and 0.01 respectively.
Integrating weights setting based on equal contribution strategy
We want to let each layer have nearly equal contribution to the
ultimate similarity matrices. After choosing of thresholds, the average
of each matrix (S [bc],S [gc],S [tc],S [bd],S [gd] and S [td]) are
calculated to be 0.017, 0.028, 0.057, 0.006, 0.028 and 0.038
respectively. Accordingly we can obtain the combination weights by
setting equal contributions to each layer. If the average of one layer
is small, we assign a large weight to enhance its final effect, on the
same time, if the average of one layer is large, we assign a small
weight to weaken its final effect. By this strategy, we set α [c],β [c]
and γ [c] to 0.53, 0.32 and 0.15; and α [d],β [d] and γ [d] to 0.72,
0.16 and 0.12 respectively.
Evaluating the performance of SSGC
Since SSGC is a network-based approach, we compared it with three
network-based methods (NBI, HGBI and TL-HGBI) on Gottlieb’s data set
using 10-folds cross validation [[99]15]. For fairness, we optimize the
parameters for each method by grid search: μ=4 and ξ=0.67 for SSGC,
α=0.7 for HGBI and α=0.2 for TL-HGBI.
Using each of four algorithms, we can respectively predict a candidate
drug list for every disease. We consider each observed drug-disease
pair in the data set has true treatment relation (positive sample).
Since we only have positive samples, the calculation of the receiver
operating characteristic (ROC) curve is different from the standard
approach [[100]21]. For an observed drug-disease pair in the data set,
if the treatment relation value (obtained from F) is greater than the
threshold, then it is regarded as a true positive (TP), otherwise a
false negative (FN). For other pairs not observed in the data set, if
the value is above the threshold, then it is regarded as a false
positive (FP), othervise a true negative (TN). In this experiment, the
threshold is set 0.05. Accordingly, we can calculate the true positive
rate (TPR) and false positive rate (FPR) for a given threshold as
follows:
[MATH: TPR=TPTP+FN;FPR=FPFP+TN :MATH]
As shown in Fig. [101]3 (left), SSGC method obtains higher AUC score
than the compared approaches.
Fig. 3.
Fig. 3
[102]Open in a new tab
Performance evaluation. The left panel is the ROC curves of original
NBI, HGBI, TL-HGBI and SSGC. The right panel is the numbers of
correctly retrieved disease-drug interactions with respect to different
percentiles
At the same time, we investigate the number of correctly retrieved
known drug-disease pairs among the top ranked prediction results.
Figure [103]3 (right) shows that SSGC performs the best. For example,
among the 1827 known drug-disease associations, 310 of them are
retrieved among the top 1% ranked predictions by SSGC, whereas only 170
(78) of them are retrieved by HGBI (TL-HGBI).
Investigating the integration strategy
In order to investigate whether our comprehensive similarities
combination strategy contributes to the good performance of SSGC, we
try to modify the compared methods so that they can adopt the same
strategies. As HGBI and TL-HGBI also utilize drug-drug and
disease-disease similarities to infer drug-disease interactions, it is
easy to modify them to employ the combined comprehensive similarities
as our method does. At the same time, SSGC can be turned to partly or
fully adopt the comprehensive similarities. After the modification, we
can investigate three methods in the way that multiple layers of data
are added gradually. Because NBI method only makes use of the topology
structure of drug-disease association network, we do not include it in
this comparing experiment.
The experiment results (Table [104]2) show that three methods are neck
and neck when just using the base layer. While along with the addition
of more layers of data, SSGC and HGBI achieve considerable improvements
in performance, TL-HGBI differs little at first, but its performance is
also improved with information in all layers and priori added in. The
results reflect the effectiveness of the comprehensive similarities
obtained by our integration strategy. It is interesting to find that
SSGC can be modified to be HGBI when setting
[MATH: Wst=
Sc(i,i′)Sd(j,j′<
/mrow>) :MATH]
, p=0 and μ=ξ, HGBI is a particular case of SSGC. Compared with HGBI,
SSGC has better performance, which illustrates that SSGC benefits from
introducing prior knowledge and removing the self-loops in the
heterogeneous network.
Table 2.
AUC scores of different algorithms modified to integrate different
layers
SSGC HGBI TL-HGBI
base 0.80 0.78 0.74
base + gene 0.87 0.85 0.74
base + gene + network 0.93 0.91 0.75
base + gene + network + priori 0.95 0.93 0.84
[105]Open in a new tab
The values in bold are the original AUC scores of three algorithms
before modification. To investigate the effect of integration strategy
of SSGC, we modified three algorithms to integrate different layers and
got other AUC scores listed in the table
Validating the predicted drug-disease associations
Distribution of predicted values
The overview of predicted interaction values is shown in Fig. [106]4.
From the histogram we can see that the predicted values of most of
drug-disease pairs are around zeros (In fact, there are only 20% of the
pairs with predicted values bigger than 0.1), suggesting that only a
small part of the unknown drug-disease pairs have repositioning
relations, which is consistent with the common sense that the
drug-disease treatments are specific. And the predicted values of
drug-disease pairs with known treatment relationships are above 0.8,
but it is not easy to find them in the histogram. To display the
distribution of significant predicted values more clearly, we further
ploted a subplot in Fig. [107]4. The predicted values of pairs with
known treatment relations (red points) are larger than most of pairs
with unknown relations (blue points), which also indicates that our
method can capture the known knowledge very well.
Fig. 4.
Fig. 4
[108]Open in a new tab
The overview of the predicted scores. The histogram represents the
distribution of predicted values of all drug-disease pairs. The red and
blue points in the subplot represent the predicted values of observed
true treatment relations and other drug-disease pairs (unknown
treatment relations) respectively
Validation in tissue-specific expression data
If a disease is manifested in a tissue in which the targets (genes) of
a drug are also expressed, then the drug is more likely to have
treatment association with the disease. Based on this hypothesis, we
utilize tissue-specific expression data to check whether our predicted
results are reasonable or not. On one hand, we gather the
disease-tissue associations from literature [[109]38]. On the other
hand, we get target-tissue (gene-tissue) associations from
tissue-specific gene expression data [[110]39], then further obtain the
drug-tissue associations. We observe the predicted association scores
of drug-disease pairs associated with the same tissue (Table [111]3).
As expected, those scores (from 0.09 to 0.33) are far greater than the
average (0.014) of all drug-disease association scores, which further
shows the efficiency and rationality of SSGC to discover the potential
drug-disease associations.
Table 3.
The drug-disease pairs related to the same tissue
Tissue Drug Disease Value
Pancreas Acetylsalicylic acid (DB00945) Diabetes Mellitus,
Noninsulin-Dependent (125853) 0.20
Pancreas Acetylsalicylic acid (DB00945) Cystic fibrosis by Pseudomonas
aeruginosa (219700) 0.32
Pancreas Acetaminophen (DB00316) Diabetes Mellitus,
Noninsulin-Dependent (125853) 0.13
Pancreas Acetaminophen (DB00316) Cystic fibrosis by Pseudomonas
aeruginosa (219700) 0.26
Skeletal Muscle Acetaminophen (DB00316) Myasthenic syndrome (601462)
0.22
Skin Lorazepam (DB00186) Immunodysregulation, Polyendo-crinopathy, And
X-Linked Enteropathy (304790) 0.17
Testis Lorazepam (DB00186) Persistent Mullerian duct syndrome, type II
(261550) 0.09
Testis Alprazolam (DB00404) Persistent Mullerian duct syndrome, type II
(261550) 0.10
Testis Acetaminophen (DB00316) Persistent Mullerian duct syndrome, type
II (261550) 0.24
Heart Acetylsalicylic acid (DB00945) Thrombosis, Susceptibility to
thrombin defect; thph1 (188050) 0.20
Heart Acetaminophen (DB00316) Thrombosis, Susceptibility to thrombin
defect; thph1 (188050) 0.33
Heart Acetaminophen (DB00316) Afibrinogenemia, congenital (202400) 0.25
Heart Acetylsalicylic acid (DB00945) Afibrinogenemia, congenital
(202400) 0.24
[112]Open in a new tab
Case studies for potential drug-disease relations
We select four diseases as case studies: Huntington disease (HD, OMIM
143100), Non-small-cell lung cancer (NSCLC, OMIM 211980), Alcohol
dependence (AD, OMIM 103780) and Small-cell lung cancer (SCLC, OMIM
182280). After excluding the known approved drugs which are also
predicted in the results (value > 0.8), we observe other predicted
top-20 ranked drugs. The investigation of the predicted drug-disease
associations included three parts as follows.
Investigation of the pathways overlapping between the disease and drugs
For a specific disease, if the related pathways of the drugs are
overlapped with those of the disease, the prediction results should be
convincible. Therefore, we first extracted the disease related genes
from OMIM, and the target genes of the top-20 drugs from DrugBank; and
then we got the enriched pathways of the two gene sets respectively
with DAVID [[113]40, [114]41], and investigated the overlap between
them.
For HD, each of the top-20 ranked drugs has KEGG pathways overlapping
with the disease pathways, shown in Fig. [115]5. The overlapped
pathways are “Neuroactive ligand-receptor interaction”, “Calcium
signaling pathway”, “Serotonergic synapse”, “Dopaminergic synapse”,
“cAMP signaling pathway” and “Cocaine addiction”. Each drug has 5
overlapped pathways in average.
Fig. 5.
Fig. 5
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Overlapped KEGG pathways between Huntington disease and the predicted
drugs. The blue hexagon nodes represent drugs predicted to treat
Huntington disease, the red vee nodes represent overlapped KEGG
pathways between drugs and Huntington disease
For NSCLC, 11 of the top-20 drugs have overlapped KEGG pathways with
the disease pathways, shown in Fig. [117]6. Especially, Caffeine
(DB00201) has 12 overlapped pathways, Sorafenib (DB00398) and Bosutinib
(DB06616) have 10 overlapped pathways, Regorafenib (DB08896) has 9
overlapped pathways.
Fig. 6.
Fig. 6
[118]Open in a new tab
Overlapped KEGG pathways between Non-small-cell lung cancer and the
predicted drugs. The blue hexagon nodes represent drugs predicted to
treat Non-small-cell lung cancer, the red vee nodes represent
overlapped KEGG pathways between drugs and Non-small-cell lung cancer
For AD, 18 of the top-20 drugs have overlapped KEGG pathways with the
disease pathways, shown in Fig. [119]7. The overlapped pathways are
“Calcium signaling pathway”, “Neuroactive ligand-receptor interaction”,
“Serotonergic synapse” and “Gap junction”.
Fig. 7.
Fig. 7
[120]Open in a new tab
Overlapped KEGG pathways between Alcohol dependence and the predicted
drugs. The blue hexagon nodes represent drugs predicted to treat
Alcohol dependence, the red vee nodes represent overlapped KEGG
pathways between drugs and Alcohol dependence
For SCLC, Carboplatin (DB00958), Adenosine triphosphate (DB00171) and
Glutathione (DB00143) have overlapped KEGG pathways with the disease
pathways. The overlapped pathways are “ABC transporters”, “Bile
secretion” and “Drug metabolism - cytochrome P450”, which are shown in
Fig. [121]8. Besides, Sorafenib (DB00398), Regorafenib (DB08896) and
Ponatinib (DB08901) have cancer related pathways, such as “Pathways in
cancer”, “Central carbon metabolism in cancer” and “Proteoglycans in
cancer”.
Fig. 8.
Fig. 8
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Overlapped KEGG pathways between Small-cell lung cancer and the
predicted drugs. The blue hexagon nodes represent drugs predicted to
treat Small-cell lung cancer, the red vee nodes represent overlapped
KEGG pathways between drugs and Small-cell lung cancer
Verification in CTD database
The Comparative Toxicogenomics Database (CTD, [123]http://ctdbase.org)
provides information about associations among chemicals, genes and
diseases [[124]42]. We search these four diseases in the CTD database,
and their related chemicals will be listed out. These listed chemicals
are associated with the disease or its descendants. If a chemical has a
curated association to the disease, it will be signed with
“marker/mechanism” or “therapeutic” in the “Direct Evidence” item,
otherwise if the chemical just has inferred association via a curated
gene interaction, there is no sign in “Direct Evidence” item. To
evaluate our approach, we check the top-20 ranked drugs predicted in
our method one by one to verify whether the drug-disease interaction
can be found in CTD database (Table [125]4).
Table 4.
The top-ranked predictions for selected diseases(Verification in CTD
database)
Disease Known drugs Part of top-ranked predictions Direct evidence
HD (143100) Baclofen (DB00181) Clozapine (DB00363, rank:01)
Tetrabenazine (DB04844) Olanzapine (DB00334, rank:03) T
Aripiprazole (DB01238, rank:06) T
Amitriptyline (DB00321, rank:10)
Risperidone (DB00734, rank:12)
NSCLC (211980) Doxorubicin (DB00997) Carboplatin (DB00958, rank:01) T
Adenosine triphosphate (DB00171, rank:02)
Glutathione (DB00143, rank:05)
Ponatinib (DB08901, rank:09)
Sorafenib (DB00398, rank:10)
Dasatinib (DB01254, rank:14)
Daunorubicin (DB00694, rank:15)
Epirubicin (DB00445, rank:16) T
Bosutinib (DB06616, rank:18)
Caffeine (DB00201, rank:19)
Cisplatin (DB00515, rank:20) T
AD (103780) Citalopram (DB00215) Lorazepam (DB00186, rank:04) T
Chlordiazepoxide (DB00475) Diazepam (DB00829, rank:10)
Acamprosate (DB00659) Clomipramine (DB01242, rank:13)
Naltrexone (DB00704) Flunitrazepam (DB01544, rank:14)
Disulfiram (DB00822) Adenosine triphosphate (DB00171, rank:17)
Ondansetron (DB00904) Trazodone (DB00656, rank:18)
Imipramine (DB00458, rank:20)
SCLC (182280) Cisplatin (DB00515) Carboplatin (DB00958, rank:01) T
Methotrexate (DB00563) Adenosine triphosphate (DB00171, rank:02)
Teniposide (DB00444) Irinotecan (DB00762, rank:04) T
Etoposide (DB00773) Glutathione (DB00143, rank:07)
Topotecan (DB01030) Doxorubicin (DB00997, rank:09) T
Daunorubicin (DB00694, rank:11)
Sorafenib (DB00398, rank:13)
Ponatinib (DB08901, rank:16)
Epirubicin (DB00445, rank:18) T
[126]Open in a new tab
In the “Direct Evidence” item, according to the instructions in CTD
database, “T” means “therapeutic”, i.e., the drug has a curated
association to the disease, other top-ranked drugs aren’t signed with
“T” in this table means that they have an inferred association via a
curated gene interaction
As shown in Table [127]4, Five drugs are associated with HD, Olanzapine
(DB00334) and Aripiprazole (DB01238) have curated association to HD,
which are signed with “T” in the “Direct Evidence” item. Eleven drugs
are associated with NSCLC, Carboplatin (DB00958), Epirubicin (DB00445)
and Cisplatin (DB00515) have curated association to NSCLC. Seven drugs
have association to AD, Lorazepam (DB00186) has curated association to
AD. Nine drugs are associated with SCLC, Carboplatin (DB00958),
Irinotecan (DB00762), Doxorubicin (DB00997) and Epirubicin (DB00445)
have curated association to SCLC.
Verification in literature
To further examine the predicted results, we check them using
literature support, and list out the drugs which have been verified in
the published papers (Table [128]5). Among the top ranked drugs, six
drugs have been reported in the treatment of HD [[129]43–[130]48];
three drugs have been found to treat NSCLC [[131]49–[132]51]; the study
of Butriptyline (DB09016) on AD has already been reported by Pani etc
[[133]52], and the clinical trial of drug Lorazepam (DB00186) on AD has
already been done [[134]53]; Carboplatin (DB00958), Irinotecan
(DB00762), Doxorubicin (DB00997) and Epirubicin (DB00445) have already
been studied to treat SCLC [[135]54–[136]58].
Table 5.
The top-ranked predictions for selected diseases(Verification in
literature)
Disease Known drugs (DrugBank IDs) Part of top-ranked predictions
HD (143100) Baclofen (DB00181) Clozapine (DB00363, rank:01)
Tetrabenazine (DB04844) Olanzapine (DB00334, rank:03)
Ziprasidone (DB00246, rank:05)
Aripiprazole (DB01238, rank:06)
Quetiapine (DB01224, rank:07)
Risperidone (DB00734, rank:12)
NSCLC (211980) Doxorubicin (DB00997) Carboplatin (DB00958, rank:01)
Epirubicin (DB00445, rank:16)
Cisplatin (DB00515, rank:20)
AD (103780) Citalopram (DB00215) Butriptyline (DB09016, rank:03)
Chlordiazepoxide (DB00475) Lorazepam (DB00186, rank:04)
Acamprosate (DB00659)
Naltrexone (DB00704)
Disulfiram (DB00822)
Ondansetron (DB00904)
SCLC (182280) Cisplatin (DB00515) Carboplatin (DB00958, rank:01)
Methotrexate (DB00563) Irinotecan (DB00762, rank:04)
Teniposide (DB00444) Doxorubicin (DB00997, rank:09)
Etoposide (DB00773) Epirubicin (DB00445, rank:18)
Topotecan (DB01030)
[137]Open in a new tab
All above results have demonstrated the effectiveness of our approach
to discover the potential drug-disease interactions.
Discussion and conclusion
In this paper, we propose a novel method, SSGC, to uncover the
potential associations between drugs and diseases. The main
contributions are as follows: Firstly, we have presented a hierarchial
framework to integrate multiple source of data, including information
of drug substructures, disease phenotypes, gene-gene interactions, and
known drug-disease treatment relationships. The integration framework
can be easily extended to integrate more data. Secondly, we measured
the comprehensive similarities of drugs and diseases from multi-view
and multiple layers, which is different with many other methods that
just obtain the similarity from the chemical structure and the disease
phenotype. The base layer reflects the drug structural similarity and
disease phenotype similarity, which are the original features. The gene
layer reflects the functional similarities of drugs and diseases, which
are calculated based on the assumption that diseases (drugs) associated
with some common genes or gene pathways might have analogous functional
mechanism. The treatment layer takes the known drug-disease
relationships into account, which can improve the similarities of drugs
and diseases. Therefore, the comprehensive similarities can improve the
prediction accuracy and are easily interpretable. Thirdly, we model the
prediction as a graph cut problem, and develop a semi-supervised
algorithm, SSGC, to resolve it. The experimental results imply that
SSGC significantly outperforms three representative approaches.
Besides, KEGG pathway enrichment analysis and the validations via CTD
database and literature also demonstrated that SSGC is useful to
predict the potential associations between drugs and diseases. In fact,
the proposed SSGC algorithm can also be used in other recommendation
systems, such as recommending products to customers.
Of course, there is a long way to go in the process of drug discovery.
And there are many other types of data (side effect data of chemicals,
clinical symptoms and signs, and so on) could be utilized to predict
drug-disease interactions. For example, Rastegar-Mojarad et al.
utilized phenome-wide association studies (PheWAS) data and further
expanded the horizon for the prediction of drug-disease interactions
[[138]59]. However, how to fuse multiple sources of data more properly
and rationally and how to develop prediction models with better
performance and interpretability are still full of challenges.
Acknowledgments