# A Unified View of Relational Deep Learning for Drug Pair Scoring

Benedek Rozemberczki1 Stephen Bonner2 Andriy Nikolov1 Michaël Ughetto1
Sebastian Nilsson1 &Eliseo Papa1 1Research Data & Analytics, Research &
Development IT, AstraZeneca
2Data Sciences and Quantitative Biology, Discovery Sciences R&D, AstraZeneca
<EMAIL_ADDRESS>
###### Abstract

In recent years, numerous machine learning models which attempt to solve
polypharmacy side effect identification, drug-drug interaction prediction and
combination therapy design tasks have been proposed. Here, we present a
unified theoretical view of relational machine learning models which can
address these tasks. We provide fundamental definitions, compare existing
model architectures and discuss performance metrics, datasets and evaluation
protocols. In addition, we emphasize possible high impact applications and
important future research directions in this domain.

##  1 Introduction

Relational deep learning has an unprecedented potential for revolutionizing
the drug discovery process and pharmaceutical industry Gaudelet et al. (2021).
A number of high value use cases for relational deep learning in the
pharmaceutical domain involve answering questions about what happens when two
drugs are administered at the same time. These potential applications might
want to answer questions such as: Will a combination of two drugs be more
effective at destroying a specific type of lung cancer cells Preuer et al.
(2018)? Is there an unexpected (polypharmacy) side effect Zitnik et al. (2018)
of using these two drugs together? Is there an unwanted chemical interaction
Sunyoung et al. (2017) that these drug molecules can have?

All of these previously mentioned questions can be answered by what we see as
drug pair scoring, a machine learning task that involves a set of drugs and
the task of predicting the behaviour of pairs in a specific context of
interest. Given an incomplete database of drug pairs, drug administration
contexts and outcomes, the goal is to train a model to accurately make
probabilistic predictions for unseen entries. The reasons for answering these
questions via algorithmic methods are multi-fold. Firstly, testing all drug
pairs in all of the contexts is not feasible due to time and financial
constraints such as drug prices and labour costs Preuer et al. (2018).
Secondly, certain pair scoring tasks such as polypharmacy side effect
prediction can only be validated in human-based trials. Finally, laboratory
testing of drug pairs is prone to human errors Liu et al. (2020).

Traditional supervised machine learning methods which solve the drug pair
scoring task use handcrafted molecular features to predict the outcome of
administering the drugs together in a specific context Sidorov et al. (2019);
Chiang et al. (2020). Another group of techniques uses an unsupervised
approach which diffuses the profile of the drug pair on a heterogeneous
biological graph Zhang et al. (2017); Li et al. (2018); Huang et al. (2019) in
order to find potential polypharmacy, synergy or interaction indications. Deep
learning techniques which solve the drug pair scoring task can be seen as a
fusion and extension of these traditional methods. Such models first generate
drug representations based either on molecular structure or the heterogeneous
graph based neighbourhood context. In the second optional step, these
representations are propagated in the biological graph and aggregated.
Finally, drug pair representations are formed and probability scores are
outputted in the specific drug administration contexts. We present a high
level summary of the drug pair scoring task idea in Figure 1.

Figure 1: Drug-drug interaction, polypharmacy side effect, and pair
combination therapy design prediction tasks follow the same template. Given a
pair of drugs with optional biological context, the task is to predict an
outcome in a specific application domain. Relational machine learning models
which solve these task can exploit molecular features, knowledge graph based
neighbourhoods or both.

Our main contributions can be summarized as:

  1. 1.

We provide a unification of drug-drug interaction, polypharmacy side effect
and synergistic drug combination prediction tasks.

  2. 2.

We present an overview on the design of relational machine learning models
which can address these predictive tasks.

  3. 3.

We highlight the publicly available datasets used to train and test the models
on these tasks and survey the literature for the most commonly used evaluation
metrics.

  4. 4.

We review the most important applications of these techniques and discuss
directions for future research in the domain.

The remainder of this survey is structured as follows. In Section 2 we
establish the foundations of a unified view of discriminative machine learning
tasks defined on pairs of drugs. Section 3 discusses the architectural details
of models that can solves these tasks. The evaluation metrics, protocols and
datasets used in the literature are detailed in Section 4. Several important
key application areas are highlighted in Section 5. We discuss the limitations
of current approaches and future research directions in Section 6. The paper
concludes with Section 7. The survey is supported by a collection of relevant
works under the https://github.com/AstraZeneca/polypharmacy-ddi-synergy-survey
repository.

##  2 Background

Our discussion of drug pair scoring models requires the introduction of a drug
set $\mathcal{D}=\\{d_{1},\dots,d_{n}\\}$ that describes compounds of interest
and a context set $\mathcal{C}=\\{c_{1},\dots,c_{k}\\}$ that contains contexts
where two drugs are used in a pair combination.

######  Definition 1.

Labeled drug pair. A labeled drug pair defined on drug set $\mathcal{D}$ and
context set $\mathcal{C}$ is the tuple $(d,d^{\prime},c,y_{d,d^{\prime},c})$,
where the binary indicator $y_{d,d^{\prime},c}\in\left\\{0,1\right\\}$ is the
outcome for drug pair $d,d^{\prime}\in\mathcal{D}$ in context
$c\in\mathcal{C}$.

A labeled drug pair is a known fact about the drug pair having an effect in a
context such as a specific polypharmacy side effect, interaction or
synergistic relationship at treating a disease. The purpose of pair scoring
models is to learn from these tuples to predict the labels for unlabeled drug
pairs and contexts.

######  Definition 2.

Database of labeled drug pairs. A database of labeled drug pairs defined on
drug and context sets $\mathcal{D}$ and $\mathcal{C}$ is the set $\mathcal{S}$
containing labeled drug pairs $(d,d^{\prime},c,y_{d,d^{\prime},c})$ where
$d,d^{\prime}\in\mathcal{D}$ and $c\in\mathcal{C}$.

Pair scoring models are trained on databases of labeled drug pairs and the
trained models are used to predict the label of pairs for which we do not know
the outcome in certain contexts.

######  Definition 3.

Heterogeneous interaction graph with drug entities. We denote with
$G(\mathcal{V},\mathcal{R},\mathcal{E})$ the heterogeneous interaction graph
with drug entities, where $\mathcal{V}$ and $\mathcal{R}$ are the entity and
relation sets, it holds that the drug set $\mathcal{D}\subset\mathcal{V}$ and
$\mathcal{E}$ is formed by typed edges of the form
$(v,r,u)\in\mathcal{V}\times\mathcal{R}\times\mathcal{V}$ .

We consider a heterogeneous graph where the drug set is a subset of the vertex
set. This definition of heterogeneous (biological) knowledge graph helps to
create knowledge graph based representation for the compounds of interest.

######  Definition 4.

Neighbourhood encoder. A neighbourhood encoder is the function:

$\displaystyle\mathbf{h}_{d}=\textsc{aggregate}(\Theta_{u},\forall
u\in\mathcal{N}(d)).$ (1)

In Equation (1) $\Theta_{u}$ is a parametric vector representation of
$u\in\mathcal{V}$ and $\mathcal{N}(\cdot)$ is a neighbourhood set.

The neighbourhood encoder function Hamilton et al. (2017) creates a vector
representation of drug vertices of the graph based on the aggregation of
trainable parameter vectors in the neighbourhood of the source node.
Neighbourhoods of a drug can be defined based on arbitrary notions of
proximity and the aggregation itself could be a parametric transformation.

######  Definition 5.

Molecular encoder. A molecular encoder is the function
$\textbf{h}_{d}=h_{\Theta}(\mathcal{M}_{d})$, parametrized by $\Theta$ where
$\textbf{h}_{d}$ is the learned vector representation and $\mathcal{M}_{d}$ is
a generic notation of molecular features describing the drug $d$.

A molecular encoder is a neural network which generates a vector
representation from the features of the molecule - these molecular features
can be derived from generic features (e.g. hydrophilicity), a string
representation, molecular graph or geometry.

######  Definition 6.

Neighbourhood informed molecular encoder. This encoder is the function :

$\textbf{h}_{d}=\textsc{aggregate}(h_{\Theta}(\mathcal{M}_{u}),\forall
u\in\mathcal{N}(d));$

where $h_{\Theta}(\mathcal{M}_{u})$ and $\textsc{aggregate}(\cdot,\forall
u\in\mathcal{N}(d))$ are molecular and neighbourhood encoders respectively.

This encoder combines the layers described in Definitions 4 and 5. It is
essentially a neighbourhood encoder parametrized by representations outputted
by a molecular encoder – molecular representations learned by the molecular
encoder are aggregated in the neighbourhood of source drug nodes in the
knowledge graph which has drug entities.

######  Definition 7.

Molecular representation combiner. Given the drugs
$d,d^{\prime}\in\mathcal{D}$ with vector representations
$\textbf{h}_{,}\textbf{h}_{d^{\prime}}$ the molecular representation combiner
is the function
$\textbf{h}_{d,d^{\prime}}=g_{\Theta}(\textbf{h}_{d};\textbf{h}_{d^{\prime}})$
that outputs $\textbf{h}_{d,d^{\prime}}$ a vector representation of the drug
pair.

The representation output by this combiner function can be drug orchestration
order dependent. This way the temporal order of drug orchestration can be
expressed by the pair scoring model. For example the concatenation of drug
vectors results in order dependent representations of pairs, while a bilinear
transformation of drug representations with a diagonal matrix does not.

######  Definition 8.

Scoring head layer. The scoring head layer is the function
$\hat{y}_{d,d^{\prime},c}=k_{\Theta}(\textbf{h}_{d,d^{\prime}},c)$, where the
predicted label proability satisfies that
$\\{\hat{y}_{d,d^{\prime},c}\in\mathbb{R}\mid
0\leq\hat{y}_{d,d^{\prime},c}\leq 1\\}$.

Given a drug pair representation and a context, the scoring head layer outputs
a probability score for the outcome.

######  Definition 9.

Drug pair scoring loss and cost functions. Given the drug pair
$d,d^{\prime}\in\mathcal{D}$ , context $c\in\mathcal{C}$, ground-truth label
$y_{d,d^{\prime},c}$ and predicted score $\hat{y}_{d,d^{\prime},c}$ the loss
is defined as the function
$\ell(y_{d,d^{\prime},c};\hat{y}_{d,d^{\prime},c})$. The cost on the whole
drug pair database $\mathcal{S}$ is defined by Equation (2).

$\displaystyle\mathcal{L}$
$\displaystyle=\sum\limits_{(d,d^{\prime},c)\in\mathcal{S}}\ell(y_{d,d^{\prime},c};\hat{y}_{d,d^{\prime},c}).$
(2)

In practical settings, drug pair scoring models are trained by the
minimization of the binary cross-entropy summed over the labeled drug pair,
context triples.

Table 1: A machine learning task, model view level, induction, interaction graph node type (entity) and drug feature based comparison of drug pair scoring machine learning models. Machine learning models that solve a specific pair scoring task are ordered chronologically in the table. |  |  |  |  | Entity Types | Drug Features
---|---|---|---|---|---|---
Task | Method | Reference | Model view | Induction | Drug | Protein | Disease | SMILES | Graph | Geometry | Generic
Polypharmacy | DECAGON | Zitnik et al. (2018) | Higher |  | $\bullet$ | $\bullet$ |  |  |  |  |
KBLRN | Malone et al. (2018) | Higher |  | $\bullet$ | $\bullet$ |  |  |  |  |
SDHINE | Hu et al. (2018) | Higher |  | $\bullet$ | $\bullet$ | $\bullet$ |  |  |  |
ESP | Burkhardt et al. (2019) | Higher |  | $\bullet$ | $\bullet$ |  |  |  |  |
MHCADDI | Deac et al. (2019) | Lower | $\bullet$ |  |  |  |  | $\bullet$ |  |
TIP | Xu et al. (2020) | Higher |  | $\bullet$ | $\bullet$ |  |  |  |  |
Interaction | DeepCCI | Sunyoung et al. (2017) | Lower | $\bullet$ |  |  |  | $\bullet$ |  |  | $\bullet$
MVGAE | Ma et al. (2018) | Hierarchical | $\bullet$ | $\bullet$ | $\bullet$ | $\bullet$ | $\bullet$ |  |  |
DeepDDI | Ryu et al. (2018) | Lower | $\bullet$ |  |  |  | $\bullet$ |  |  |
D3I | Peng et al. (2019) | Hierarchical |  | $\bullet$ |  |  |  |  |  | $\bullet$
MR-GNN | Xu et al. (2019) | Lower | $\bullet$ |  |  |  |  | $\bullet$ |  |
SkipGNN | Huang et al. (2020a) | Higher |  | $\bullet$ | $\bullet$ | $\bullet$ |  |  |  |
CASTER | Huang et al. (2020b) | Lower | $\bullet$ |  |  |  | $\bullet$ |  |  |
DeepDrug | Cao et al. (2020) | Lower | $\bullet$ |  |  |  | $\bullet$ | $\bullet$ | $\bullet$ |
GoGNN | Wang et al. (2020) | Hierarchical |  | $\bullet$ |  |  |  | $\bullet$ |  |
DPDDI | Feng et al. (2020) | Lower | $\bullet$ |  |  |  |  |  |  | $\bullet$
KGNN | Lin et al. (2020) | Higher |  | $\bullet$ | $\bullet$ | $\bullet$ |  |  |  |
BiGNN | Bai et al. (2020) | Hierarchical | $\bullet$ | $\bullet$ | $\bullet$ |  |  | $\bullet$ |  |
MIRACLE | Wang et al. (2021b) | Hierarchical | $\bullet$ | $\bullet$ |  |  |  | $\bullet$ |  |
EPGCN-DS | Sun et al. (2020a) | Lower | $\bullet$ |  |  |  |  |  |  |
SumGNN | Yu et al. (2021) | Higher |  | $\bullet$ | $\bullet$ | $\bullet$ |  |  |  |
DANN-DDI | Liu et al. (2021b) | Higher |  | $\bullet$ | $\bullet$ |  |  |  |  |
SSI-DDI | Nyamabo et al. (2021) | Lower |  |  |  |  |  | $\bullet$ |  |
MTDDI | Feng et al. (2021) | Hierarchical |  | $\bullet$ | $\bullet$ | $\bullet$ |  |  |  | $\bullet$
MUFFIN | Chen et al. (2021) | Hierarchical |  | $\bullet$ | $\bullet$ | $\bullet$ | $\bullet$ |  |  |
DDIAAE | Dai et al. (2021) | Higher |  | $\bullet$ | $\bullet$ | $\bullet$ |  |  |  |
RWGCN | Feeney et al. (2021) | Higher |  | $\bullet$ | $\bullet$ | $\bullet$ |  |  |  |
SmileGNN | Han et al. (2021) | Hierarchical |  | $\bullet$ | $\bullet$ |  | $\bullet$ |  |  |
| GCN-BMP | Chen et al. (2020) | Lower | $\bullet$ | $\bullet$ |  |  | $\bullet$ |  |  |
Synergy | DeepSynergy | Preuer et al. (2018) | Lower | $\bullet$ |  |  |  |  |  |  | $\bullet$
MCDC | Chen et al. (2019) | Hierarchical |  | $\bullet$ | $\bullet$ |  | $\bullet$ |  |  |
DTF | Sun et al. (2020b) | Higher |  | $\bullet$ |  |  |  |  |  |
DeepSignalFlow | Zhang et al. (2021a) | Hierarchical |  | $\bullet$ | $\bullet$ | $\bullet$ |  |  |  |
DeepDDS | Wang et al. (2021a) | Lower | $\bullet$ |  |  |  | $\bullet$ |  |  |
GraphSynergy | Yang et al. (2021) | Higher |  | $\bullet$ | $\bullet$ |  |  |  |  |
TranSynergy | Liu et al. (2021a) | Hierarchical | $\bullet$ | $\bullet$ | $\bullet$ |  |  |  |  | $\bullet$
MatchMaker | Brahim et al. (2021) | Lower | $\bullet$ |  |  |  | $\bullet$ |  |  | $\bullet$
AuDNNSynergy | Zhang et al. (2021b) | Lower | $\bullet$ |  |  |  | $\bullet$ |  |  |
AID | Kim et al. (2021) | Hierarchical | $\bullet$ | $\bullet$ | $\bullet$ |  | $\bullet$ |  |  |
MOOMIN | Rozemberczki et al. (2021a) | Hierarchical | $\bullet$ | $\bullet$ | $\bullet$ |  |  | $\bullet$ |  |

##  3 Drug Pair Scoring Models

Our discussion of the drug pair scoring models introduces our unified view
about the general architecture of these models and compares state-of-the-art
architecture designs.

###  3.1 Unified View: The Drug Pair Scoring Model

Based on the definitions outlined in Section 2 we propose a unified view of
drug pair scoring models. We postulate that the abstract design of drug pair
scoring models irrespective of the specific subtask solved always has the
following architecture:

  1. 1.

An encoder to generate drug representations - this can be one of the functions
described by Definitions 4, 5 and 6.

  2. 2.

A molecular representation combiner function to generate a drug pair
representation – see Definition 7.

  3. 3.

The scoring head layer to predict the probability of a context dependent
outcome proposed by Definition 8.

  4. 4.

The loss function of Definition 9 which depends on ground-truth labels and the
probabilities output by the head layer.

This architecture and design allows for the joint end-to-end training of the
individual model components – gradient descent based update of the layer
weights.

###  3.2 Specific Architecture Designs

We compare state-of-the-art model architectures in Table 1 that can solve pair
scoring tasks. Our comparison considers the model level, induction
capabilities, specific subtask, node types of the heterogeneous graph and the
molecular features exploited by the model. Model attributes used for
comparison were the following:

  * •

Model level: A model operates at the following levels based on the encoder
architecture used for generating the drug representations: (a) higher-view –
neighbourhood encoder, (b) lower-view – molecular encoder, (c) hierarchical-
view – neighbourhood informed molecular encoder.

  * •

Machine learning task: The drug pair scoring task of interest solved by the
dedicated model architecture proposed in the research paper. It has to be one
of interaction, polypharmacy or synergy prediction.

  * •

Induction: A model is inductive if it can predict the label of drug pairs
where at least one of the drugs was not in the training set drug pairs.

  * •

Entities: The types of hetereogeneous graph entities (drugs, proteins,
diseases) used by the model to solve the task.

  * •

Drug features: Molecular features and information about the compound encoded
by the molecular encoder function.

Our comparison highlights that there is a hard trade-off between induction and
the exclusion of compound features. It is also evident that there is a
connection between the machine learning subtask and the model architecture
design: for example, polypharmacy side effect prediction models are mostly
high level transductive neighbourhood encoders with a scoring layer on top.
Synergy scoring models are mostly inductive techniques which exploit the
molecular information about the drugs. Currently, there is no single pair
scoring model which includes all of the considered biological modalities.

##  4 Evaluation

The evaluation of machine learning models requires performance metrics, train-
test split strategies and publicly accessible datasets.

###  4.1 Performance Metrics

The predictive performance of drug pair scoring models is evaluated by metrics
tailored to binary classification tasks. We summarise how these metrics are
used for the evaluation of state-of-the-art drug pair scoring architectures in
Table 2.

Table 2: Predictive performance evaluation metrics used by the research papers which proposed novel drug pair scoring techniques. Models are grouped by the pair scoring task and ordered chronologically. |  | Evaluation metric
---|---|---
Model | Reference | AUPRC | AUROC | Precision | Recall | Accuracy | $\textbf{F}_{1}$
DECAGON | Zitnik et al. (2018) | $\bullet$ | $\bullet$ | $\bullet$ |  |  |
KBLRN | Malone et al. (2018) | $\bullet$ | $\bullet$ | $\bullet$ |  |  |
SDHINE | Hu et al. (2018) |  | $\bullet$ | $\bullet$ |  |  |
ESP | Burkhardt et al. (2019) | $\bullet$ | $\bullet$ | $\bullet$ |  |  |
MHCADDI | Deac et al. (2019) |  | $\bullet$ |  |  |  |
TIP | Xu et al. (2020) | $\bullet$ | $\bullet$ | $\bullet$ |  |  |
DeepCCI | Sunyoung et al. (2017) |  | $\bullet$ |  |  | $\bullet$ | $\bullet$
MVGAE | Ma et al. (2018) | $\bullet$ | $\bullet$ |  |  |  |
DeepDDI | Ryu et al. (2018) |  |  | $\bullet$ | $\bullet$ | $\bullet$ | $\bullet$
D3I | Peng et al. (2019) |  |  | $\bullet$ | $\bullet$ | $\bullet$ | $\bullet$
MR-GNN | Xu et al. (2019) |  | $\bullet$ |  | $\bullet$ |  | $\bullet$
SkipGNN | Huang et al. (2020a) | $\bullet$ |  |  |  |  | $\bullet$
CASTER | Huang et al. (2020b) | $\bullet$ | $\bullet$ |  |  |  | $\bullet$
DeepDrug | Cao et al. (2020) | $\bullet$ | $\bullet$ |  |  |  |
GoGNN | Wang et al. (2020) |  | $\bullet$ | $\bullet$ |  |  |
DPDDI | Feng et al. (2020) | $\bullet$ | $\bullet$ | $\bullet$ | $\bullet$ | $\bullet$ | $\bullet$
KGNN | Lin et al. (2020) | $\bullet$ | $\bullet$ |  |  | $\bullet$ | $\bullet$
BiGNN | Bai et al. (2020) |  | $\bullet$ | $\bullet$ |  |  | $\bullet$
MIRACLE | Wang et al. (2021b) | $\bullet$ | $\bullet$ |  |  |  | $\bullet$
EPGCN-DS | Sun et al. (2020a) |  | $\bullet$ |  |  |  | $\bullet$
SumGNN | Yu et al. (2021) | $\bullet$ | $\bullet$ | $\bullet$ |  |  | $\bullet$
DANN-DDI | Liu et al. (2021b) | $\bullet$ | $\bullet$ | $\bullet$ | $\bullet$ | $\bullet$ | $\bullet$
SSI-DDI | Nyamabo et al. (2021) | $\bullet$ | $\bullet$ |  |  | $\bullet$ |
MTDDI | Feng et al. (2021) | $\bullet$ | $\bullet$ | $\bullet$ | $\bullet$ | $\bullet$ | $\bullet$
MUFFIN | Chen et al. (2021) |  | $\bullet$ | $\bullet$ | $\bullet$ | $\bullet$ | $\bullet$
DDIAAE | Dai et al. (2021) | $\bullet$ | $\bullet$ | $\bullet$ |  |  |
RWGCN | Feeney et al. (2021) | $\bullet$ | $\bullet$ |  |  |  |
SmileGNN | Han et al. (2021) |  | $\bullet$ |  |  | $\bullet$ | $\bullet$
GCN-BMP | Chen et al. (2020) | $\bullet$ | $\bullet$ |  |  |  | $\bullet$
DeepSynergy | Preuer et al. (2018) | $\bullet$ | $\bullet$ | $\bullet$ |  | $\bullet$ |
MCDC | Chen et al. (2019) | $\bullet$ | $\bullet$ |  |  |  |
DTF | Sun et al. (2020b) | $\bullet$ | $\bullet$ | $\bullet$ |  | $\bullet$ |
DeepSignalFlow | Zhang et al. (2021a) |  |  |  |  | $\bullet$ |
DeepDDS | Wang et al. (2021a) | $\bullet$ | $\bullet$ | $\bullet$ |  | $\bullet$ |
GraphSynergy | Yang et al. (2021) | $\bullet$ | $\bullet$ |  | $\bullet$ | $\bullet$ | $\bullet$
TranSynergy | Liu et al. (2021a) | $\bullet$ | $\bullet$ |  |  |  |
MatchMaker | Brahim et al. (2021) | $\bullet$ | $\bullet$ |  |  |  |
AuDNNSynergy | Zhang et al. (2021b) | $\bullet$ | $\bullet$ | $\bullet$ |  | $\bullet$ |
AID | Kim et al. (2021) | $\bullet$ |  |  |  |  |
MOOMIN | Rozemberczki et al. (2021a) | $\bullet$ | $\bullet$ |  |  |  | $\bullet$

Looking at Table 2 it is evident that the evaluation metrics used in the
literature can be grouped into two categories:

  * •

Score based metrics: These quantify predictive performance based over the
whole domain of discrimination thresholds. The precision-recall area under the
curve (AUPRC) considers the precision-recall trade off under the whole domain
of discrimination thresholds while the receiver operating characteristic area
under the curve (AUROC) considers false and true positive rates.

  * •

Hard cut off evaluation metrics: These performance metrics (accuracy,
$\text{F}_{1}$ score, precision, recall) apply a hard discrimination threshold
to assign a label to the data points based on the scores output by the pair
scoring model. In order to calculate these, one needs to set a discrimination
threshold.

Our findings demonstrate that pair scoring models are predominantly evaluated
by score based metrics (AUPRC and AUROC) which do not require manual setting
of a discrimination threshold. It is also evident that seminal research works
which defined the key pair scoring tasks influenced the later evaluation
metric choices – polypharmacy prediction models adapted the evaluation metrics
from Zitnik et al. (2018) for example.

###  4.2 Train-Test Split Strategies

The evaluation of drug pair scoring tasks allows for the use of various train-
test split strategies Preuer et al. (2018) to test the performance of the
model under cold-start and inductive scenarios Dewulf et al. (2021). Given a
labeled drug pair-context database $\mathcal{S}$, defined on the drug and
context sets $\mathcal{D}$ and $\mathcal{C}$, we assume that one can create
the randomized splits $\mathcal{S}_{Train}$ and $\mathcal{S}_{Test}$. We
summarized these splitting strategies in Figure 2.

Figure 2: The train and test split of drug pair scoring datasets allows for
various stratified splits. Stratification of the pairs can happen across the
evaluated drugs or the outcomes being tested. Drug pairs used for training the
pair scoring model are denoted with white, pairs used for testing are denoted
with gray.

Using the formalism established to describe the pair scoring models, the
splitting strategies are defined as:

  * •

Random split: labeled drug pair - context entries of $\mathcal{S}$ are
randomly split between $\mathcal{S}_{Train}$ and $\mathcal{S}_{Test}$.

  * •

Drug pair stratified split: A drug pair $d,d^{\prime}\in\mathcal{D}$ that
appears in entries of $\textit{S}_{Train}$ does not appear in entries of
$\mathcal{S}_{Test}$. This split requires a pair scoring model which is
inductive with respect to drugs.

  * •

Drug stratified split: A drug $d\in\mathcal{D}$ that appears in entries of
$\mathcal{S}_{Train}$ does not appear in entries of $\mathcal{S}_{Test}$. Like
the drug pair stratified split this requires the model to be inductive with
respect to new drugs.

  * •

Context stratified split: A context $c\in\mathcal{C}$ that appears in entries
of $\mathcal{S}_{Train}$ does not appear in entries of $\mathcal{S}_{Test}$.
This requires that the pair scoring model is inductive with respect to the set
of contexts.

###  4.3 Datasets

We detail public sources for drug pair data which have been used by the
approaches in this review in Table 3. Datasets are listed chronologically
according to subtask and the licence and any restrictions for commercial use
are detailed where available. It can be seen that the majority of datasets
contain a small number of drugs, indicating most focus on approved drugs
rather than all possible compounds, with the interactions captured in drug
pairs being much more numerous.

Table 3: Public drug pair scoring datasets ordered chronologically with the subtask, number of compounds, count of tested compound pairs, cardinality of the context set, licence and if commercial use is explicitly restricted. Dataset | Reference | Subtask | Compounds | Pairs | Contexts | Licence | Restricted
---|---|---|---|---|---|---|---
TWOSIDES | Tatonetti et al. (2012) | Polypharmacy | 1,918 | 211,990 | 12,726 | Not Specified |
DrugBank 5 | Wishart et al. (2018) | Polypharmacy | 14,575 | 365,000+ | 86+ | CC BY-NC 4.0 | $\bullet$
DeepDDI | Ryu et al. (2018) | Polypharmacy | 1,710 | 191,995 | 86 | Not Specified |
TDC (TWOSIDES) | Huang et al. (2021) | Polypharmacy | 645 | 63,473 | 1,317 | CC BY 4.0 |
TDC (DrugBank) | Huang et al. (2021) | Polypharmacy | 1,706 | 191,519 | 86 | CC BY-NC 4.0 | $\bullet$
STITCH-CCI 5 | Szklarczyk et al. (2016) | Interaction | 389,393 | 17,705,799 | 4 | CC BY-NC-SA 4.0 | $\bullet$
ZhangDDI | Zhang et al. (2017) | Interaction | 548 | 48,548 | - | Not Specified |
ChCh-Miner | Marinka Zitnik et al. (2018) | Interaction | 1,514 | 48,514 | - | Not Specified |
DCDB | Liu et al. (2010) | Synergy | 485 | 499 | – | Not Specified |
DCDB 2.0 | Liu et al. (2014) | Synergy | 904 | 1,363 | – | Not Specified |
ASDCD | Chen et al. (2014) | Synergy | 105 | 215 | – | Not Specified |
O’Neil | O’Neil et al. (2016) | Synergy | 38 | 583 | 39 | Not Specified |
NCI-ALMANAC | Holbeck et al. (2017) | Synergy | 104 | ¿5,000 | 60 | CC BY 4.0 |
DrugComb | Zagidullin et al. (2019) | Synergy | 2,276 | 437,932 | 93 | CC BY-NC-SA 4.0 |
SynergyXDB | Seo et al. (2020) | Synergy | 1,977 | 22,507 | 151 | Not Specified |
DrugCombDB | Liu et al. (2020) | Synergy | 2,887 | 448,555 | 124 | Not Specified | $\bullet$
TDC (OncoPolyPharm) | Huang et al. (2021) | Synergy | 38 | 583 | 39 | CC BY 4.0 |
DrugComb 2.0 | Zheng et al. (2021) | Synergy | 8,397 | 751,498 | 2,320 | CC BY-NC-SA 4.0 |
TDC (DrugComb) | Huang et al. (2021) | Synergy | 129 | 5,628 | 29 | CC BY-NC-SA 4.0 |

It should be noted that established resources such as TWOSIDES and DrugBank
are frequently filtered, cleaned and split into new datasets. For example the
Therapeutics Data Commons (TDC) resource contains filtered versions of both of
these datasets designed for benchmark use Huang et al. (2021). It is also
common for datasets to be named differently in publications, for example the
split of TWOSIDES contained in TDC is also called ChChSe-Decagon in some works
Marinka Zitnik et al. (2018).

##  5 Applications

In this section we introduce three key, yet currently largely, unexplored
applications for the methods detailed in this review.

###  5.1 Combination Therapy for COVID-19

One topical application of these methods is in relation to COVID-19 pandemic.
Patients affected by polypharmacy of certain drug types (anti-psychotics and
opiates being prominent examples) had a significantly higher chance of a
negative clinical outcome from COVID-19 Iloanusi et al. (2021); Jin et al.
(2021). Using methods covered in this review to predict which combinations may
have a negative effect for COVID-19 patients, could enable high risk groups to
seek alternative treatments, reducing the risk of a negative outcome.

###  5.2 Antibiotic Evolutionary Pressure

The prevalent use of antibiotics has resulted in microbes evolving resistance
to the drugs, reducing efficacy and potentially eliminating cost effective
ways of treating severe bacterial-related diseases such as Tuberculosis.
Interestingly, it has been shown that the combination of different antibiotics
can slow, and even reverse, this evolutionary resistance Singh et al. (2017).
However discovering these suppressive interactions using traditional methods
is a complex and slow process, yet one currently unexplored using the methods
covered in this review.

###  5.3 Reducing Toxicity

Although drug combinations can result in an increase of unwanted side effects,
one promising application is that the combination of two or more drugs can
actually lead to a reduced level of toxicity for patients. This is due to the
fact that synergistic drugs, which together posses a higher level of efficacy
at targeting a certain condition, means that the levels of each individual
compound can actually be lowered, reducing toxicity issues associated with
higher doses Ianevski et al. (2020). Thus, accurate prediction of synergistic
drug combinations can reduce the impact of toxicity resulting from the
individual compounds.

##  6 Discussion and Future Directions

The body of work regarding relational machine learning for drug pair scoring
primarily focuses on the design of novel architectures and applications. Our
unification survey identified a number of potential shortcomings of existing
approaches and venues for novel research in the domain.

###  6.1 Encoding Molecular Geometry

Our summary on the design of relational machine learning architectures for
drug pair scoring tasks in Table 1 highlighted that molecular geometry and
spatial structure of the molecules is rarely encoded by existing models.
Recent advances in geometric deep learning applied to chemistry Qi et al.
(2017); Xie et al. (2018); Fey et al. (2018) would allow the inclusion of
geometric information which could lead to better predictive performance on the
pair scoring tasks. The modularity of existing architectures makes replacing
the molecular encoders with state-of-the-art geometric encoder layers a
possibility.

###  6.2 Higher Order Drug Combinations

Existing research about the interactions, unwanted side effects and synergy of
drugs is primarily focused on the evaluation of binary pair combinations. This
is driven by the lack of datasets focused on the outcomes of using higher
order drug combinations and the lack of architectures designed specifically
for these higher order combinations. By using set based representation
aggregation layers Vinyals et al. (2016); Baek et al. (2020), the existing
pair scoring models could be adapted to generate drug subset representations.

###  6.3 Transfer Learning

Self-supervised and unsupervised learning for pretraining molecular encoders
is already widely used for single molecule machine learning tasks Dewulf et
al. (2021). This provides an opportunity for pretraining the molecular
encoders on single molecule tasks and fine-tuning them on the data scarce,
pair scoring tasks. Another opportunity for transfer learning comes from the
fact that certain pair scoring tasks have a greater quantity of labeled data
available. The summary of drug pair scoring datasets in Table 2 demonstrated
that the drug-drug interaction prediction task has datasets such as STITCH-
CCI-5 which covers a large number of pair combinations, while the polypharmacy
side effect and synergy prediction tasks have smaller databases. Pretraining
models by performing drug-drug interaction prediction and fine-tuning these
models for other tasks seems to be an important future research direction for
training accurate, and therefore useful, models.

###  6.4 Multimodal Learning

A heterogeneous graph based representation of drugs allows for the fusion of
multiple data modalities. Our survey of existing models in Table 1 has
demonstrated that only a handful of existing architectures integrates
multimodal data effectively Rozemberczki et al. (2021a); Liu et al. (2021a)
without losing induction. Integrating multi-omics data such as proteomics,
molecular structure and biological pathway information could be an important
venue for designing novel pair scoring architectures.

###  6.5 Software for Drug Pair Scoring

Currently there is no dedicated open-source machine learning library which was
specifically designed for solving the drug pair scoring task. Developing a
dedicated relational machine learning framework on top of existing geometric
deep learning Fey et al. (2019); Wang et al. (2019); Rozemberczki et al.
(2021b) and deep chemistry frameworks Ramsundar et al. (2019); Korshunova et
al. (2021) could be an important contribution to the domain. This would
require curated datasets and the architectural design of encoder, combiner,
scoring layers and drug pair iterators.

##  7 Conclusion

We have provided an exhaustive overview of relational machine learning models
designed to solve drug pair scoring tasks. We outlined a general theoretical
framework which unifies the drug-drug interaction, polypharmacy side effect
and drug synergy prediction tasks and created a taxonomy of models which
address these. By surveying the literature, considering the architecture and
evaluation of existing models, we identified key real world application areas
and important directions for future research.

## Acknowledgement

The authors would like to thank Peizhen Bai, Piotr Grabowski, Haiping Lu,
Rocío Mercado, and Paul Scherer for help and feedback throughout the
preparation of this manuscript. Stephen Bonner is a fellow of the AstraZeneca
postdoctoral program.

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