# Precision Anti-Cancer Drug Selection via Neural Ranking

Vishal Dey  The Ohio State UniversityColumbusUSA<EMAIL_ADDRESS>and  Xia Ning
The Ohio State UniversityColumbusUSA<EMAIL_ADDRESS>
(2018)

###### Abstract.

Personalized cancer treatment requires a thorough understanding of complex
interactions between drugs and cancer cell lines in varying genetic and
molecular contexts. To address this, high-throughput screening has been used
to generate large-scale drug response data, facilitating data-driven
computational models. Such models can capture complex drug-cell line
interactions across various contexts in a fully data-driven manner. However,
accurately prioritizing the most sensitive drugs for each cell line still
remains a significant challenge. To address this, we developed neural ranking
approaches that leverage large-scale drug response data across multiple cell
lines from diverse cancer types. Unlike existing approaches that primarily
utilize regression and classification techniques for drug response prediction,
we formulated the objective of drug selection and prioritization as a drug
ranking problem. In this work, we proposed two neural listwise ranking methods
that learn latent representations of drugs and cell lines, and then use those
representations to score drugs in each cell line via a learnable scoring
function. Specifically, we developed a neural listwise ranking method,
$\mathop{\mathtt{List\text{-}One}}\limits$, on top of the existing method
ListNet. Additionally, we proposed a novel listwise ranking method,
$\mathop{\mathtt{List\text{-}All}}\limits$, that focuses on all the sensitive
drugs instead of the top sensitive drug, unlike
$\mathop{\mathtt{List\text{-}One}}\limits$. Our results demonstrate that
$\mathop{\mathtt{List\text{-}All}}\limits$ outperforms the best baseline with
significant improvements of as much as 8.6% in hit@20 across 50% test cell
lines. Furthermore, our analyses suggest that the learned latent spaces from
our proposed methods demonstrate informative clustering structures and capture
relevant underlying biological features. Moreover, our comprehensive empirical
evaluation provides a thorough and objective comparison of the performance of
different methods (including our proposed ones).

Cancer Drug Sensitivity, Learning to Rank, Listwise Ranking

††copyright: acmcopyright††journalyear: 2018††doi:
XXXXXXX.XXXXXXX††conference: Proceedings of 22nd International Workshop on
Data Mining in Bioinformatics; August 09, 2023; Long Beach, CA††price:
15.00††isbn: 978-1-4503-XXXX-X/18/06††ccs: Computing methodologies Learning to
rank††ccs: Computing methodologies Neural networks††ccs: Applied computing
Bioinformatics

##  1\. Introduction

Precision cancer treatment aims to tailor therapies to individual patients by
identifying effective anti-cancer drugs for each patient based on their unique
genetic and molecular characteristics. However, this requires an in-depth
understanding of complex interactions between drugs and patients in different
genetic and molecular contexts, which presents a significant challenge. To
address this challenge, high-throughput screening methods(Gupta et al., 2009)
have been used to generate large-scale drug response data(Yang et al., 2012;
Barretina et al., 2012), providing a valuable resource for developing data-
driven models. However, developing models that can accurately encode complex
interactions between cell lines and drugs and prioritize the most promising
anti-cancer drugs for each cell line still remains a challenging task. To
tackle these challenges, data-driven models jointly utilize drug response data
across multiple cell lines and cancer types, motivated by findings from pan-
cancer studies(Weinstein et al., 2013). These studies suggest that there are
commonalities in genetic and molecular features among different cancer
types(Kandoth et al., 2013). Following such insights, in this paper, we
develop computational approaches that can leverage drug response data across a
large number of cell lines from diverse cancer types to identify and
prioritize anti-cancer drugs in each cell line. Unlike existing computational
approaches, our approach is inspired by learning-to-rank (LeToR)
methods(Burges et al., 2005), which can naturally formulate the objective of
anti-cancer drug selection and prioritization.

In this work, we develop neural listwise LeToR methods that learn latent
representations of cell lines and drugs in a data-driven manner, and then use
those representations to score drugs in each cell line via a learnable scoring
function. We utilize the existing listwise ranking objective(Cao et al., 2007)
to develop a neural listwise ranking method, denoted as
$\mathop{\mathtt{List\text{-}One}}\limits$, which considers the entire ranking
structure at a time and learns the probability of the most sensitive drugs in
each cell line being ranked at the top (i.e., top-one probability
distribution). By minimizing the discrepancy between the predicted and ground-
truth top-one probability distributions,
$\mathop{\mathtt{List\text{-}One}}\limits$ learns to appropriately score the
drugs leading to an accurate selection of the most sensitive drug in each cell
line.

In addition, we propose another listwise ranking method for drug selection,
denoted as $\mathop{\mathtt{List\text{-}All}}\limits$, that focuses on
selecting all the sensitive drugs. Additionally, we evaluated our proposed
methods against strong regression and pairwise ranking baselines. Our results
demonstrate that $\mathop{\mathtt{List\text{-}All}}\limits$ mostly outperforms
the best baselines with significant improvements of much as 8.6% in hit@20
across 50% test cell lines. Furthermore, our analyses suggest that the learned
latent spaces from our proposed methods demonstrate informative clustering
structures and capture relevant underlying biological features (e.g., cancer
types, drug mechanism of action).

The rest of the manuscript is organized as follows. Section 2 presents the
related work on computational methods in anti-cancer drug response prediction
and drug prioritization. Section 3 presents the proposed listwise methods and
Section 4 describes the datasets, baseline methods, experimental settings and
evaluation metrics. Section 5 presents an overall comparison of all methods in
one experimental setting across both datasets and detailed analyses of
embeddings. Section 6 concludes the paper.

##  2\. Related Works

###  2.1. Computational Methods in Drug Response Prediction

With an increasing abundance of large-scale drug response data and advanced
high-throughput screening(Gupta et al., 2009), data-driven computational
approaches have been developed for drug response prediction in cancer cell
lines. Following pan-cancer studies(Weinstein et al., 2013), these approaches
have been extended beyond singe-drug or single-cell line modeling to jointly
leverage the drug response data across multiple drugs and cell lines. This
enables such approaches to capture the interactions among multiple drugs,
among multiple cell lines, and between drugs and cell lines. Typically, these
approaches either focus on regression(Su et al., 2019) which estimates the
drug responses for a given cell line, or on classification(Bonanni et al.,
2022) which predicts whether a drug is sensitive or not in a given cell line.
These approaches employ various machine learning techniques such as kernel
methods(He et al., 2018), matrix factorization(Wang et al., 2017), and deep
learning(Baptista et al., 2020; Zuo et al., 2021). We refer the readers to a
comprehensive survey(Firoozbakht et al., 2021) for broader coverage of the
existing literature in this area. In contrast to the most popular approaches
toward drug response prediction, our work is more related to LeToR approaches
since it naturally models drug selection and prioritization.

###  2.2. LeToR methods in Drug Prioritization

Unlike the aforementioned regression and classification methods, LeToR methods
for drug prioritization are relatively under-explored (He et al., 2018, 2020;
Gerdes et al., 2021; Prasse et al., 2022). LeToR methods focus on learning to
appropriately score the candidate drugs and to optimize different objectives
so as to achieve accurate ranking. LeToR methods can be broadly categorized
into three approaches: pointwise(Burges et al., 2005), pairwise(Burges et al.,
2005) and listwise(Cao et al., 2007). In fact, the pointwise approach
typically performs inferior to both pairwise and listwise approaches(Cao et
al., 2007) since the ranking structure is not explicitly leveraged. One of the
popular pairwise ranking approaches for drug prioritization,
$\mathop{\mathtt{pLETORg}}\limits$(He et al., 2020), do not explicitly
leverage auxiliary information such as molecular structures, which are known
to be well correlated to activity(Gillet et al., 1998), drug-
likeliness(Bickerton et al., 2012), and other pharmacological
properties(Lipinski et al., 2001). This may hinder such models to learn the
above-mentioned structure-activity correlations, a key to many aspects in drug
discovery(Perkins et al., 2003).

In addition to pairwise approaches, listwise approaches have been utilized in
recent works. Kernelized Rank Learning (KRL)(He et al., 2018) is a listwise
LeToR method that optimizes an upper bound of the Normalized Discounted
Cumulative Gain (NDCG@k), and learns to approximate the drug sensitivities via
a kernelized linear regression. However, KRL notably underperforms
$\mathop{\mathtt{pLETORg}}\limits$ across multiple experimental settings as
demonstrated by He et al(He et al., 2020). Another neural listwise ranking
method developed by Prasse et al.(Prasse et al., 2022) optimizes a smooth
approximation of NDCG@k. However, the experiments from this study are not
adequately comprehensive and may not be directly comparable to other studies
in the literature due to their usage of multi-omics profiles and customized
definitions of ground-truth drug relevance scores, which deviates from the
standard approach in other studies. Additionally, the proposed method was not
evaluated against state-of-the-art pointwise or pairwise approaches.
Furthermore, the experiments were limited to one experimental setting (‘Cell
cold-start’), which may restrict the generalizability of their findings.

##  3\. Methods

Table 1. Notations and Definitions Notation |  Definition
---|---
$\mathcal{C}$ |  Set of cell lines
$\mathcal{D}$ |  Set of drugs
$d_{i}$ |  Drug $i$
$\mbox{$\mathcal{D}$}^{+}_{c}$ / $\mbox{$\mathcal{D}$}^{-}_{c}$ |  Set of sensitive/insensitive drugs for a cell line $c$
$\mbox{$\mathbf{u}$}_{c}$ / $\mbox{$\mathbf{v}$}_{d}$ |  embedding for cell line $c$/drug $d$

Table 1 presents the key notations used in the manuscript. Drugs are indexed
by $i$ and $j$ in the set of drugs $\mathcal{D}$, and cell lines are denoted
by $c\in\mbox{$\mathcal{C}$}$. In this manuscript,
$\mbox{$\mathcal{D}$}^{+}_{c}$ / $\mbox{$\mathcal{D}$}^{-}_{c}$ indicate the
set of sensitive and insensitive drugs, respectively, in the cell line $c$.
For example, $d_{i}\in\mbox{$\mathcal{D}$}^{+}_{c}$ denotes a sensitive drug
$i$ in cell line $c$; $d_{j}\in\mbox{$\mathcal{D}$}^{-}_{c}$ denotes an
insensitive drug $j$ in cell line $c$. In this section, we proposed two
listwise learning-to-rank methods ($\mathop{\mathtt{List\text{-}One}}\limits$
and $\mathop{\mathtt{List\text{-}All}}\limits$) for anti-cancer drug selection
and prioritization. We first introduce the overall architecture of our methods
in Section 3.1, and then discuss each component in detail in Sections 3.2 and
3.3. We discuss each of our proposed methods and their ranking optimization
process in subsequent sections.

###  3.1. Overall Framework

Figure 1. Overall Framework. The cell line embeddings
$\mbox{$\mathbf{u}$}_{c}$ and drug embeddings $\mbox{$\mathbf{v}$}_{d_{i}}$
are used to score the drugs $d_{i}\in\mbox{$\mathcal{D}$}_{c}$. Each ranking
method utilizes a different ranking objective and thus utilizes the scores
$f_{c}(d_{i})$ differently. The pretrained encoder
$\mathop{\mathtt{GeneE}}\limits$ is finetuned during ranking optimization.

In order to select and prioritize sensitive drugs in each cell line, our
proposed LeToR methods optimize different objectives that inducing the correct
ranking structure among the top-sensitive or all involved drugs in each cell
line. Figure 1 presents an overall scheme of our proposed methods. To induce
the correct ranking structure, each method learns to accurately score drugs in
each cell line using the learned cell line and drug embeddings. The embeddings
and scoring function are learned in a fully data-driven manner from the drug
response data. Intuitively, the cell line latent space embeds the genomic and
response information of cell lines, while the drug latent space embeds the
structural and sensitivity information for drugs. The cell line embeddings are
initially learned from the gene expression profiles using a pre-trained auto-
encoder model $\mathop{\mathtt{GeneAE}}\limits$ (Section 3.2). The drug
embeddings are learned from the molecular fingerprints (Section 3.3). During
training, the cell line and drug embeddings are then used and updated to
correctly score drugs against each cell line using a learnable scoring
function (Section 3.4.1). Note that $\mathop{\mathtt{List\text{-}One}}\limits$
and $\mathop{\mathtt{List\text{-}All}}\limits$ utilize the same scoring
function, however, optimize separate ranking objectives.

###  3.2. Pretraining for Cell Line Embeddings

Figure 2. Pretraining framework. Given a gene expression $\mathbf{x}_{c}$,
$\mathop{\mathtt{GeneAE}}\limits$ reconstructs it as
$\widetilde{\mathbf{x}}_{c}$ through the auto-encoder, meanwhile learning an
embedding $\mbox{$\mathbf{u}$}_{c}$ in the latent space.

In order to learn rich informative cell line embeddings, we pretrain a stacked
auto-encoder framework $\mathop{\mathtt{GeneAE}}\limits$, similar to existing
gene expression auto-encoder frameworks(Xie et al., 2017; Dincer et al.,
2020). Figure 2 presents the architecture of
$\mathop{\mathtt{GeneAE}}\limits$. $\mathop{\mathtt{GeneAE}}\limits$ embeds
the rich genomic information into a latent space, and learns the complex and
non-linear interactions among genes. Specifically,
$\mathop{\mathtt{GeneAE}}\limits$ leverages the gene expression profile
$\mathbf{x}_{c}$ to learn a low-dimensional embedding
$\mbox{$\mathbf{u}$}_{c}$ via the encoder $\mathop{\mathtt{GeneE}}\limits$,
followed by reconstruction of the expression profile from
$\mbox{$\mathbf{u}$}_{c}$ via the decoder $\mathop{\mathtt{GeneD}}\limits$.
These embeddings out of the pretrained $\mathop{\mathtt{GeneE}}\limits$ are
used to score drugs in each cell line during the downstream ranking (Section
3.4.1). Such embeddings can be utilized as transferable representations of
cell lines that can potentially enable better generalizability of downstream
drug scoring/ranking models. In summary, these embeddings can potentially
improve the performance of drug ranking models by leveraging the shared
biological features across cell lines.

As any other pretraining module(Erhan et al., 2010),
$\mathop{\mathtt{GeneAE}}\limits$ has two training stages: pretraining, and
finetuning. During pretraining, the model parameters are learned via back-
propagation by minimizing the reconstruction error (here, MSE) from the actual
and reconstructed gene expression data as,

(1)
$\min\nolimits_{\theta_{\textsc{\mbox{$\mathop{\mathtt{GeneE}}\limits$}}},\theta_{\textsc{\mbox{$\mathop{\mathtt{GeneD}}\limits$}}}}\frac{1}{|\mbox{$\mathcal{C}$}|}\sum_{c\in\mbox{$\mathcal{C}$}}||\mathbf{x}_{c}-\widetilde{\mathbf{x}}_{c}||_{2}^{2},$

where $\mathbf{x}_{c}$ denotes the input gene expression of cell line $c$,
$\widetilde{\mathbf{x}}_{c}=\mbox{$\mathop{\mathtt{GeneD}}\limits$}(\mbox{$\mathop{\mathtt{GeneE}}\limits$}(\mathbf{x}_{c}))$
denotes the corresponding reconstructed gene expression,
$\theta_{\textsc{\mbox{$\mathop{\mathtt{GeneE}}\limits$}}}$ and
$\theta_{\textsc{\mbox{$\mathop{\mathtt{GeneD}}\limits$}}}$ denote the
learnable parameters of $\mathop{\mathtt{GeneE}}\limits$ and
$\mathop{\mathtt{GeneD}}\limits$, respectively, and $\mathcal{C}$ denotes the
set of input cell lines. During pretraining, parameters of both
$\mathop{\mathtt{GeneE}}\limits$ and $\mathop{\mathtt{GeneD}}\limits$ modules
are learned, and the learned parameters of $\mathop{\mathtt{GeneE}}\limits$
are transferred and finetuned during the optimization for downstream ranking
tasks. The finetuning of pretrained $\mathop{\mathtt{GeneE}}\limits$ adapts
the output embeddings toward the specific downstream ranking.

###  3.3. Embedding Drugs from Fingerprints

In this work, molecular fingerprints(Rogers and Hahn, 2010) are leveraged to
learn informative drug embeddings via a low-dimensional projection. These
fingerprints are discrete feature vectors representing the presence of
molecular substructures in a drug given a fixed vocabulary. Typically, such
fingerprints need to be high-dimensional to sufficiently capture all relevant
structural information. On the other hand, the drug embeddings can selectively
encode relevant structural information (specific to the ranking task) as non-
linear functions of input fingerprints. These embeddings are further used to
score drugs in each cell line, and are learned during ranking optimization
given drug response data across multiple cell lines. Such learned embeddings
enable accurate drug scoring since similar drugs in terms of structures and
sensitivities across multiple cell lines obtain similar embeddings. To learn
such embeddings of dimension $M$ ($M$ is a hyperparameter), we used a fully
connected neural network $\mathop{\mathtt{DrugE}}\limits$. As inputs to
$\mathop{\mathtt{DrugE}}\limits$, we used Morgan count fingerprints(Rogers and
Hahn, 2010) with radius = 3 and 2,048 bits. While graph neural networks
(GNNs)(Wu et al., 2021) have demonstrated promising empirical performance in
molecular prediction tasks(Zhang et al., 2022), we observed inferior ranking
performance from the drug embeddings learned from GNNs compared to those
learned from fingerprints, from preliminary experiments. This is possibly due
to the limited number of unique drugs in our datasets.

###  3.4. Listwise Ranking for Top-One Drug:
$\mathop{\mathtt{List\text{-}One}}\limits$

We adopted the standard ListNet(Cao et al., 2007) objective to develop a
neural listwise ranking method, $\mathop{\mathtt{List\text{-}One}}\limits$.
$\mathop{\mathtt{List\text{-}One}}\limits$ considers the entire ranking
structure at a time and focuses on accurately estimating the top-one
probability of drugs. The top-one probability of a drug $d$, denoted as
$p_{c}(d)$, is its probability of being ranked at the top given the scores of
all involved drugs in the cell line $c$. Formally, the predicted top-one
probability denoted as $p_{c}^{f}(d)$ is defined as follows:

(2)
$p_{c}^{f}(d)=\frac{\exp{(f_{c}(d))}}{\sum_{d_{j}\in\mbox{$\mathcal{D}$}_{c}}\exp{(f_{c}(d))}},$

where $f_{c}(d)$ denotes the score of drug $d$ in cell line $c$ (which will be
discussed later in Section 3.4.1). The top-one probabilities are optimized
using the cross-entropy loss as follows:

(3)
$\min_{\Theta}-\sum_{c\in\mbox{$\mathcal{C}$}}\left[\sum_{d\in\mbox{$\mathcal{D}$}_{c}}p_{c}^{top}(d)\log(p_{c}^{f}(d))\right],$

where $\Theta$ denotes the learnable parameters in the model; and
$p_{c}^{top}(d)$ denotes the ground-truth top-one probability of drug $d$ in
the cell line $c$ according to the ground-truth drug responses. In this study,
the drug responses are quantified with Area Under the dose-response Curve
denoted as AUC, where smaller AUC values indicate higher drug sensitivities.
$p_{c}^{top}(d)$ is computed via Equation 2 by replacing $f_{c}(d)$ with the
negated AUCs (since lower AUCs indicate higher drug sensitivities). Minimizing
the above loss reduces the discrepancy between the predicted and the ground-
truth top-one probability distribution over drugs in each cell line. This
results in an accurate estimation of the top-one probability, which enables an
accurate selection of the most sensitive drug in each cell line. During the
optimization, $\mathop{\mathtt{List\text{-}One}}\limits$ (and
$\mathop{\mathtt{List\text{-}All}}\limits$ presented in the following section
similarly) finetunes $\mathop{\mathtt{GeneE}}\limits$ (Section 3.2) and learns
$\mathop{\mathtt{DrugE}}\limits$ (Section 3.3). This enables the cell line and
drug embeddings out of $\mathop{\mathtt{GeneE}}\limits$ and
$\mathop{\mathtt{DrugE}}\limits$, respectively, to encode task-relevant
information.

####  3.4.1. Drug Scoring

In order to score the drug $d$ in a cell line $c$, we used a parameterized
bilinear function denoted as $f_{c}(d)$. The function $f_{c}(d)$ is
parameterized via a learnable weight matrix
$\mathbf{W}\in\mathbb{R}^{|\mbox{$\mathbf{u}$}_{c}|\times|\mbox{$\mathbf{v}$}_{d}|}$,
and is applied over the
$\mbox{$\mathbf{u}$}_{c}\in\mathbb{R}^{|\mbox{$\mathbf{u}$}_{c}|}$ and
$\mbox{$\mathbf{v}$}_{d}\in\mathbb{R}^{|\mbox{$\mathbf{v}$}_{d}|}$ as follows:

(4)
$f_{c}(d)=\mbox{$\mathbf{u}$}_{c}^{\intercal}\mathbf{W}\mbox{$\mathbf{v}$}_{d},$

where, $\mathbf{W}$ is learned via backpropagation in an end-to-end manner
during optimization. Intuitively, the learnable full-rank weight matrix
$\mathbf{W}$ in the bilinear scoring function can capture complex and relevant
interactions between the two latent vectors. Once the scores for all drugs in
a cell line $c$ (i.e., $\mbox{$\mathcal{D}$}_{c}$) are obtained, the drugs
$\mbox{$\mathcal{D}$}_{c}$ are sorted based on such scores in descending
order. The most sensitive drugs in $c$ will have higher scores than the
insensitive ones in $c$. Note that ranking-based methods such as our proposed
ones will achieve optimal ranking performance as long as these scores induce
correct ranking structure; the scores do not need to be exactly identical to
the drug response scores (i.e., AUC values).

###  3.5. Listwise Ranking for All Sensitive Drugs:
$\mathop{\mathtt{List\text{-}All}}\limits$

Since $\mathop{\mathtt{List\text{-}One}}\limits$ focuses solely on the top-
ranked drug, it may lead to suboptimal performance in terms of selecting all
the sensitive drugs in each cell line, as demonstrated in our experiments
(Section 5.1), To address this, we proposed a new listwise neural ranking
method, $\mathop{\mathtt{List\text{-}All}}\limits$ with an objective that can
optimize the selection of all sensitive drugs in each cell line.
$\mathop{\mathtt{List\text{-}All}}\limits$ leverages the entire ranking
structure at a time and follows a similar architecture to
$\mathop{\mathtt{List\text{-}One}}\limits$. But unlike
$\mathop{\mathtt{List\text{-}One}}\limits$,
$\mathop{\mathtt{List\text{-}All}}\limits$ estimates the probability of a drug
being sensitive given the scores of all drugs, where higher scores induce
higher probabilities. Since the estimated probability of each drug being
sensitive is dependent on the scores of all other drugs in the list,
$\mathop{\mathtt{List\text{-}All}}\limits$ is a listwise ranking method.
$\mathop{\mathtt{List\text{-}All}}\limits$ aims to minimize the distance
between such estimated score-induced probabilities and the ground-truth
sensitivity labels across all drugs in each cell line. Specifically,
$\mathop{\mathtt{List\text{-}All}}\limits$ is trained by minimizing the
following loss:

(5)
$\min_{\Theta}-\sum_{c\in\mbox{$\mathcal{C}$}}\left[\sum_{d\in\mbox{$\mathcal{D}$}_{c}}l_{c}(d)\log(s_{c}^{f}(d))\right],$

where $\Theta$ denotes the learnable parameters in the model; $l_{c}(d)$ is a
binary sensitivity label indicating whether drug $d$ is sensitive in cell line
$c$; and $s_{c}^{f}(d)$ denotes the probability of drug $d$ to be sensitive in
the cell line $c$. Formally, $s_{c}^{f}(d)$ is computed from the predicted
scores via the parameterized softmax as:

(6)
$s_{c}^{f}(d)=\frac{\exp{(f_{c}(d)/\tau)}}{\sum_{d_{j}\in\mbox{$\mathcal{D}$}_{c}}\exp{(f_{c}(d)/\tau)}},$

where $\tau$ is the temperature (a scaling factor > 0) that controls the
softness/sharpness of the score-induced probability distribution while
maintaining the relative ranks. A lower scaling factor results in a sharper
probability distribution with higher probabilities on very few drugs. Note
that the scaling factor can also be applied similarly in Equation 2, however,
we observed no notable performance difference empirically. For
$\mathop{\mathtt{List\text{-}All}}\limits$, we fix $\tau$ to 0.5. Note that
the optimization objective (Equation 5) resembles the ListNet objective
(Equation 3) in the sense that both aim to minimize the cross-entropy between
two score-induced empirical probability distributions.

##  4\. Materials

In this section, we present the data sets and baselines used in Sections 4.1
and 4.2, respectively; the experimental setting in Section 4.3; and the
evaluation metrics adopted to evaluate ranking performance in Section 4.4.

###  4.1. Dataset

Table 2. Dataset Overview

Dataset | |$\mathcal{C}$ | | |$\mathcal{D}$ | | #AUCs | #d/$\mathcal{C}$ | c/$\mathcal{D}$ | m%
---|---|---|---|---|---|---
CTRP | 809 | 545 | 357,544 | 442 | 656 | 18.9

  * •

In this table, the columns $|\mbox{$\mathcal{C}$}|$, $|\mbox{$\mathcal{D}$}|$,
and #AUCs denote the number of unique cell lines, drugs and cell-line drug
response pairs, respectively. The columns #d/$\mathcal{C}$, c/$\mathcal{D}$
and m% denote the average number of drugs per cell line, average number of
cell lines per drug, and the missing percentage of responses, respectively.

We collected the drug response data set from the Cancer Therapeutic Response
Portal version 2
(CTRP)111https://ctd2-data.nci.nih.gov/Public/Broad/CTRPv2.0_2015_ctd2_ExpandedDataset/
(accessed on 01/20/22)(Seashore-Ludlow et al., 2015). We focused on this data
set because it covers a large number of cell lines and drugs compared to other
available data sets222Due to space limitations, we present the results only on
one dataset in this workshop paper. Additional results for other experimental
settings and datasets will be published in a forthcoming full-paper version..
We utilized the Cancer Cell Line Encyclopedia version 22Q1
(CCLE)333https://depmap.org/portal/download/ (accessed on 01/20/22)(Barretina
et al., 2012) for the gene expression data. CCLE provides multi-omics data
(genomic, transcriptomic and epigenomic) for more than 1,000 cancer cell
lines. However, in this study, we only used the gene expression
(transcriptomic) data following (He et al., 2020). The drug responses are
measured using AUC sensitivity scores, with lower AUC indicating higher
sensitivity of a drug in a cell line. For the drugs with missing responses in
a cell line, the corresponding drug-cell line pairs were not included in the
training of models. For the cell lines that could not be mapped to CCLE, those
cell lines and their associated drug responses were excluded from our
experiments. Since CTRP has more cell lines than other available datasets in
the literature, it is an appropriate choice for evaluating computational
methods in drug selection for new cell lines, which is the primary focus of
this work. This work is motivated based on the belief that such a setup is
more relevant to real-life scenarios where the goal is to suggest potential
anti-cancer drugs for new patients.

###  4.2. Baselines

We use two strong baseline methods: $\mathop{\mathtt{pLETORg}}\limits$ (He et
al., 2020) and $\mathop{\mathtt{DeepCDR}}\limits$ (Liu et al., 2020). Unlike
our proposed methods, $\mathop{\mathtt{pLETORg}}\limits$ is a pairwise ranking
approach that learns the drug and cell line embeddings by explicitly pushing
sensitive drugs to the top of the ranking list and by further optimizing the
ranking structure among the sensitives. Unlike
$\mathop{\mathtt{pLETORg}}\limits$, our proposed methods leverage drug
structural and gene expression information to learn more informative
embeddings that may enable improved ranking performance. Additionally,
different from $\mathop{\mathtt{pLETORg}}\limits$, our proposed methods
utilize a learnable scoring function to capture the complex interactions
between embeddings. While $\mathop{\mathtt{pLETORg}}\limits$ explicitly
enforces similarity regularization on cell line embeddings using the gene
expression-based similarity of cell lines, our methods enforce such genomic
similarity by embedding cell lines in the latent space via the pretrained
$\mathop{\mathtt{GeneE}}\limits$. Different from our proposed methods and the
baseline $\mathop{\mathtt{pLETORg}}\limits$,
$\mathop{\mathtt{DeepCDR}}\limits$, one of the state-of-the-art regression
models for anti-cancer drug response prediction, learns to estimate the exact
response scores of every drug in each cell line.

###  4.3. Experimental Setting

According to the setting of He et al. (He et al., 2020), a percentile labeling
scheme was used to label drugs as sensitive or insensitive. The sensitivity
threshold for each cell line was determined as the top-5 percentile of its
drug responses. In order to assess the ranking performance on new cell lines,
we employed a leave-cell-lines-out (LCO) validation setting such that this
setting resembles the real-world scenario when known drugs are investigated
for their sensitivity or anti-cancer potential in new patients. We randomly
split all the cell lines from each cancer type into five folds. In each run,
we used the four folds from each cancer type for training and the other fold
for testing. We use the cell lines from all the cancer types for 4 folds and
their corresponding drug response data collectively for training. We use the
cell lines in the other left-out fold as new (unseen) cell lines for model
testing. This process was repeated five times with each fold serving as the
test fold exactly once. For $\mathop{\mathtt{pLETORg}}\limits$, we follow the
‘leave-one-out’ setup(He et al., 2020) in that the cell line embeddings were
learned only for the training cell lines, and the embeddings for the test cell
lines were interpolated from the nearest neighboring training cell lines in
the latent space. For our proposed methods, we use the gene expression
profiles of only the training cell lines to pretrain
$\mathop{\mathtt{GeneAE}}\limits$.

###  4.4. Evaluation Metrics

In order to evaluate the ranking performance, we generated the true ranking
list using the ground-truth AUC response values and the predicted ranking list
using the estimated scores out of the models. We then compared the two ranking
lists (or a portion of them) using popular evaluation metrics: average
precision at $K$ ($\mathop{\mathtt{AP}}\limits$@K), and average hit at $K$
($\mathop{\mathtt{AH}}\limits$@K), which are commonly used in Information
Retrieval systems. Higher $\mathop{\mathtt{AP}}\limits$@K and
$\mathop{\mathtt{AH}}\limits$@K indicate better drug selection where the top-
ranked drugs in the predicted ranking list are sensitive. In addition to
$\mathop{\mathtt{AP}}\limits$ and $\mathop{\mathtt{AH}}\limits$, concordance
index ($\mathop{\mathtt{CI}}\limits$) and concordance index among the
sensitive drugs ($\mathop{\mathtt{sCI}}\limits$) (He et al., 2020) are also
used to evaluate the overall quality of the predicted ranking structure among
all drugs and sensitive drugs, respectively. Note that high
$\mathop{\mathtt{CI}}\limits$ and $\mathop{\mathtt{sCI}}\limits$ values do not
necessarily result in high $\mathop{\mathtt{AP}}\limits$ or
$\mathop{\mathtt{AH}}\limits$ since the ranking structure can be well
preserved without pushing the few sensitive drugs (which constitutes only 5%
of the total drugs) to the very top. On the other hand, high
$\mathop{\mathtt{AP}}\limits$/$\mathop{\mathtt{AH}}\limits$ indicates the most
sensitive drugs are ranked at the top, but this does not necessarily result in
high $\mathop{\mathtt{CI}}\limits$/$\mathop{\mathtt{sCI}}\limits$. In this
work, since we primarily focus on identifying the top-$k$ most sensitive drugs
in each cell line, we prioritize and emphasize the
$\mathop{\mathtt{AP}}\limits$ and $\mathop{\mathtt{AH}}\limits$ metrics over
the $\mathop{\mathtt{sCI}}\limits$ and $\mathop{\mathtt{CI}}\limits$ metrics
when evaluating and interpreting our results.

##  5\. Results

###  5.1. Overall Comparison

Table 3. Overall Comparison for CTRP in LCO validation

model | AP@1 | AP@3 | AH@3 | AP@5 | AH@5 | AP@10 | AH@10 | AP@20 | AH@20 | AP@40 | AH@40 | AP@60 | AH@60
---|---|---|---|---|---|---|---|---|---|---|---|---|---
$\mathop{\mathtt{pLETORg}}\limits$ | 0.9308* | 0.9586 | 2.6853 | 0.9391 | 4.2454 | 0.8962 | 7.3525 | 0.8178 | 11.9248 | 0.7286 | 17.1087 | 0.6877 | 19.5646
$\mathop{\mathtt{pLETORg}}\limits$ | 0.9306 | 0.9598* | 2.6944 | 0.9402 | 4.2756 | 0.9018 | 7.4802 | 0.8255 | 12.0889 | 0.7361 | 17.3179 | 0.7011 | 19.3712
$\mathop{\mathtt{pLETORg}}\limits$ | 0.9306 | 0.9596 | 2.6968* | 0.9402 | 4.2731 | 0.9018 | 7.4716 | 0.8250 | 12.0936 | 0.7351 | 17.3506* | 0.7002 | 19.4150
$\mathop{\mathtt{pLETORg}}\limits$ | 0.9306 | 0.9593 | 2.6951 | 0.9410* | 4.2582 | 0.8999 | 7.3960 | 0.8222 | 12.0270 | 0.7328 | 17.2086 | 0.6951 | 19.4621
$\mathop{\mathtt{pLETORg}}\limits$ | 0.9306 | 0.9597 | 2.6943 | 0.9402 | 4.2829* | 0.9023 | 7.4804* | 0.8257* | 12.0962* | 0.7364* | 17.3279 | 0.7023* | 19.3091
$\mathop{\mathtt{pLETORg}}\limits$ | 0.9306 | 0.9595 | 2.6878 | 0.9395 | 4.2791 | 0.9026* | 7.4467 | 0.8246 | 12.0456 | 0.7353 | 17.2695 | 0.6995 | 19.3624
$\mathop{\mathtt{pLETORg}}\limits$ | 0.9306 | 0.9587 | 2.6748 | 0.9376 | 4.2236 | 0.8988 | 7.3600 | 0.8192 | 12.0065 | 0.7304 | 17.2451 | 0.6893 | 19.7447*
$\mathop{\mathtt{DeepCDR}}\limits$ | 0.9260* | 0.9296* | 2.4716 | 0.9015 | 4.0904 | 0.8646 | 7.4440* | 0.8025 | 11.5779 | 0.7155 | 16.7472* | 0.6736 | 19.3054*
$\mathop{\mathtt{DeepCDR}}\limits$ | 0.9129 | 0.9271 | 2.5151* | 0.9035 | 4.1096* | 0.8665* | 7.4384 | 0.8036* | 11.7047* | 0.7211* | 16.7447 | 0.6791* | 19.3008
$\mathop{\mathtt{DeepCDR}}\limits$ | 0.9209 | 0.9282 | 2.5087 | 0.9064* | 4.0324 | 0.8599 | 7.3529 | 0.7984 | 11.5311 | 0.7118 | 16.5821 | 0.6700 | 19.2082
$\mathop{\mathtt{List\text{-}One}}\limits$ | 0.9478* | 0.9523* | 2.5284 | 0.9170 | 3.9832 | 0.8614 | 7.2736 | 0.7929 | 12.0092 | 0.7152 | 17.4724 | 0.6773 | 20.0047
$\mathop{\mathtt{List\text{-}One}}\limits$ | 0.9359 | 0.9499 | 2.6392* | 0.9278 | 4.1952* | 0.8830 | 7.4661 | 0.8128 | 12.3445 | 0.7344 | 17.6828 | 0.6963 | 20.1293
$\mathop{\mathtt{List\text{-}One}}\limits$ | 0.9423 | 0.9507 | 2.6285 | 0.9293* | 4.1583 | 0.8833* | 7.4334 | 0.8115 | 12.1450 | 0.7304 | 17.5116 | 0.6902 | 20.0350
$\mathop{\mathtt{List\text{-}One}}\limits$ | 0.9393 | 0.9485 | 2.6315 | 0.9269 | 4.1909 | 0.8828 | 7.5999* | 0.8174* | 12.4297 | 0.7389* | 17.9255 | 0.7024* | 20.2904
$\mathop{\mathtt{List\text{-}One}}\limits$ | 0.9165 | 0.9371 | 2.5749 | 0.9152 | 4.1013 | 0.8694 | 7.5055 | 0.8065 | 12.5335* | 0.7330 | 17.8804 | 0.6970 | 20.2376
$\mathop{\mathtt{List\text{-}One}}\limits$ | 0.9030 | 0.9300 | 2.5543 | 0.9106 | 4.0587 | 0.8640 | 7.4101 | 0.8009 | 12.4205 | 0.7262 | 17.9959* | 0.6924 | 20.3382*
$\mathop{\mathtt{List\text{-}All}}\limits$ | 0.9480* | 0.9610* | 2.6985 | 0.9420 | 4.2885 | 0.9087 | 7.6208 | 0.8333 | 12.1992 | 0.7429 | 17.4686 | 0.7012 | 20.0028
$\mathop{\mathtt{List\text{-}All}}\limits$ | 0.9295 | 0.9537 | 2.7142* | 0.9403 | 4.3000 | 0.9060 | 7.6104 | 0.8327 | 12.2481 | 0.7442 | 17.5094 | 0.7035 | 19.9869
$\mathop{\mathtt{List\text{-}All}}\limits$ | 0.9421 | 0.9597 | 2.6984 | 0.9442* | 4.2919 | 0.9094 | 7.6224 | 0.8345 | 12.1688 | 0.7436 | 17.4484 | 0.7020 | 19.9981
$\mathop{\mathtt{List\text{-}All}}\limits$ | 0.9365 | 0.9604 | 2.6934 | 0.9411 | 4.3119* | 0.9067 | 7.6108 | 0.8334 | 12.1745 | 0.7429 | 17.4458 | 0.7014 | 19.9993
$\mathop{\mathtt{List\text{-}All}}\limits$ | 0.9395 | 0.9581 | 2.7076 | 0.9414 | 4.3056 | 0.9102* | 7.6232 | 0.8339 | 12.1874 | 0.7432 | 17.4571 | 0.7020 | 19.9871
$\mathop{\mathtt{List\text{-}All}}\limits$ | 0.9255 | 0.9452 | 2.6474 | 0.9255 | 4.2547 | 0.8890 | 7.7577* | 0.8276 | 12.6216 | 0.7489 | 17.9918 | 0.7116 | 20.3199
$\mathop{\mathtt{List\text{-}All}}\limits$ | 0.9418 | 0.9598 | 2.6903 | 0.9409 | 4.3037 | 0.9067 | 7.6969 | 0.8361* | 12.3357 | 0.7478 | 17.6577 | 0.7073 | 20.0894
$\mathop{\mathtt{List\text{-}All}}\limits$ | 0.8586 | 0.9120 | 2.5588 | 0.8989 | 4.1607 | 0.8678 | 7.6558 | 0.8130 | 12.7728*† | 0.7412 | 18.2956 | 0.7084 | 20.4696
$\mathop{\mathtt{List\text{-}All}}\limits$ | 0.9188 | 0.9417 | 2.6518 | 0.9268 | 4.2490 | 0.8901 | 7.7238 | 0.8274 | 12.6474 | 0.7497* | 17.9691 | 0.7117* | 20.3631
$\mathop{\mathtt{List\text{-}All}}\limits$ | 0.8147 | 0.8828 | 2.4717 | 0.8734 | 4.0153 | 0.8461 | 7.5360 | 0.7965 | 12.7146 | 0.7291 | 18.3331*† | 0.6980 | 20.5291*†

  * •

The performances of the best performing model are in bold. * indicates the
best observed performance in a metric for a given model. $\dagger$ indicates
that the model performs significantly better compared to
$\mathop{\mathtt{pLETORg}}\limits$ according to a Wilcoxon signed rank test
with Bonferroni correction at 5% significance level.

Table 3 shows that, overall, $\mathop{\mathtt{List\text{-}All}}\limits$
consistently outperforms all other methods in most metrics. Specifically,
$\mathop{\mathtt{List\text{-}All}}\limits$ achieved the best
$\mbox{$\mathop{\mathtt{AH}}\limits$}@K$ scores with impressive results of
2.7142, 4.3119, 7.7577, 12.7728, and 18.3331 for $K=$ 3, 5, 10, 20, and 40,
respectively. Following $\mathop{\mathtt{List\text{-}All}}\limits$, the other
listwise ranking method, $\mathop{\mathtt{List\text{-}One}}\limits$ achieved
the second-best performance in terms of
$\mbox{$\mathop{\mathtt{AH}}\limits$}@K$. Overall,
$\mathop{\mathtt{List\text{-}All}}\limits$ achieved better
$\mathop{\mathtt{AH}}\limits$@10, $\mathop{\mathtt{AH}}\limits$@20 and
$\mathop{\mathtt{AH}}\limits$@40 over
$\mathop{\mathtt{List\text{-}One}}\limits$, whereas both methods achieved
competitive hit rates up to $K\leq 5$. This suggests that
$\mathop{\mathtt{List\text{-}All}}\limits$ is particularly effective in
pushing almost all sensitive drugs to the top while
$\mathop{\mathtt{List\text{-}One}}\limits$ was able to push only a few most
sensitive drugs. This is further reflected in the consistent improvements
observed in $\mathop{\mathtt{AH}}\limits$ and $\mathop{\mathtt{AP}}\limits$.
Compared to $\mathop{\mathtt{List\text{-}One}}\limits$,
$\mathop{\mathtt{List\text{-}All}}\limits$ improved
$\mathop{\mathtt{H}}\limits$@10, $\mathop{\mathtt{H}}\limits$@20, and
$\mathop{\mathtt{H}}\limits$@40 for 33.9% (55), 44.6% (72) and 39.5% (64) of
162 new cell lines by 3.8%, 3.0% and 1.4%, respectively. Such superior
performance of $\mathop{\mathtt{List\text{-}All}}\limits$ over
$\mathop{\mathtt{List\text{-}One}}\limits$ can be attributed to the ability of
$\mathop{\mathtt{List\text{-}All}}\limits$ to accurately estimate the
probability of drugs being sensitive in each cell line while
$\mathop{\mathtt{List\text{-}One}}\limits$ focuses solely on the most
sensitive (i.e., top-ranked) drug while ignoring the other sensitive drugs.

Furthermore, $\mathop{\mathtt{List\text{-}All}}\limits$ outperformed the best
baseline method, $\mathop{\mathtt{pLETORg}}\limits$, across all metrics.
Moreover, compared to $\mathop{\mathtt{pLETORg}}\limits$, both
$\mathop{\mathtt{List\text{-}All}}\limits$ and
$\mathop{\mathtt{List\text{-}One}}\limits$ demonstrated significantly better
or competitive performance in $\mathop{\mathtt{AH}}\limits$ and
$\mathop{\mathtt{AP}}\limits$. This implies that all our proposed methods can
improve the ranking performance over $\mathop{\mathtt{pLETORg}}\limits$ by
explicitly leveraging auxiliary information such as gene expression profiles
and molecular fingerprints. Specifically, compared to
$\mathop{\mathtt{pLETORg}}\limits$, the best-performing method,
$\mathop{\mathtt{List\text{-}All}}\limits$, demonstrated statistically
significant improvement in $\mathop{\mathtt{H}}\limits$@20,
$\mathop{\mathtt{H}}\limits$@40 and $\mathop{\mathtt{H}}\limits$@60 for 50.6%
(82), 53.0% (86) and 45.7% (74) of 162 new cell lines by 8.6%, 6.3% and 5.0%,
respectively, while achieving marginally better hit rates for $K<20$.
Additionally, $\mathop{\mathtt{List\text{-}All}}\limits$ achieved better
$\mathop{\mathtt{AP}}\limits$@20 and $\mathop{\mathtt{AP}}\limits$@40 than
$\mathop{\mathtt{pLETORg}}\limits$, improving $\mathop{\mathtt{P}}\limits$@20
and $\mathop{\mathtt{P}}\limits$@40 for 53.7% (87) and 58.0% (94) of 162 new
cell lines by 1.1% and 3.0% on average, respectively. Such consistent and
significant improvement across multiple $\mathop{\mathtt{AH}}\limits$ and
$\mathop{\mathtt{AP}}\limits$ metrics on a large percentage of cell lines
provides strong evidence that $\mathop{\mathtt{List\text{-}All}}\limits$
clearly outperforms the best baseline method
$\mathop{\mathtt{pLETORg}}\limits$ in drug selection and prioritization.

These results suggest that $\mathop{\mathtt{List\text{-}All}}\limits$ can
effectively leverage the drug structure information and the entire ranking
structure to learn richer latent representations while focusing on learning to
select all the sensitive drugs in a cell line. The consistent sub-par
performance of $\mathop{\mathtt{pLETORg}}\limits$ compared to
$\mathop{\mathtt{List\text{-}All}}\limits$ could be due to the fact that
$\mathop{\mathtt{pLETORg}}\limits$ only focuses on the pairwise relative
ordering without considering the overall ranking structure. Since there are
significantly more insensitive drugs than sensitive ones in each cell line,
such pairwise methods may struggle to preserve the ordering between pairs of
sensitive and insensitive drugs, thereby leading to a sub-optimal selection of
all sensitive drugs. Overall, all ranking-based methods outperformed the
state-of-the-art regression model, $\mathop{\mathtt{DeepCDR}}\limits$, across
all metrics. This indicates that learning to estimate the exact drug responses
while obtaining a lower overall MSE does not necessarily guarantee accurate
score estimation for the sensitive drugs, which constitutes only 5% of all
drugs in a cell line. This leads to sub-par performance of
$\mathop{\mathtt{DeepCDR}}\limits$ in terms of selecting and prioritizing the
most sensitive drugs in a cell line.

###  5.2. Study of Cell Line embeddings

We evaluated the quality of cell line embeddings based on their ability to
capture the drug response profiles. In order to quantitatively evaluate this,
we computed the pairwise similarities of cell lines in two different ways: 1)
using the radial basis function (RBF) kernel on the learned cell line
embeddings out of the best baseline, $\mathop{\mathtt{pLETORg}}\limits$, and
the best method, $\mathop{\mathtt{List\text{-}All}}\limits$, denoted as
$\mathop{\mathtt{sim_{c}\text{-}{B}}}\limits$ and
$\mathop{\mathtt{sim_{c}\text{-}{M}}}\limits$, respectively; and 2) using
Spearman rank correlation on the ranked lists of drugs given their drug
response profiles, denoted as $\mathop{\mathtt{sim_{c}\text{-}{R}}}\limits$.
Intuitively, $\mathop{\mathtt{sim_{c}\text{-}{B}}}\limits$ and
$\mathop{\mathtt{sim_{c}\text{-}{M}}}\limits$ are higher for pairs of cell
lines that are close in their corresponding latent spaces. Meanwhile,
$\mathop{\mathtt{sim_{c}\text{-}{R}}}\limits$ is higher for pairs of cell
lines if they share similar drug response profiles. Note that since every drug
may not have recorded responses in each cell line,
$\mathop{\mathtt{sim_{c}\text{-}{R}}}\limits$ for a pair of cell lines $p$ and
$q$ is computed from drug response data of the shared set of drugs,
$\mbox{$\mathcal{D}$}_{p}\cap\mbox{$\mathcal{D}$}_{q}$, whose responses are
recorded for both cell lines.

We hypothesize that the latent space captures the ranking structures across
drugs, implying that the cell lines close in the latent space have similar
drug response profiles (i.e., $\mathop{\mathtt{sim_{c}\text{-}{B}}}\limits$
and $\mathop{\mathtt{sim_{c}\text{-}{M}}}\limits$ are well correlated with
$\mathop{\mathtt{sim_{c}\text{-}{R}}}\limits$). In order to validate our
hypothesis, we calculated the Pearson correlations between
$\mathop{\mathtt{sim_{c}\text{-}{B}}}\limits$ and
$\mathop{\mathtt{sim_{c}\text{-}{R}}}\limits$, denoted as
$\mathtt{corr_{c}(B,R)}$, and between
$\mathop{\mathtt{sim_{c}\text{-}{M}}}\limits$ and
$\mathop{\mathtt{sim_{c}\text{-}{R}}}\limits$, denoted as
$\mathtt{corr_{c}(M,R)}$. We observed that the pairwise cell line similarities
induced by their drug response profiles are better correlated with the
similarities induced in the latent space learned by
$\mathop{\mathtt{List\text{-}All}}\limits$ compared to
$\mathop{\mathtt{pLETORg}}\limits$ (Pearson correlations
$\mathtt{corr_{c}(M,R)}$ vs. $\mathtt{corr_{c}(B,R)}$: 0.162 vs. 0.151). This
suggests that $\mathop{\mathtt{List\text{-}All}}\limits$ learns informative
cell line embeddings that can capture the overall ranking structure more
effectively than $\mathop{\mathtt{pLETORg}}\limits$. Intuitively,
$\mathop{\mathtt{List\text{-}All}}\limits$ may benefit from the fact that it
uses the gene expression profile to learn cell line embeddings; and because
cell lines with similar gene expression profiles typically demonstrate similar
drug response profiles. Although $\mathop{\mathtt{pLETORg}}\limits$ uses a
weighted regularizer to constrain cell line embeddings based on their genomic
similarity it may not fully capture the complex relationships between the gene
expressions of two cell lines. Explicitly learning embeddings from gene
expressions allows $\mathop{\mathtt{List\text{-}All}}\limits$ to extract more
nuanced task-relevant relationships and a desired notion of similarity between
cell lines.

Figure 3. Scatter plot of intra-cluster similarities, computed as the average
of $\mathop{\mathtt{sim_{c}\text{-}{R}}}\limits$ and
$\mathop{\mathtt{sim_{c}\text{-}{M}}}\limits$ within each cluster.

We further evaluated the quality of their latent spaces in more detail with
respect to clustering compactness and different cancer types. We applied a
20-way clustering using CLUTO(Karypis, 2002) on the embeddings. Figure 3
presents the intra-cluster similarities, i.e.,
$\mathop{\mathtt{sim_{c}\text{-}{R}}}\limits$ vs.
$\mathop{\mathtt{sim_{c}\text{-}{M}}}\limits$ averaged across cell lines in
each cluster. We observed that compact clusters in the latent space contained
cell lines with more similar drug-ranking structures. This is evident from the
fitted line with a positive slope as shown in Figure 3. This further supports
our hypothesis that the cell line latent space learned by
$\mathop{\mathtt{List\text{-}All}}\limits$ effectively captures the drug
response profiles. Moreover, our clustering analysis can uncover unobvious or
previously unknown similarities among cell lines from different cancer types,
which may not be apparent from the observed drug response data.

(a) Based on the distribution
of cell lines across clusters.

(b) Based on average $\mathop{\mathtt{sim_{c}\text{-}{R}}}\limits$
among cell lines

Figure 4. Comparison of two pairwise similarity matrices across different
cancer types.

Figure 4a presents the average pairwise similarities with respect to
clustering distribution of cell lines grouped by different cancer types. The
cell line similarities in this matrix are computed using the Jaccard
coefficient on the normalized distribution of cell lines over the top-10
compact clusters. Intuitively, the color in each cell in Figure 4a indicates
the degree of clustering overlap between cell lines from two different cancer
types. In other words, if cell lines from two different cancer types are
clustered together or distributed identically over multiple clusters, they
will be more similar and will have darker shades in the respective cell in
this figure. For example, the cell lines from kidney and ovary cancer types
are often clustered together, such is the case for bladder and gastric cancer
types. Figure 4b presents the average pairwise
$\mathop{\mathtt{sim_{c}\text{-}{R}}}\limits$ similarities among cell lines
from different cancer types. Specifically, if cell lines from two different
cancer types share similar drug ranking structures (i.e., high
$\mathop{\mathtt{sim_{c}\text{-}{R}}}\limits$) on average, the corresponding
pair of cancer types in this figure will have a darker shade.

Overall, we observed a moderate correlation between the cluster overlap-based
similarities (Figure 4a) and the drug ranking structure-based similarities
(Figure 4b) with a Pearson correlation of 0.493 ($p$-value = 1e-33).
Additionally, Figure 4a can provide clinically significant and valuable
insights while uncovering similarities between cell lines of different cancer
types even though their drug-ranking structures or drug response profiles do
not exhibit significant similarities. For instance, the liver cancer cell
lines tend to be clustered with cell lines of different cancer types such as
bone, brain, breast and lung cancers (Figure 4a) even though their drug
ranking structures are apparently different (Figure 4b). As a matter of fact,
several studies(Ananthakrishnan et al., 2006; Riihimäki et al., 2018) in the
medical literature provide evidence of secondary liver cancers (i.e.,
metastatic liver tumors) spreading from primary tumors of breast and lung
origins. Moreover, the most common mutations causing liver cancer (namely,
TP53, CTNNB1, AXIN1, ARID1A, CDKN2A and CCND1 genes)(Khemlina et al., 2017)
are commonly associated with multiple cancers. Similar observations can be
made from the figure for prostate, bladder, sarcoma, and thyroid cancers,
which also tend to be co-occurring according to reports in the literature
(Tomaszewski et al., 2014; Davis et al., 2014; Fan et al., 2017).

We further validate that the cell line latent space in
$\mathop{\mathtt{List\text{-}All}}\limits$ is capable of grouping cell lines
based on their cancer types, and in fact, does so better than that in
$\mathop{\mathtt{pLETORg}}\limits$. In order to validate this, we calculated
$k$-nearest-neighbor accuracy of a cell line $c$ in the latent space, denoted
as $\mbox{$\mathop{\mathtt{acc_{\scriptsize{kNN}}}}\limits$}(c)$, as follows:

(7)
$\mbox{$\mathop{\mathtt{acc_{\scriptsize{kNN}}}}\limits$}(c)=\frac{1}{k}\sum_{\scriptsize{c^{\prime}\in\mathtt{kNN}(c,k)}}\mathbb{I}[\mathtt{Cancer}(c^{\prime})=\mathtt{Cancer}(c)],$

where $\mathtt{kNN}(c,k)$ returns $k$-nearest neighbors of a cell line $c$ in
the latent space, $\mathbb{I}$ is the indicator function, and
$\mathtt{Cancer}(c)$ returns the cancer type of cell line $c$. Specifically,
$\mbox{$\mathop{\mathtt{acc_{\scriptsize{kNN}}}}\limits$}(c)$ is the expected
fraction of $k$ nearest neighboring cell lines that share the same cancer type
as the cell line $c$. We observed that the average
$\mathop{\mathtt{acc_{\scriptsize{kNN}}}}\limits$ over all unseen cell lines
were higher in $\mathop{\mathtt{List\text{-}All}}\limits$ compared to
$\mathop{\mathtt{pLETORg}}\limits$ ($\mathop{\mathtt{List\text{-}All}}\limits$
vs. $\mathop{\mathtt{pLETORg}}\limits$: 0.364 vs. 0.162, 0.181 vs. 0.110,
0.126 vs 0.082) for $k=1,3,5$, respectively. This suggests that the latent
space in $\mathop{\mathtt{List\text{-}All}}\limits$ is better clustered with
respect to cancer types, even though the cancer type information is never fed
to the model. This is likely due to the fact that
$\mathop{\mathtt{List\text{-}All}}\limits$ incorporates the gene expression
profile during pretraining, and typically cell lines from the same cancer type
tend to share similar gene expression profiles. In summary, not only the
latent space in $\mathop{\mathtt{List\text{-}All}}\limits$ clusters cell lines
based on their drug ranking structures, it also maps cell lines from the same
cancer types (i.e., of the same origin) to close proximity. These properties
of the latent space can have potential clinical applications, such as
determining cancer types for cell lines with unknown origin, and matching such
cell lines with those having known cancer types for additional wet-lab
experiments.

###  5.3. Study of Drug embeddings

We evaluated the quality of drug embeddings based on the extent to how well
the latent space captures the sensitivity profiles of drugs across cell lines.
The sensitivity profile of a drug was defined as a binary embedding, with a
value of 1 indicating that the drug is sensitive in a cell line, and 0 if
insensitive. To quantitatively evaluate the quality of the latent space, we
calculated the pairwise similarities of drugs in two ways: 1) using the RBF
kernel on the learned drug embeddings out of the best baseline method,
$\mathop{\mathtt{pLETORg}}\limits$, and the best method,
$\mathop{\mathtt{List\text{-}All}}\limits$, denoted as
$\mathop{\mathtt{sim_{d}\text{-}{B}}}\limits$ and
$\mathop{\mathtt{sim_{d}\text{-}{M}}}\limits$, respectively; and, 2) using the
Jaccard coefficient on the corresponding sensitivity profiles of drugs across
cell lines, denoted as $\mathop{\mathtt{sim_{d}\text{-}{S}}}\limits$. Clearly,
$\mathop{\mathtt{sim_{d}\text{-}{B}}}\limits$ and
$\mathop{\mathtt{sim_{d}\text{-}{M}}}\limits$ are higher for drug pairs that
are close in their corresponding latent spaces;
$\mathop{\mathtt{sim_{d}\text{-}{S}}}\limits$ is higher for drug pairs if they
share similar sensitivity profiles across many cell lines. It is important to
note that not all drugs have recorded responses in each cell line. Thus,
$\mathop{\mathtt{sim_{d}\text{-}{S}}}\limits$ for a pair of drugs $p$ and $q$
was calculated from the sensitivity profiles of the shared set of cell lines
for which the responses were recorded for both drugs.

Figure 5. Scatter plot of intra-cluster similarities, computed as the average
of $\mathop{\mathtt{sim_{d}\text{-}{S}}}\limits$ and
$\mathop{\mathtt{sim_{d}\text{-}{M}}}\limits$ within each cluster.

We hypothesize that the learned latent space locally captures the sensitivity
profiles of drugs. In other words, drugs that are close in the latent space
have similar sensitivity profiles, leading to a correlation between the
similarities in the latent space (i.e.,
$\mathop{\mathtt{sim_{d}\text{-}{B}}}\limits$ and
$\mathop{\mathtt{sim_{d}\text{-}{M}}}\limits$) and those computed from the
sensitivity profiles (i.e., $\mathop{\mathtt{sim_{d}\text{-}{S}}}\limits$). To
test this hypothesis, we computed the Pearson correlations among the three
similarities as follows: 1) correlation between
$\mathop{\mathtt{sim_{d}\text{-}{B}}}\limits$ and
$\mathop{\mathtt{sim_{d}\text{-}{S}}}\limits$, denoted as
$\mathtt{corr_{d}(B,S)}$; and, 2) correlation between
$\mathop{\mathtt{sim_{d}\text{-}{M}}}\limits$ and
$\mathop{\mathtt{sim_{d}\text{-}{S}}}\limits$, denoted as
$\mathtt{corr_{d}(M,S)}$. We observed that the pairwise drug similarities
induced by cell sensitivity profiles are better correlated to the pairwise
similarities induced in the latent space learned by
$\mathop{\mathtt{List\text{-}All}}\limits$ compared to
$\mathop{\mathtt{pLETORg}}\limits$ (Pearson correlations
$\mathtt{corr_{d}(M,S)}$ and $\mathtt{corr_{d}(B,S)}$: 0.906 vs. 0.352). This
suggests that $\mathop{\mathtt{List\text{-}All}}\limits$ can learn effective
drug embeddings that can better capture the sensitivity profiles compared to
$\mathop{\mathtt{pLETORg}}\limits$. This may be due to the fact that
$\mathop{\mathtt{List\text{-}All}}\limits$ leverages molecular fingerprints,
unlike $\mathop{\mathtt{pLETORg}}\limits$, to learn drug embeddings that can
encode structural information; and it is well known that structurally similar
drugs tend to exhibit similar sensitivities.

(a) Based on the distribution
of drugs across clusters.

(b) Based on average $\mathop{\mathtt{sim_{d}\text{-}{S}}}\limits$
among drugs

Figure 6. Comparison of two pairwise similarity matrices across different
MoAs.

Furthermore, we evaluated the quality of drug embeddings out of
$\mathop{\mathtt{List\text{-}All}}\limits$ via clustering. We applied a 10-way
clustering (using CLUTO) on the drug embeddings. Figure 5 presents the intra-
cluster similarities, $\mathop{\mathtt{sim_{d}\text{-}{S}}}\limits$ vs.
$\mathop{\mathtt{sim_{d}\text{-}{M}}}\limits$ averaged across all drugs in
each cluster. We observed that the compact clusters in the latent space
contained drugs with similar sensitivity profiles. This further supports our
previous hypothesis that the latent space for drugs effectively captures the
sensitivity profiles.

Furthermore, we studied the drug clusters in more detail and identified some
qualities of the latent space with respect to uncovering the mechanism of
action (MoA) of drugs. Figure 6a presents the average pairwise similarities
among drugs grouped by different MoAs, where the similarities are computed
using the Jaccard coefficient on the normalized distribution of drugs across
clusters (Figure 5). In other words, if drugs with different MoAs are
clustered together or co-occurs over multiple clusters, they are considered
similar and have darker shades in the respective cells in this figure. Figure
6b presents the average pairwise $\mathop{\mathtt{sim_{d}\text{-}{S}}}\limits$
similarities among drugs with different MoAs. Notably, we find that certain
MoAs, such as MTOR, RARA, EGFR, and NAMP, exhibit similarities in their
clustering patterns, suggesting potential shared characteristics or pathways.
Similarly, we observe similarities among ABL1, BRDT, and FLT1, as well as BCL2
and AURK. These findings might indicate potential commonalities among drugs
with different MoAs, even when their sensitivity profiles may not be similar
(Figure 6b).

(a) Cluster A

(b) Cluster B

Figure 7. Comparison of sensitivity profiles for all drugs in clusters A and B
in Figure 5. Darker color indicates that the drug is sensitive in
corresponding cell lines.

We further examined clusters A and B depicted in Figure 5 to gain deeper
insights into their characteristics. Despite both clusters being compact, they
exhibit distinct characteristics in terms of their
$\mathop{\mathtt{sim_{d}\text{-}{S}}}\limits$ similarities. Figure 7 presents
the sensitivity profiles of all the drugs in each cluster. Clearly, compared
to cluster B, most drugs in cluster A share multiple cell lines in which they
are sensitive, thus resulting in higher
$\mathop{\mathtt{sim_{d}\text{-}{S}}}\limits$ for cluster A than for cluster
B. Specifically, from our preliminary fact-checking, we found that many drugs
in cluster A (left-most drugs in Figure 7a) share some common pathways such as
EGFR, mTOR. This suggests that these drugs possess broader effectiveness
across multiple cancer types. In summary, our analysis reveals that the latent
drug space learned by $\mathop{\mathtt{List\text{-}All}}\limits$ captures
similarities in sensitivity profiles, molecular structures, and pathway
mechanisms. These findings highlight the potential for exploring synergistic
effects among drugs with different MoAs, and developing novel therapeutic
strategies.

##  6\. Conclusion

In this work, we developed two listwise neural ranking methods to select anti-
cancer drugs out of all known drugs for new cell lines. Our experiments
suggest that our listwise ranking method,
$\mathop{\mathtt{List\text{-}All}}\limits$, can select all the sensitive drugs
instead of the few top-most sensitive drugs. Moreover, our experimental
comparison with strong ranking and regression baselines demonstrated the
efficacy of formulating drug selection as a LeToR problem. Notably, our
method, $\mathop{\mathtt{List\text{-}All}}\limits$ demonstrated significant
improvements over the baseline $\mathop{\mathtt{pLETORg}}\limits$ in average
hit rates across a large proportion of cell lines. Additionally, by leveraging
deep networks and pretraining techniques, our methods can learn informative
embeddings. Our analyses of such learned embeddings revealed commonalities
among cell lines and among drugs from different cancer types and MoAs,
respectively. Overall, our work represents a step forward in the development
of robust and effective methods for precision anti-cancer drug selection.
Future work may explore on leveraging 3D molecular structures, multiple
modalities or pretrained chemical foundational models to further enhance
ranking performance.

##  7\. Code Availibility

The processed data and code are publicly available at
https://github.com/ninglab/DrugRanker. All the required softwares to execute
the code are freely available.

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##  Appendix A Reproducibility

As the encoder $\mathop{\mathtt{GeneE}}\limits$, we used a fully-connected
neural network consisting of 2 hidden layers with 4,096 and 1,024 units,
respectively; each hidden layer is followed by a ReLU activation. The last
hidden layer is followed by an output layer with 128 units which outputs the
cell line latent embedding (from preliminary experiments, the best results
were obtained with 128 units). We implemented $\mathop{\mathtt{DrugE}}\limits$
as a fully-connected neural network with one hidden layer of 128 hidden units
followed by ReLU non-linearity, and the output layer of $M$ units, where
$M\in\\{25,50,100,200\\}$. The hyperparameters for all the baselines and
proposed methods were systematically fine-tuned via a random grid search. The
learning rate and learning rate annealing scheme for
$\mathop{\mathtt{pLETORg}}\limits$ were in accordance with its original
implementation. Other methods were trained using ADAM optimization with an
initial learning rate of 0.001. All the baselines were trained for 100 epochs
or until the convergence of their respective training objectives. In contrast,
the listwise ranking models were trained for 300 epochs. Each experiment was
conducted on a computing node equipped with NVIDIA Volta V100 GPUs and Dual
Intel Xeon 8268s processors. The hyperparameters for all the methods are
reported in Table 4 to facilitate the reproducibility of results.

Table 4. Hyper-parameters used in grid search

Method | Hyper-parameter |  Values
---|---|---
$\mathop{\mathtt{pLETORg}}\limits$ | $l$ |  5, 10, 25, 50
$\alpha$ |  0, 0.05, 0.1, 0.5, 1
$\beta$ |  0.1, 1
$\gamma$ |  0, 1, 10, 100
$\mathop{\mathtt{DeepCDR}}\limits$ | $l$ |  25, 50, 100
$\mathop{\mathtt{DrugE}}\limits$ | hidden_units |  128, 256
$M$ |  25, 50, 100

  * •

$l$ denotes the dimension of the latent embeddings for
$\mathop{\mathtt{pLETORg}}\limits$ and $\mathop{\mathtt{DeepCDR}}\limits$;
$\alpha$, $\beta$ and $\gamma$ for $\mathop{\mathtt{pLETORg}}\limits$ refer to
the original notations as used in (He et al., 2020);