# Towards quantum computing for clinical trial design and optimization: A
perspective on new opportunities and challenges

Hakan Doga 111Correspondence<EMAIL_ADDRESS>IBM Quantum, Almaden Research
Center, San Jose, California 95120, USA  M. Emre Sahin  The Hartree Centre,
STFC, Sci-Tech Daresbury, Warrington, WA4 4AD, United Kingdom  Joao
Bettencourt-Silva  IBM Research Europe, Dublin, Ireland  Anh Pham  Deloitte
Consulting LLP, Atlanta, GA, USA  Eunyoung Kim  Deloitte Consulting LLP,
Morristown, NJ, USA  Alan Andress  Deloitte Consulting LLP, Philadelphia, PA,
USA  Sudhir Saxena  My Next Health, Pleasanton, CA, USA  Aritra Bose  IBM
Research, Yorktown Heights, NY  Laxmi Parida  IBM Research, Yorktown Heights,
NY  Jan Lukas Robertus  Hideaki Kawaguchi  Keio University, Quantum Computing
Center, Yokohama, Japan  Radwa Soliman  My Next Health, Pleasanton, CA, USA
Daniel Blankenberg  The Cleveland Clinic, Lerner Research Institute,
Cleveland, Ohio 44106, USA

###### Abstract

Clinical trials are pivotal in the drug discovery process to determine the
safety and efficacy of a drug candidate. The high failure rates of these
trials are attributed to deficiencies in clinical model development and
protocol design. Improvements in the clinical drug design process could
therefore yield significant benefits for all stakeholders involved. This paper
examines the current challenges faced in clinical trial design and
optimization, reviews established classical computational approaches, and
introduces quantum algorithms aimed at enhancing these processes.
Specifically, the focus is on three critical aspects: clinical trial
simulations, site selection, and cohort identification. This study aims to
provide a comprehensive framework that leverages quantum computing to innovate
and refine the efficiency and effectiveness of clinical trials.

##  1 Introduction

The clinical trial design is a process that undergoes significant rigor from
many stakeholders and is ultimately aimed at proving both the safety and
efficacy of a drug product across the target patient population that is
impacted by the disease. By starting with clearly defined study objectives, a
protocol can be developed which encompasses comprehensive criteria for how the
trial should be executed while maximizing the safety of patients and the
quality of data collected. Without proper selection and exclusion criteria for
patients, the drug maker runs the risk of not completing the study or
exhausting resources that could be better spent in other areas such as
downstream patient support programs and lower drug prices.

Patient cohort selection is one of the most important factors in the overall
success of the trial such that an event rate is achieved that is statistically
significant. The event can either represent the disease state or the treatment
response or outcome. Adverse events and toxicity also must be tracked, and to
be thorough must represent a diverse population to validate that the drug has
evidence that demonstrates its safety and efficacy for all those it may be
prescribed to for the intended use. Once the trial has design parameters it
can be optimized for the patients, investigators, and sites that can be
selected in order to balance the cost of the trial with a statistically
significant outcome that supports a safe and effective claim that will be
approved by the FDA. In order to evaluate patients, a set of multi-modal
clinical, demographic, and geographic data is required to assess fit at an
individual level.

Quantum computing is a new frontier in advanced computing technologies that
offers immense potential to enhance current classical computational methods.
Based on the fundamentals of quantum mechanics [1, 2], quantum computing
harnesses the power of entanglement, superposition and interference to
manipulate quantum bits (qubits) and perform computations on quantum
computers. Mapping the computational problem to a quantum computer, these
principles allow quantum computers to perform certain computations potentially
more efficiently. In particular, for certain classically intractable problems
such as prime factorization [3], unstructured database search [4], solving
linear systems [5], computing topological invariants [6, 7] and quantum
simulations [8], it has been proven theoretically that quantum computers
provide speed ups in the computations.

Our work proposes using quantum computational methods to improve the outcome
of clinical trials. To the best of our knowledge, this is the first
comprehensive work that represents a first step on how to utilize quantum
computing for clinical trial design and optimization. For different components
of each subproblem we have identified, namely clinical trial simulation,
cohort and site selection, we establish workflows with quantum optimization
and quantum machine learning methods that can potentially improve the clinical
trial design process (See Figure 1). In Section 2, we describe the general
challenges faced in today’s clinical trial design and optimization methods.
Section 3 discusses widely used classical computational methods and particular
challenges that these methods have. Section 4 provides a brief overview of
quantum optimization and quantum machine learning methods, and delves deeper
into the proposed quantum algorithms for enhancing clinical trial design. We
conclude by discussing some future directions in the final section.

Figure 1: Protocol design is a crucial step for successfully optimizing the
logistics of the trial. Using quantum differential solvers can enhance our
understanding of mechanistic properties of the drug. Once protocols are set,
this will inform the logistical optimization steps of the trial about how to
select sites and how to identify the correct cohort. We propose portfolio-
based quantum optimization to determine the best set of trial sites and
quantum generative models to improve cohort identification.

##  2 Challenges in clinical trial design and optimization

Ninety-percent of drug candidates after they have entered clinical studies
fail during trial phases I, II, III or during the final drug approval stage
[9]. Four main reasons for drug candidate failures in clinical trials have
been reported: “lack of clinical efficacy (40%–50%), unmanageable toxicity
(30%), poor drug-like properties (10%–15%), and lack of commercial needs and
poor strategic planning (10%)” [9]. These are important factors that often
require drug candidates to move back to the early development stages.

As a small number of drug candidates are selected to advance to human trials,
additional challenges emerge about trial design and conduct. During these
stages, the most common reasons for clinical trial failures have been
attributed to poor participant selection and recruitment. Since the early
2000s, different studies have reported recruitment-attributed fail rates of
approximately 30% [10, 11] including reports that nearly 19% of trial-
initiated sites never recruited any participant [12]. In order to improve
trial success rates, the FDA introduced new guidance specifically aimed at
prospectively “selecting a subset of the population in which the effect of the
intervention can more readily be demonstrated” [13]. In parallel with cohort
selection, site selection plays an important role for the success of the
clinical trials. As reported in [14], choosing the optimal sites increase the
chances of recruiting and retaining the target population. The location and
easy access to trial site can prevent long travel times for patients, reducing
potential patient drop outs. Site selection and cohort selection are two very
important aspects of the clinical trial design process that needs to be
modeled and planned symbiotically.

While these challenges may seem separate in nature, we believe there are
underlying threads that connect them. Hence, we explore three overarching
mechanisms that challenge the successful completion of trials

  * •

by constraining the study data (e.g. inadequate samples or cohort size, lack
of historical site data),

  * •

by introducing bias (e.g. imbalanced distributions, missing modalities in
data),

  * •

or by detecting study endpoints or outcomes related to clinical effectiveness
(e.g. toxicity-efficacy, optimal dosage and frequency).

For each of these mechanisms there is a range of contributing factors that may
be cohort-specific (e.g. patient identification, insufficient participants),
operational (e.g. inadequate site selection, resources and costs) or a
combination of both. In this section and the following sections, we expand and
detail these mechanisms and their impact on trial outcomes. These factors may
arise during different stages of trial design and conduct, which we address in
this work in three areas: clinical trial simulations, site selection and
cohort identification.

###  2.1 Clinical trial simulations

The journey of drug development is notably long and expensive, often spanning
10 years and necessitating an investment of over $1-2 billion, with the rate
of success lingering below 7%, due to the complexity of the pre-clinical and
clinical trials essential for validating safety and efficacy [15, 16, 17].
Factors contributing to this scenario include the inadequate consideration of
biophysical and physiological characteristics of molecules in initial protocol
definitions, leading to disparities between in vitro experiments and in vivo
studies [18, 19], and between disease models in animals and humans [20].
Furthermore, the preliminary stage calculations for dosage and the mechanism
of action often fall short in accurately foreseeing efficacy and toxicity in
humans [20], compounded by less than optimal event rates and high dropout
rates in clinical trials. To mitigate these challenges, it is important to
predict the effects of drugs on specific subpopulations, segmented by genomic
and epigenetic profiles [21]. The development of sophisticated models that can
accurately predict efficacy and toxicity, particularly by evaluating the
mechanism of action in human pharmacokinetics and pharmacodynamics (PBPK/PD),
is important. A precise determination of drug dosages and regimens that take
into account the full spectrum of human physiology and potential interactions
with other drugs is crucial for enhancing the drug development paradigm.

Optimizing clinical trials presently leans more towards an empirical approach
rather than a rigorous scientific method. Establishing a robust scientific
foundation for the design and optimization of the protocol, along with
cohort/site selection, requires the identification and collection of
sufficient data points. These data points should provide insights necessary
for informed protocol design.

  1. 1.

Understanding pharmacokinetics, pharmacodynamics and pharmacogenomics –
Designing a clinical trial with real people for a new molecule requires a
thorough understanding of how a body would process that drug, and how the drug
would impact the body. There is, thus, an underlying requirement to consider
the pharmacokinetics (what happens to the molecule as it passes through the
human body) and pharmacodynamics (what happens to the body as the molecule
passes through it) properties related to the molecule in question for the
condition(s) in question. Furthermore, understanding the genomic and
epigenetic influence on underlying patient physiology based properties, and
their interplay with the drug molecule characteristics is critical, as this
serves as the basis for designing the trial protocol and the criteria for site
and cohort selection.

  2. 2.

Understanding dosage and mechanism of action - without proper prediction
algorithms to identify the correct dosage and the mechanism of action at a
preclinical stage, it is not viable to construct a true predictor of the
efficacy toxicity in real humans. Preclinical efficacy data is not an accurate
predictor of efficacy in clinical trials. There are biological discrepancies
between in vitro and in vivo, and between disease in animal and humans.
Consequently designing clinical trial protocols based on in vitro and in vivo
data can result in lower event rates, and higher drop out rates.

###  2.2 Site Selection

Adequate site selection is one of the most critical steps for the successful
completion of a trial [22]. An appropriate trial site must be equipped with
necessary study-specific infrastructure and resources, such as staff and
equipment, as well as provide access to a catchment area that enables the
selection and recruitment of an adequate number of participants. Trials may
also be conducted across multiple locations to ensure that a more
representative sample of the population can be studied and, in some cases,
expanding to additional sites may also help counteract trial delays and
bottlenecks [22].

Site-specific characteristics are therefore important and can contribute to
serious downstream bottlenecks for the timely conduct and completion of
trials. Examples of cohort-specific characteristics include a non-homogeneous,
diverse population within a site’s catchment area, and operational-specific
characteristics include quality electronic records and available data capture
infrastructure, domain-specific expert trialists, equipment or laboratories.

The majority of industry experts select a trial site based on three dimensions
[22]: (1) Knowledge about the site (e.g. experience in conducting trials, site
success rates, therapeutic specialization); (2) Patient access (e.g.
recruitment performance or access to required patient population); and (3)
Working culture (e.g. known investigators’ interest and commitment to driving
studies).

Site selection should also take into account geographical considerations that
are specific to the site location such as an increased incidence of certain
diseases, particular exposures to environmental factors, possible burdens for
patient participation and retention, or regulatory requirements. Overall,
existing approaches and algorithms to rank the most adequate sites for a trial
require modelling these complex and diverse criteria involving both cohort-
specific as well as operational-specific characteristics. Successful methods
must cope with limited data availability and site-specific biases, which
further make comparisons across sites a non-trivial challenge.

###  2.3 Cohort Identification

Identifying the relevant inclusion and exclusion criteria so that patient
selection can occur adequately at different clinical sites is a challenging
task. For instance, if the eligibility criteria are too strict, even though
they can satisfy clinical concerns, this can create barriers to trial
enrolment and recruitment [23, 24]. In addition, when the criteria are
narrowly defined, they can prevent trial results from being generalized[25].
Furthermore, trials do not often include certain population groups based on
age [26], gender [27], and ethnicity[28]. As a result, new regulation from the
US Food and Drug Administration (FDA) requires adequate representation of the
population in clinical trials [29], which requires the modification of the
exclusion and inclusion criteria and protocols to balance clinical concern
with adequate sample size and representation. However, currently there is a
lack of consensus on how to remove specific criteria [30].

There are noticeable race, ethnicity and gender disparities in populations
participating in clinical trials. This causes issues such as the lack of
generalization of data emanating from trials and lack of information on the
effectiveness of drugs in certain population groups [31]. In many cases, the
implementation of current guidelines on clinical trial design is sub-optimal
in the population at large, but especially among ethnic minority groups,
women, people living in rural communities, uninsured or under-insured
individuals, lower education and income, and in general individuals in
vulnerable socio-economical conditions [32]. Clinical trials lack diversity
due to historical limitations, but also due to their early geo-spatially
restricted origins [33] as well as the multiple barriers to participation
which disproportionately affect certain population groups more than others
[34]. Thus, equity is an important factor in clinical trial design to improve
generalizability, misclassification of drugs, targeted personalized treatment,
and reduce implicit bias.

To further enhance the personalization of treatment, reducing disparities, and
lowering the number of enrolled required patients, enrichment methods like
prognostic and predictive strategies have been proposed to overcome several
deficiencies in current cohort identification and recruitment processes.
Prognostic enrichment refers to the targeted recruitment of patients with
certain diseases outcome and progression. Alternatively, another process known
as predictive enrichment refers to the recruitment of patient population with
the potential for maximum positive response to the trialed therapy or drugs.
Such a method will help to reduce the number of patients required for the
intervention group, while prognostic enrichment will help to enhance the power
of the study. In practice, these two methods have been used as complements to
each other since they can benefit trials for personalized medicine treatment
where a prediction of treatment’s efficacy is intricately linked to the
disease progression like sepsis [35, 36]. However, the task of predicting
disease progression, as well as treatment outcome using using patients’
genome-to-exposome profile [37] is a scientifically challenging task.

From a technical perspective, the cohort identification process has relied on
expert knowledge to select the criteria based on physicians’ clinical
expertise [38] in conjunction with manual queries in patients’ medical
records. However, this can potentially result in bias in identifying the
eligibility criteria [39], as well as slowing down the recruitment process. As
a result, many computational methods like AI/machine learning (ML) models have
been proposed to enhance the criteria selection process, to complement the
clinical expertise and experience of the trial investigator [40]. Despite
major benefits that have been demonstrated by applying ML models to cohort
selection, many challenges still remain. Most prominently is the heterogeneous
nature of biomedical and healthcare datasets. Specifically, electronic health
record (EHR) are known to have several data quality issues from medical codes,
sparse or missing data, as well as the differences in how medical data is
recorded when comparing records between sites [41]. In addition, new
personalized medical treatments targeting specific biomarkers will also
require other data types in conjunction with EHRs like omics data [42], making
the application of data driven techniques, such as machine learning,
challenging due to the heterogeneous nature of different data types [43].
Furthermore, for rare disease cases, it can be difficult to obtain datasets
with the appropriate sample sizes, thus making it difficult to train robust
machine learning models [44]. An emerging approach to tackle sample size
limitations is the use of uncontrolled trials where synthetic control arms
(SCA) may be used. Unlike traditional RCTs, in uncontrolled trials, only the
treatment arm needs to be recruited and the controls may be generated using
existing data (e.g., EHRs) or synthetically generated data based on the trial
protocol. ML can support this task by automatically generating synthetic
control arms to supplement single arm treatment-only trials. However, this
approach may have unique challenges with regards to generalizability,
interpretation, and statistical methodology [45].

Finally, a potential concern for the application of machine learning
techniques in clinical trials is the lack of explainability due to their
black-box nature. For instance, ML models have been proven to be effective to
predict the personalized advantage index (PAI), which is a measurement of the
optimal treatment within a patient cohort [46] with psychiatric conditions.
However, the potential drawback of using machine learning to predict PAI
values is the lack of exaplainability in the decision making process of the
model. As a result, it is imperative that explainability should be built into
the model to inform the decision outcome [47], thus satisfying regulatory
concern as well as enabling cross validation/confirmation by clinicians
conducting the trials.

##  3 Classical computational methods in clinical trial design and
optimization

###  3.1 Clinical trial simulations

In computational clinical trials, the key challenge is to effectively simulate
the outcomes of clinical trials using computational models [48]. The goal is
to predict drug efficacy, side effects, and outcomes without conducting
physical trials, which has the potential to lower costs, save time, and
address ethical concerns inherent in conventional trials [49]. This process
utilizes a range of techniques, including advanced algorithms [50],
statistical methods [51], machine learning, and various simulation approaches
such as patient virtualization and pharmacokinetic/pharmacodynamic (PK/PD)
modeling. The focus is on virtual rather than physical simulations, to
accurately forecast outcomes as they would occur in the real world.

The modeling of pharmacokinetics and pharmacodynamics plays an important role
in evaluating drug safety and efficacy, confronting the challenges posed by
biological complexity and the extensive data required. As these trials
progress, there is a need to enhance the accuracy and efficiency of these
models. Overcoming these obstacles requires advancements in computational
methodologies and robust datasets.

PBPK is a powerful modeling technique that requires computational tools to
solve ordinary differential equations. These equations describes the movement
of the drug between the different tissues/organs in the biological systems.
PBPK modeling represents a mechanistic approach that integrates 2 important
components : (1) drug-dependent component that includes properties specific to
the drug and (2) drug-independent component that includes biological system
properties, study protocol and formulation properties. A third component
related to both the drug and the biological system, allows for a priori
simulation of drug concentration–time profiles. Such predictions are of high
pharmacological value because they enable estimating drug exposure not only in
plasma but also at the site of action, which may be difficult or impossible to
measure experimentally [52].

PBPK models simulate the concentration–time profile of a drug in a species by
integrating the physicochemical properties of the compound with the physiology
of the species. Being mechanistic, PBPK models can be used to simulate and to
predict the next set of data and to plan the next experiment.

Simulated clinical trials using PBPK population modeling of these complex
clinical scenarios need to be fully explored. [53]. Many reviews emphasized
the significance of PBPK modeling for personalized medicine. [54, 55, 56].
These models have the potential to guide physicians in prescribing the right
dosing regimen [21, 57] as these models utilize the relationship between the
drug dose, physiology and plasma concentration, which helps determine dosing
regimen within a target therapeutic window [58]. Such models can be used to
design more inclusive clinical trials, by conducting in silico simulations
across diverse population groups to evaluate patient risk and benefits, and
providing dosage guidance [59].

PK/PD modeling can optimize the design of clinical trials, guide the dose and
regimen that should be tested further, help evaluate proof of mechanism in
humans, anticipate the effect in certain subpopulations, and better predict
drug-drug interactions; all of these effects could lead to a more efficient
drug development process. Because of certain peculiarities of immunotherapies,
such as PK and PD characteristics, PK/PD modeling could be particularly
relevant and thus have an important impact on decision making during the
development of these agents.

By looking at the disease behavior patterns, we can actually classify the drug
candidates based on their potency and based on the tissue exposure. One can
also predict drug - drug interaction, and use that to determine the dosage and
frequency regimen before initiating trial design.

###  3.2 Site Selection

Clinical trial site selection is a complex process that requires both
quantitative and qualitative analysis of multiple factors [60]. While the
focus of this work is on adequate site selection for clinical trials, similar
problems occur when selecting optimal sites in other industries such as
renewable energy sites [61], landfill sites [62] or facility sites [63], and
we observe similar computational methods employed to analyze the relevant
factors for optimal site selection. In the case of clinical trials, some of
these factors can be more generic while the other are trial-specific.
Depending on the scope, the overall goals and the logistics of the particular
trial, sites are selected to maximize a successful outcome. Viewed this way,
site selection can be seen as an optimization problem over multiple parameters
or a machine learning problem where we would like to understand most
significant features to train a model for predicting best sites.

When selecting appropriate sites for clinical trials, most classical methods
rely on historical trial data from the candidate sites and their catchment
population. Site-specific data may be collected, for example, from publicly
available databases such as ClinicalTrials.gov, through Contract Research
Organizations (CROs), or from proprietary data sets. Cohort or patient-
specific information may be collected from electronic health records (EHRs),
databases of geographical distribution statistics of disease and patient
demographic characteristics. When available, this information can be used by
trialists to rank trial sites that are more likely to be successful in
recruiting participants and completing the trial.

Ranking based approaches may use statistical summaries [64, 65] and portfolio
optimization [66]. The latter is a constrained utility-maximization problem
where an optimal portfolio (i.e. a trial site and its characteristics) is
selected from a pool of considered portfolios (i.e. candidate trial sites)
according to an objective (i.e. successful trial completion or successful
trial participant recruitment).

Additionally, machine learning based approaches have also been used to select
ideal trial sites. Traditionally, site selection has been conducted by experts
with heuristics or rules [67]. However, rule-based methods are extremely
costly, time-consuming and dependent on existing trialists’ expert knowledge.
More recently, methods to predict which sites should be selected and to match
sites with clinical trials by efficiently using machine learning for site
selection have been attracting attention [68, 69]. For example, a method that
introduces constraints to ensure the diversity of patients to be enrolled in a
ranking-based method [70] has been developed and can be easily implemented
[71].

Knowledge graph based methods have been used to create novel representations
and perform analyses using embeddings and graph learning models [72, 73].
Although these are promising approaches, both graph-based and non-graph-based
neural networks require large amounts of training data to achieve model
accuracy performance. However, site-specific and patient-specific data are
heterogeneous, sparse, and are often missing, which further add obstacles to
current classical methods.

###  3.3 Cohort Identification

Eligibility criteria are identified to select patients for clinical trials by
the investigators at the trial sites. Currently there are different techniques
which have been used to recruit participants for trials. Specifically, the
traditional methods of cohort selections have been rule-based methods, which
can be time intensive. Furthermore, longer cohort selection process can
negatively impact on the timeliness of the clinical trial. Consequently,
researchers have taken advantage of data-driven techniques like machine
learning algorithms to speed up the screening of participants in clinical
trials based on inclusion-exclusion criteria. In this section, we will review
exiting statistical, optimization, and machine learning methods which have
been used to screen patients based on eligibility criteria. In addition, more
advanced applications of machine learning to identify relevant subgroups for
personalized medicine treatments, as well as the emergence of generative
models to generate synthetic data will also be reviewed.

####  3.3.1 Rule based approach

The traditional methods of cohort selections have used rule-base methods.
Those rules are often crafted to satisfy specific criteria for a clinical
trial or specific types of trials. Longer cohort selection time makes negative
impact on the timeliness of the clinical trial. Crafting those rules takes a
lot of time and efforts including medical experts, yet it has less relevance
to future clinical trials cohort selection. Also, although candidates are
suitable to clinical trial criteria, it is harder to predict their length of
stay (LOS) or discover risk factors of LOS in advance using the rule based
approach. The candidates’ prolonged LOS and the finding the risk factors of
LOS are key factors for successful cohort selection.

####  3.3.2 Machine learning

Using machine learning algorithms, researchers can not only classify, cluster,
predict more suitable candidates but also have ability to predict their length
of stay or discover risk factors or group for LOS. Those were hidden factors
that may have not been defined as a rule. Many studies that utilized machine
learning methods have been tested on electronic health records (EHRs). However
due to the complexity of EHR dataset, multiple ML models need to be tested to
maximize the prediction outcome. For example, Segura-Bedma et al. [74] applied
different deep learning methods to select robust cohort selection. Similarly,
Chen et al. [75] used four machine learning models – Neural Network (NN),
random forest, histogram-based gradient boosting, and k-nearest neighbor to
identify patients at high risk for prolonged LOS following primary total hip
arthroplasty. Other researchers leveraged NLP (Natural Language Processing)
and used bag of words document representation model, which considers the text
as an unordered set of words, for 13 classifiers and other pattern matching
approach. To select the candidate, the authors investigated four different
classification methods - support vector machine, logistic regression, naïve
Bayesian classifier, and gradient tree boosting[76]. More advanced development
in ML model like transformer-based approach designed specifically for EHR [77]
has shown promising results in performance with potential for generalization.

In addition to typical ML models and advanced transformer model, generative
models like the generative adversarial network (GAN)[78] has also shown
promising applications to generate synthetic data [79, 80]. In clinical
trials, synthetic data can be used to create synthetic patients, with
statistical properties of real patients but are not linked them, thus
maintaining patients’ privacy and confidentiality. These synthetic patients
can also act as a synthetic control arm, in conjunction with the real patients
in the intervention group. As a result, the usage of the synthetic control
group can reduce the number of participants needed to be recruited in a trial,
thus speeding up the trial process and reducing the budget requirement.

GAN structure consists of a generator and a discriminator [81]. The
generator’s role is to generate synthetic data, while the discriminator plays
the role of a classifier to distinguish between fake and real data. These two
models compete against each other, thus resulting in a Nash equilibrium
whereby the quality of the synthetic data produced by the generator can
resemble the real data. However, GAN requires the usage of pseudo-random
number generator to inject noise to the generator, thus potentially resulting
in large computation time, and potential statistical bias in the model.

Another challenge for current ML techniques is how to embed and train models
that can process multi-model data to improve the selection of eligibility
criteria. The multi-modal dataset typically involves different data formats
such as EHR, which typically represented as tabular data (e.g., age,
demographics), image data (e.g., x-rays, magnetic resonance imaging, pathology
slides), time-series data (e.g., pulse oximetry, ultra-sounds, wearable
sensors), structured sequence data (e.g., genomics, proteomics, metabo-lomics)
and unstructured sequence data (e.g., notes, forms, written reports, video)
among other sources [82]. Fusion strategies have been proposed as a solution
to ingest and train machine learning models for multi-model dataset, depending
on the stage or methods of the data fusion, it is called early fusion or late
fusion or joint fusion [43, 83]. This includes combining features from the
relevant data, extracting the relevant features from dataset and aggregating
them, or applying assemble learning models for different data modalities [82].

####  3.3.3 Personalized treatment, genomics, and equity

Cohort selection is not just restricted to rule-based and machine learning
aspects. Trial participants are also chosen for the trial based on their
underlying similarities stemming from genomics. In some cases, patients might
have the same tissue-of-origin diagnosis, or genomic alterations. In recent
years, due to advancement in genomics technology and subsequently, better
understanding of the biological underpinnings of complex diseases, there is a
consensus that complex diseases such as cancer, cardiovascular disease,
neurological diseases need customization to an individual for optimal therapy.
Hence, next-generation trials need to be patient-centered rather than drug-
centered [84].

Trials modeled around specific biomarkers for certain drugs treating
heterogeneous complex diseases aim to match patients with specific
interventions based on their molecular characteristics. Single and multiple
integral biomarker trials classified as basket, umbrella, and adaptive trials
have been proposed as novel approaches for clinical trial design for
personalized treatment. Basket trials group patients with same molecular
abnormality regardless of disease outcome; umbrella trial design tests
multiple drugs targeting a common pathway, but in genetically distinct
subgroups; while adaptive trails allow for adjustments to the design mid-
course based on feedback from the targeted cohort [85]. These biomarker-driven
approaches also necessitate understanding of genetic diversity with respect to
drug target identification. Machine learning models and natural language
processing techniques as described above can help identify individuals with a
high likelihood of responding positively to a specific treatment, as well as
survey social determinants of health that could impact trial participation and
outcomes. For instance, ensemble machine learning model has been used to
predict the treatment outcome of patients with type 2 diabetes given DPP-4
inhibitors in comparison to conventional therapy [86].

Extending specific biomarker oriented trials to increase clinical trial
efficiency, another way is to selectively enroll participants based on
clinical and biological characteristics [87]. Lately, polygenic risk scores
(PRS) which take into effect the cumulative impact of many genetic variants
across the genome to compute potential genetic predisposition or risk of a
disease have been considered for cohort identification [88]. It was observed
in post hoc analyses of clinical trials that healthy individuals with highest
PRS for cardiovascular disease demonstrated the greatest benefit when
randomized to statin or placebo to prevent cardiovascular disease, with a 44%
relative risk reduction versus 24% in the remainder of participants [89, 90].
Beyond post hoc analyses, PRS can also be used to understand the presence of
racial disparities in large biobanks which are used to identify cohorts in
clinical trials [91]. However, PRS are known to suffer from lack of
generalizability and loss of predictive power in non-European populations due
to the predominant focus of genome-wide association studies on European
populations [92]. Recent studies have shown that even with a small number of
non-European participants predictive power of PRS increases in
underrepresented populations [93]. Machine learning methods are often applied
to improve generalizability of PRS across diverse cohorts for complex diseases
[94, 95, 96].

By incorporating machine learning algorithms into response-adaptive
randomization designs, trials can achieve better performance than traditional
designs, resulting in more ethical and appropriate clinical trials [97].

##  4 Quantum computational methods in clinical trial design and optimization

In this section, we briefly discuss some quantum algorithms that are relevant
for this work and present our perspective on how to utilize quantum
computational methods for enhancing clinical trial design and optimization.
For a more in-depth discussion of quantum computing, especially in the context
of healthcare and life sciences, the reader is referred to Sections 1 and 2 of
[98].

###  4.1 Quantum Optimization and Quantum Machine Learning Algorithms

In general, optimization problems aim to find the global minima/maxima of an
objective function. As the parameter space for the problem increases,
searching for this global extremum point becomes harder and more costly for
classical methods. Quantum optimization methods [99, 100, 101] have been
proposed, studied and implemented with the goal of achieving a speed-up over
the classical optimization techniques. For near-term implementations of
quantum optimization algorithms, a common method is using variational quantum
algorithms [102]. These are quantum-classical hybrid algorithms that can
efficiently explore the high-dimensional Hilbert space to find the optimal
solution. To that end, a trial quantum state is prepared and appropriate
mapping of the problem Hamiltonian is set up. Classical optimizer updates the
quantum state in every iteration of this pipeline until a solution state is
recovered. The work [103] provides a rigorous and detailed analysis of the
current landscape for quantum optimization algorithms, their complexity and
potential for certain optimization problems such as maximum independent set
(MIS), knapsack/market share problem, sports timetabling problems and several
others.

Quantum machine learning (QML) [104, 105, 106, 107] is another growing field
within quantum computing with the potential to improve data analysis. In a
typical machine learning scheme, an algorithm is designed to learn the
structure of the data, and identify patterns for various prediction and
inference tasks. These learning algorithms are usually considered under three
main categories, supervised machine learning, unsupervised machine learning
and reinforcement learning. While data is labeled in supervised ML for the
training of the model, in unsupervised learning the algorithm finds the
patterns in the data and learns them. In reinforcement learning, the training
is done on a reward/punishment basis. Despite there being no general and
complete QML theory, all these machine learning schemes have counterparts in
QML. For example, quantum neural networks (QNN) [108] can be used for computer
vision tasks for labeled data or solve a MAXCUT problem on a graph by learning
the distances as an unsupervised learning model [109]. A more in-depth look
into the field of QML can be found in [107] with a main focus on QNNs and
quantum kernel methods.

Figure 2: Table lists some of the problem classes within optimization and
machine learning problems, along with some commonly used examples of quantum
algorithms for optimization and machine learning.

In general, it is an ongoing and active research area to map the quantum
algorithms to various use cases and identify how and where quantum computing
can improve the existing computational methods. This interest has led quantum
computing research to find a large variety of applications in various fields
ranging from molecular chemistry and molecular simulation [110, 111, 112, 113,
114, 115, 116, 117, 118, 119, 120], material sciences [121], encryption [122,
123], search and optimization [124, 125], protein structure prediction and
drug discovery [126, 127], cell-centric therapeutics [98], financial
optimization [128], computational pathology [129], causal discovery [130], and
other potential applications in health and medicine [131].

###  4.2 Clinical trial simulations

The limitation of the PBPK models originate from the uncertainty in regard to
the degree of accuracy and reliability of its input. The reduced confidence in
input data is understandable since accuracy of PBPK models comes from the
quality of its input parameters. Therefore, if the incorporated data contain
errors, inconsistencies or miscalculations, the resulting simulations may not
truly represent in vivo conditions and performance. Inaccuracies in input data
may originate from a variety of reasons such as the high inherent variability
of biological systems [132, 133] Another challenge of PBPK models is severe
lack of detailed databases for physiological parameters, particularly for
certain subpopulations. Consequently, much of the input data must be obtained
from multiple sources. [134] Finally, a deficiency of information regarding
human physiology/anatomy and information related to drug metabolism and active
transport leads to poor prediction of the observed data [132]. Clinical trials
necessitate the use of high-quality data [135, 136], typically characterized
by a limited dataset size. QML algorithms have demonstrated effectiveness in
scenarios with few data, as evidenced by various studies [137, 138]. To bridge
the gap between the necessity for high-quality data in clinical trials and the
demonstrated effectiveness QML algorithms in scenarios with limited datasets,
it is essential to find efficient embeddings that can accurately translate
classical data characteristics into quantum-compatible formats. Specific
metrics for analyzing the classical data and its corresponding feature map can
be adopted [138, 139, 140, 141, 142, 143], allowing for the potential of QML
algorithms to be more effectively realized for these specialized applications.

A mechanistic understanding of PK processes and a deeper knowledge of these
specialized physiologies is key for improving confidence in specialized PBPK
models and therefore achieving the ultimate goal of personalized medicine
[144]. Integrating systems biology (target expression) with PBPK and
Pharmacodynamics modeling will further increase the usefulness and adoption of
PBPK modeling. This is even more relevant in personalized medicine where
individual patient outcomes can be improved by delivering the personalized
optimal dose at the right time [145, 146, 147]. The use of imaging techniques
for tissue partitioning to eliminate the uncertainty related to predicted
tissue-to unbound plasma partition coefficients (Kp), key set of parameters
used to characterize the distribution or “movement” of drugs into different
tissues in the body [148]. The development of more stable and viable in vitro
systems is also important[149], as is development of competitive binding assay
for highly bound compounds [150].

Figure 3: Schematic Representation of the PBPK Model Development and
Estimation Workflow for Clinical Trials: The process begins with the
construction of the model, incorporating drug properties and biological system
attributes. It proceeds with data preprocessing, including feature selection,
dimensionality reduction and topological data analysis. The final phase
involves model estimation, leveraging quantum computational techniques such as
quantum differential equation solvers, QSVMs, QNNs, and QGNNs, leading to the
formulation of the model.

PBPK models often require solving systems of ordinary differential equations
(ODEs), a task that demands considerable computational resources, particularly
for drug interaction simulations within intricate physiological contexts.
Quantum computing has been identified as a promising solution for accelerating
both linear [5] and non-linear [151, 152, 153] equations. Quantum differential
equation solvers offer the potential to simulate PBPK models by solving
differential equations that represent the non-linear and time-varying
behaviour of drugs in the body. Furthermore, their ability to handle large-
scale models, where the body is divided into several compartments, such as the
liver, kidneys, lungs, and other organs appears very promising. Nonetheless,
the deployment of such quantum algorithms is constrained by the current state
of quantum hardware, which is yet to reach the necessary level of advancement.
During this transitional phase, variational algorithms [102] for quantum
machine learning and quantum kernel methods emerge as more viable options for
the existing quantum hardware, albeit with caution [107, 154, 155]. Besides
the algorithms discussed in Section 4, research [156] has shown that
integrating trainable parameters within data-encoding Hamiltonians could
significantly improve the model’s flexibility and forecasting precision. This
strategy might allow for the fine-tuning of model frequencies for PBPK by
enhancing the representation of complex drug distribution and metabolism
processes. Additionally, the recent development of a spectral method which
introduces an efficient technique for solving differential equations in high-
dimensional spaces [157, 158] by utilising a robust set of fitting
polynomials, providing substantial expressiveness.

###  4.3 Site Selection

Selecting sites for a clinical trial can be formulated as an optimization
problem. A straightforward approach is first determining which sites are
feasible for the trial, followed by ranking the “best” sites according to its
features and assigned weighted scores. The features are usually site specific
historical performance data, and based on the final ranking of the sites,
certain tiers are constructed to make a decision. These tiers can reflect the
risks associated with the sites, namely the expense, enrollment rate and
availability of expert PIs. A novel portfolio-based optimization approach is
presented in [64] as an improvement over the traditional approach. This more
flexible model is designed to accommodate the study goals of the trial.
Instead of ranking the sites and making a selection based on this ranking,
portfolio-based optimization creates a portfolio of sites where the overall
weight of the sites is optimal. This allows the model to consider “what if”
scenarios, trial specific constraints such as multiple sites in a country or
preferred sites. A similar approach can be taken using quantum optimization
algorithms. In particular, the problem formulation as a mixed-integer
programming (MIP) can be mapped to a quantum setting. Interestingly, it is
also possible to map the financial portfolio optimization quantum algorithm in
[159] to clinical trial site selection setting. In this one-to-one mapping of
the problem, we have the usual binary decision variables $x_{i}\in\\{0,1\\}$
to determine if the sites are selected in the portfolio or not. The quantum
optimization can be set as:

$\min_{x\in\\{0,1\\}^{n}}qx^{T}\Sigma x-R^{T}x$ $\text{subject to:}\,A^{T}x=S$

where $R\in\mathbb{R}^{n}$ is the expected enrollment rate for trial sites,
$\Sigma\in\mathbb{R}^{n\times n}$ is the covariance between trial sites, $q>0$
captures the risk that the trial design can specify which may be informed by
trial specific constraints, $A\in\mathbb{R}^{n\times n}$ declares the trial
constraints and $S$ denotes the number of sites to be selected in each
portfolio. This optimization problem can be solved using either a Variational
Quantum Eigensolver (VQE) or a Quantum Approximate Optimization Algorithm
(QAOA) in near-term quantum computers. In principal, the ground state of the
Hamiltonian returns the selection of a portfolio of sites. In the case of a
high-dimensional parameter space where one considers all the sites in a
country, or if the optimization problem exhibits non-convex behavior, we
expect the quantum portfolio optimization method to perform well. For fault-
tolerant quantum computers, it is shown in [159] that the proposed algorithm
can solve the portfolio optimization in poly(log($N$)) run time compared to
classical poly($N$), where $N$ is the total number of sites in our mapping.

Figure 4: After the site-related data is collected and processed, we propose
two approaches that utilize quantum computing. Portfolio-based optimization
maps the problem with site-specific parameters and trial-specific constraints
to select the best portfolio of sites. If the historical site performance data
is limited, we propose in parallel, one can set a QSVC to classify which sites
are feasible.

Another important bottleneck for site selection tasks is the availability of
historical performance data from the potential trial sites. While some
publicly available data can be used to identify sites, these are usually
limited and can lack crucial information for optimal site selection. This can
potentially create unwanted bias in the site selection process, impacting the
cohort selection and the successful completion of the trial. As reported in
[65], missing modalities in the data can impact the site selection process.
Quantum kernel methods [160] that map the feature space to a higher
dimensional space to classify the data have been used in various QML
applications. In particular, the work [161] demonstrates some significant
results for QSVM for electronic health records (EHR) data and constructs a
framework for empirical quantum advantage (EQA). The data they use is of
similar nature to clinical trial site data, in the sense that samples are
limited with high dimensional feature space. In this setting, we propose to
use QSVM [162] for classifying the sites into feasible/not feasible classes.
In particular, we expect quantum to provide utility where the sample-feature
ratio is low with a high terrain ruggedness index as defined in [161]. This
can potentially help overcome the bias towards selecting the same sites for
running clinical trials, analyze the outcome of trials at new sites and
provide access to more diverse cohorts.

###  4.4 Cohort Identification

Machine learning algorithms have shown promise for different aspects of cohort
identification and selection, as well as aiding several enrichment strategies
like prognostic and predictive enrichment to lower the failure rate and the
required number of participants need to be recruited for clinical trials.
However, a potential challenge of applying machine learning techniques to
identify the cohorts based on the eligibility criteria is the diverse nature
of the dataset. Classically several strategies have been developed known as
fusion techniques to process diverse dataset like EHR, genomics, proteomics,
and longitudinal data [43]. Quantum feature map can potentially present a
pathway to embed different biomedical data types more efficiently to train
different quantum machine learning models ranging from supervised (e.g. QSVM
[161, 163, 164]), and unsupervised methods (e.g. quantum neural network[165]).
A potential development within the field of quantum-encoding that can impact
cohort selection is the research of a universal feature map that can encode
various data types ranging from images, EHR and gene expression to identify
sub-population that has the highest positive response to certain clinical
treatments. Such an advancement can provide unique benefits in
predictive/prognosis enrichment strategy for high value trials like oncology
[166], immunotherapy [167] or cardiovascular diseases [168] since the usage of
multimodal data (EHR, diagnostic imaging, multi-omics) can enhance the
accuracy of ML models in predicting the efficacy of the treatments .

Quantum feature map is a unique method to map classical data into the complex
Hilbert space, which in theory can represent correlation between variables in
complex dataset that is hard to simulate classically [169, 170]. Specifically,
some feature maps involve constructing different forms of parameterized
quantum circuits which encode the classical feature values. It has been shown
that by encoding classical data in certain quantum circuit structure, this can
induce correlation that does not exist in the dataset, but mimicking the
behaviour of certain quantum states, thus potentially informing the
performance of certain quantum machine learning algorithms in downstream
applications like classification or regression [171].

Another promising application of the quantum machine learning comes in the
form of equivariant quantum neural network [172, 173]. Equivariant quantum
neural networks (EQNNs), also known as geometric quantum machine learning
(GQML), is a class of quantum neural networks where the design of the quantum
circuits contain the symmetries of the original dataset through the process of
inductive bias [174]. Specifically, the quantum circuits are constructed based
on the symmetry groups of the original datasets. EQNNs are designed to solve
certain challenges of quantum neural networks such as barren plateau and
excessive local minima, inhibiting their applications for different datasets
[175]. For biomedical dataset, it is expected that EQNNs can have important
impact due to the various symmetries that intrinsically exist in different
data modalities. For instance, medical images are known to contain symmetries
like translation equivariance, rotation and reflection [176], while sing-cell
transcriptomics can contain unique local and global symmetrical structures
[177]. As a result, EQNNs can be used to classify multi-model dataset to
identify the right populations for clinical trials based on certain
eligibility criteria.

In addition to the usage QNNs for machine learning task like classification, a
class of QNN known as quantum generative adversarial neural network (QGAN) has
gained significant interest due to their unique advantages. Quantum GAN has
been proposed as an alternative to overcome many disadvantages of classical
GAN. For instance, it has been proved that QGAN will require less training
data to produce robust model [178]. There are many different implementation of
the QGAN such as hybrid model with quantum generator and classical
discriminator, as well as a full quantum version with QNNs acting as generator
and discriminator. In the fully quantum settings, the quantum GAN exhibits a
unique advantage with the optimization between the generator and discriminator
is a linear programming optimization, with a convex state-space as described
by the Kakutani fixed-point theorem [179]. In practice, full quantum GAN has
been used to produce simple synthetic images based on the MNIST dataset [180],
while hybrid versions with quantum generator and classical discriminator have
been used to synthesize random distributions [181]. As a result, by using
either a hybrid QGAN or a full quantum version, these setups can generate
complex distribution mimicking the distribution from real patient biomedical
data with much lower training data, acting as synthetic control arm for
clinical trial. The usage of QGAN can potentially benefit rare disease trial
since the training data for the generative model tends to be small due to
complex nature of the disease.

Figure 5: Overview of the cohort identification process with multi-modal data,
and applications of quantum machine learning for classification and generative
model in the cohort identification process.

##  5 Prospect of quantum computing in clinical trial design and optimization

Our work proposes various quantum algorithms to improve the outcome of
clinical trials, and discusses in depth how practitioners of the field can
utilize these new computational tools. By simulating the drug properties more
accurately, we can determine the trial protocol that can ensure a successful
outcome. Furthermore, optimizing the procedures of site selection and cohort
identification based on the protocol design, we can reduce the cost of the
clinical trials and prevent adverse events. As quantum computing technology
matures, we see utility-scale quantum experiments displaying real promise to
advance our computational capabilities [182]. In parallel with that, more
efficient quantum error correction methods [183] bring the arrival of fault-
tolerant quantum computers closer than expected. Without a doubt, quantum
computing will play an important role to advance science in the next decade,
and this work explores the potential of quantum computing to enhance clinical
trial outcomes.

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