citenum

# Causal Machine Learning
for Healthcare and Precision Medicine

Pedro Sanchez
University of Edinburgh
<EMAIL_ADDRESS>
&Jeremy P. Voisey
Canon Medical Research Europe
&Tian Xia
University of Edinburgh
&Hannah I. Watson
Canon Medical Research Europe
&Alison Q. O’Neil
Canon Medical Research Europe
&Sotirios A. Tsaftaris
University of Edinburgh
The Alan Turing Institute

###### Abstract

Causal machine learning (CML) has experienced increasing popularity in
healthcare. Beyond the inherent capabilities of adding domain knowledge into
learning systems, CML provides a complete toolset for investigating how a
system would react to an intervention (e.g. outcome given a treatment).
Quantifying effects of interventions allows actionable decisions to be made
whilst maintaining robustness in the presence of confounders. Here, we explore
how causal inference can be incorporated into different aspects of clinical
decision support (CDS) systems by using recent advances in machine learning.
Throughout this paper, we use Alzheimer’s disease (AD) to create examples for
illustrating how CML can be advantageous in clinical scenarios. Furthermore,
we discuss important challenges present in healthcare applications such as
processing high-dimensional and unstructured data, generalisation to out-of-
distribution samples, and temporal relationships, that despite the great
effort from the research community remain to be solved. Finally, we review
lines of research within causal representation learning, causal discovery and
causal reasoning which offer the potential towards addressing the
aforementioned challenges.

##  1 Introduction

Considerable progress has been made in predictive systems for medical imaging
following the advent of powerful machine learning (ML) approaches such as deep
learning (Litjens et al., 2017). In healthcare, clinical decision support
(CDS) tools make predictions for tasks such as detection, classification
and/or segmentation from electronic health record (EHR) data such as medical
images, clinical free-text notes, blood tests, and genetic data. These systems
are usually trained with supervised learning techniques. However, most CDS
systems powered by ML techniques learn only associations between variables in
the data, without distinguishing between causal relationships and (spurious)
correlations.

CDS systems targeted at precision medicine (also known as personalised
medicine) need to answer complex queries about how individuals would respond
to interventions. A precision CDS system for Alzheimer’s disease (AD), for
instance, should be able to _quantify_ the effect of treating a patient with a
given drug on the final outcome, e.g. predict the subsequent cognitive test
score. Even with the appropriate data and perfect performance, current ML
systems would predict the best treatment based only on previous correlations
in data, which may not represent _actionable_ information. Information is
defined as _actionable_ when it enables treatment (interventional) decisions
to be based on a comparison between different scenarios (e.g. outcomes for
treated vs not treated) for a given patient. Such systems need causal
inference (CI) in order to make actionable and individualised treatment effect
predictions (Bica et al., 2021).

A major upstream challenge in healthcare is how to acquire the necessary
information to causally reason about treatments and outcomes. Modern
healthcare data is multimodal, high-dimensional and often unstructured.
Information from medical images, genomics, clinical assessments, and
demographics must be taken into account when making predictions. A multimodal
approach better emulates how human experts use information to make
predictions. In addition, many diseases are progressive over time, thus
necessitating that time (the temporal dimension) is taken into account.
Finally, any system must ensure that these predictions will be generalisable
across deployment environments such as different hospitals, cities, or
countries.

Interestingly, it is the connection between causal inference and machine
learning that can help alleviate these challenges. ML allows causal models to
process high-dimensional and unstructured data by learning complex non-linear
relations between variables. CI adds an extra layer of understanding about a
system with expert knowledge, which improves information merging from
multimodal data, generalisation, and explainability of current ML systems.

The _causal machine learning_ (CML) literature offers several directions for
addressing the aforementioned challenges when using observational data. Here,
we categorise CML into three directions:  (i) Causal Representation Learning–
given high-dimensional data, learn to extract low-dimensional informative
(causal) variables and their causal relations;  (ii) Causal Discovery– given a
set of variables, learn the causal relationships between them; and  (iii)
Causal Reasoning– given a set of variables and their causal relationships,
analyse how a system will react to interventions.  These directions are
illustrated in Fig. 1.

In this paper, we discuss how CML can improve personalised decision making as
well as help to mitigate pressing challenges in clinical decision support
systems. We review representative methods for CML, explaining how they can be
used in a healthcare context. In particular, we  (i) present the concept of
causality and causal models;  (ii) show how they can be useful in healthcare
settings;  (iii) discuss pressing challenges; and  (iv) review potential
research directions from CML.

Figure 1: Causal machine learning in healthcare. Healthcare data is
multimodal, unstructured and high-dimensional. The research fronts within
causal machine learning (discussed in Section 5) can be further divided into
causal representation learning, causal discovery, and causal reasoning.

##  2 What is causality?

We use a broad definition of causality: if $A$ is a cause and $B$ is an
effect, then $B$ relies on $A$ for its value. As causal relations are
directional, the reverse is not true; $A$ does not rely on $B$ for its value.
The notion of _causality_ thus enables analysis of how a system would respond
to an _intervention_.

Questions such as “How will this disease progress if a patient is given
treatment X?” or “Would this patient still have experienced outcome Z if
treatment Y was received?” require methods from causality to understand how an
intervention would affect a specific individual. In a clinical environment,
causal reasoning can be useful for deciding which treatment will result in the
best outcome. For instance, in an AD scenario, causality can answer queries
such as “Which of drug $A$ or drug $B$ would best minimise the patient’s
expected cognitive decline within a 5 year time span?”. Ideally, we would
compare the outcomes of alternative treatments using observational
(historical) data. However, the “fundamental problem of causal inference”
(Holland, 1986) is that for each unit (i.e. patient) we can observe either the
result of treatment $A$ or of treatment $B$, but never both at the same time.
This is because after making a choice on a treatment, we cannot turn back time
to undo the treatment. These queries that entertain hypothetical scenarios
about individuals are called _potential outcomes_. Thus, we can observe only
one of the potential consequences of an action; the unobserved quantity
becomes a counterfactual. Causality’s mathematical formalism pioneered by
Judea Pearl (Pearl, 2009) and Donald Rubin (Imbens and Rubin, 2015) allows
these more challenging queries to be answered.

Most machine learning approaches are not (currently) able to identify cause
and effect, because causal inference is fundamentally impossible to achieve
without making assumptions (Pearl, 2009; Peters et al., 2017). Several of
these assumptions can be satisfied through study design or external contextual
knowledge, but none can be discovered solely from observational data.

Next, we introduce the reader to two ways of defining and reasoning about
causal relationships: with structural causal models and with potential
outcomes. We wrap up this section with an introduction to determining causal
relationships, including the use of randomised controlled trials.

###  2.1 Structural Causal Models

The mathematical formalism around the so-called do-calculus and _structural
causal models_ (SCMs) pioneered by the Turing Award winner Judea Pearl (Pearl,
2009) has allowed a graphical perspective to reasoning with data which heavily
relies on domain knowledge. This formalism can model the data generation
process and incorporate assumptions about a given problem. An intuitive and
historical description of causality can be found in Pearl and Mackenzie
(2018)’s recent book _The Book of Why_.

An SCM $\mathfrak{G}:=(\mathbf{S},P_{\boldsymbol{N}})$ consists of a
collection $\mathbf{S}=(f_{1},....,f_{K})$ of structural assignments (called
mechanisms)

$X_{k}:=f_{k}(\mathbf{PA}_{k},N_{k}),$ (1)

where $\mathbf{PA}_{k}$ is the set of parent variables of $X_{k}$ (its direct
causes) and $N_{k}$ is a noise variable for modeling uncertainty.
$\boldsymbol{N}=\\{N_{1},N_{2},...,N_{d}\\}$ is also referred to as
_exogenous_ noise because it represents variables that were not included in
the causal model, as opposed to the _endogenous_ variables
$\boldsymbol{X}=\\{X_{1},X_{2},...,X_{d}\\}$ which are considered known or at
least intended by design to be considered, and from which the set of parents
$Pa_{k}$ are drawn. This model can be defined as a direct acyclic graph (DAG)
in which the nodes are the variables and the edges are the causal mechanisms.
One might consider other graphical structures which incorporate cycles and
latent variables (Bongers et al., 2021), depending on the nature of the data.

It is important to note that the causal mechanisms are representations of
physical mechanisms that are present in the real world. Therefore, according
to the principle of _independent causal mechanisms_ (ICM), we assume that the
causal generative process of a system’s variables is composed of autonomous
modules that do not inform or influence each other (Peters et al., 2017;
Schölkopf et al., 2021). This means that exogenous variables $\boldsymbol{N}$
are mutually independent with the following joint distribution
$P(\boldsymbol{N})=\prod_{k=1}^{d}P(N_{k})$. Moreover, the joint distribution
over the endogenous variables $\boldsymbol{X}$ can be factorised as a product
of independent conditional mechanisms

$P_{\mathfrak{G}}(X_{1},X_{2},..,X_{K})=\prod_{k=1}^{K}P_{\mathfrak{G}}\left(X_{k}\mid\mathbf{PA}_{k}\right).$
(2)

The causal framework now allows us to go beyond  (i) associative predictions,
and begin to answer  (ii) interventional and  (iii) counterfactual  queries.
These three tasks are also known as Pearl’s causal hierarchy (Pearl and
Mackenzie, 2018). The _do-calculus_ introduces the notation $do(A)$, to denote
a system where we have _intervened_ to fix the value of $A$. This allows us to
sample from an interventional distribution
$P^{\mathfrak{G};do(...)}_{\boldsymbol{X}}$, which has the advantage over an
observational distribution $P^{\mathfrak{G}}_{\boldsymbol{X}}$ that the causal
structure enforces that only the descendants of the variable intervened upon
will be modified by a given action.

###  2.2 Potential Outcomes

An alternative approach to causal inference is the _potential outcomes_
framework proposed by Rubin (2005). In this framework, a response variable $Y$
is used to measure the effect of some cause or treatment for a patient, $i$.
The value of $Y$ may be affected by the treatment assigned to $i$. To enable
the treatment effect to be modelled, we represent the response with _two_
variables $Y_{i}^{(0)}$ and $Y_{i}^{(1)}$ which denote “untreated” and
“treated” respectively. The effect of the treatment on $i$ is then the
difference, $Y_{i}^{(1)}-Y_{i}^{(0)}$.

As a patient may _potentially_ be untreated or treated, we refer to
$Y_{i}^{(0)}$ and $Y_{i}^{(1)}$ as _potential outcomes_. It is, however,
impossible to observe both simultaneously, according to the previously
mentioned _fundamental problem of causal inference_ (Holland, 1986). This does
not mean that causal inference itself is impossible, but it does bring
challenges (Imbens and Rubin, 2015). Causal reasoning in the potential outcome
frameworks depends on obtaining an estimate for the joint probability
distribution, $P(Y^{(0)},Y^{(1)})$.

Both SCM and potential outcomes approaches have useful applications, and are
used where appropriate throughout this article. We note that single world
intervention graphs (Richardson and Robins, 2013) have been proposed as a way
to unify them.

###  2.3 Determining Cause and Effect

Determining causal relationships often requires carefully designed
experiments. There is a limit to how much can be learned using purely
observational data.

The effects of causes can be determined through prospective experiments to
observe an effect $E$ after a cause $C$ is tried or withheld, keeping constant
all other possible factors. It is hard, and in most cases impossible, to
control for all possible confounders of $C$ and $E$. The gold standard for
discovering a true causal effect is by performing a randomised controlled
trial (RCT), where the choice of $C$ is randomised, thus removing confounding.
For example, by randomly assigning a drug or a placebo to patients
participating in an interventional study, we can measure the effect of the
treatment, eliminating any bias that may have arisen in an observational study
due to other confounding variables, such as lifestyle factors, that influence
both the choice of using the drug and the impact of cognitive decline
(Mangialasche et al., 2010).

Note that the conditional probability $P(E\mid C)$ of observing $E$ after
observing $C$ can be different from the interventional probability $P(E\mid
do(C))$ of observing $E$ after doing / intervening on $C$. $P(E\mid do(C))$
means that only the descendants of $C$ (in a causal graph) change after an
intervention, all other variables maintain their values. In RCTs, the ‘$do$’
is guaranteed and unconditioned, while with observational data such as
historical Electronic Health Records (EHRs), it is not, due to the presence of
confounders.

Determining the causes of effects (the aetiology of diseases) requires
hypotheses and experimentation where interventions are performed and studied
to determine the necessary and sufficient conditions for an effect or disease
to occur.

##  3 Why should we consider a causal framework in healthcare?

Causal inference has made several contributions over the last few decades to
fields such as social sciences, econometrics, epidemiology, and aetiology
(Pearl, 2009; Imbens and Rubin, 2015), and it has recently spread to other
healthcare fields such as medical imaging (Castro et al., 2020; Pawlowski et
al., 2020; Reinhold et al., ) and pharmacology (Bica et al., 2021). In this
section, we will elaborate on how causality can be used for improving medical
decision making.

Even though data from EHRs, for example, are usually observational, they have
already been successfully leveraged in several machine learning applications
(Piccialli et al., 2021), such as modeling disease progression (Lim, 2018a),
predicting disease deterioration (Tomašev et al., 2019), and discovering risk
factors (McCauley and Darbar, 2016), as well as for predicting treatment
responses (Athreya et al., 2019). Further, we now have evidence of algorithms
which achieve superhuman performance in imaging tasks such as segmentation
(Isensee et al., 2021), detection of pathologies and classification (Korot et
al., 2021). However, predicting a disease with almost perfect accuracy for a
given patient is not what precision medicine is trying to achieve (Wilkinson
et al., 2020). Rather, we aim to build machine learning methods which extract
_actionable_ information from observational patient data in order to make
interventional (treatment) decisions. This requires _causal inference_ , which
goes beyond standard supervised learning methods for prediction as detailed
below.

In order to make actionable decisions at the patient level, one needs to
estimate the treatment effect. The treatment effect is the _difference_
between two potential outcomes: the _factual_ outcome and the _counterfactual_
outcome. For actionable predictions, we need algorithms that learn how to
reason about hypothetical scenarios in which different actions could have been
taken, creating, therefore, a decision boundary that can be navigated in order
to improve patient outcome. There is recent evidence that humans use
counterfactual reasoning to make causal judgements (Gerstenberg et al., 2021),
lending support to this reasoning hypothesis.

This is what makes the problem of inferring treatment effect fundamentally
different from standard supervised learning (Bica et al., 2021) as defined by
the potential outcome framework (Rubin, 2005; Imbens and Rubin, 2015). When
using observational datasets, by definition, we never observe the
counterfactual outcome. Therefore, the best treatment for an individual – the
main goal of precision medicine (Zhang et al., 2018) – can only be identified
with a model that is capable of causal reasoning as will be detailed in
Section 3.3.

###  3.1 Alzheimer’s Disease practical example

We now illustrate the notion of causal machine learning for healthcare with an
example from Alzheimer’s disease (AD). A recent attempt to understand AD from
a causal perspective (Shen et al., 2020; Uleman et al., 2020) takes into
account many biomarkers and uses domain knowledge (as opposed to RCTs) for
deriving ground truth causal relationships. In this section, we present a
simpler view with only three variables: chronological age111Age can otherwise
be measured in biological terms using, for instance, DNA methylation (Horvath,
2013)., magnetic resonance (MR) images of the brain, and Alzheimer’s disease
diagnosis. The diagnosis of Alzheimer’s disease is made by a clinician who
takes into account all available clinical information, including images. We
are particularly interested in MR images because analysing the relationship of
high-dimensional data such as medical images, is a task that can be more
easily handled with machine learning techniques, the main focus of this paper.

AD is a type of cognitive decline that generally appears later in life (Jack
et al., 2015). Alzheimer’s disease is associated with brain atrophy (Karas et
al., 2004; Qian et al., 2019) i.e. volumetric reduction of grey matter. We
consider that Alzheimer’s disease causes the symptom of brain morphology
change, following Richens et al. (2020), by arguing that a high-dimensional
variable such as the MR image is caused by the factors that generated it; this
modelling choice has been previously used in the causality literature
(Schölkopf et al., 2012; Kilbertus et al., 2018; Heinze-Deml and Meinshausen,
2021). Further, it is well established that atrophy also occurs during normal
ageing (Sullivan et al., 1995; Good et al., 2001). Time does not depend on any
biological variable, therefore chronological age cannot be caused by
Alzheimer’s disease nor any change in brain morphology. In this scenario, we
can assume that age is a confounder of brain morphology, measured by the MR
image, and Alzheimer’s disease diagnosis. These relationships are illustrated
in the causal graph in Fig. 2.

To model the effect of having age as a confounder of brain morphology and
Alzheimer’s disease, we use a conditional generative model from Xia et al.
(2021)222We take the model from Xia et al. (2021) and run new demonstrative
experiments for illustration in this paper., in which we condition on age and
Alzheimer’s disease diagnosis for brain MRI image generation. We then
synthesise images of a patient at different ages and with different
Alzheimer’s disease status as depicted in Fig. 2. In particular, we control
for (i.e. condition on) one variable while intervening on the other. That is,
we synthesise images based on a patient who is cognitively normal (CN) for
their age of 64 years. We then fix the Alzheimer’s status at CN and increase
the age by 3 years for 3 steps, resulting in images of the same CN patient at
ages 64, 67, 70, 73. At the same time, we synthesise images with different
Alzheimer’s status by fixing the age at 64 and changing the Alzheimer’s status
from mild cognitive impairment (MCI) to a clinical diagnosis of Alzheimer’s
disease (AD).

This example illustrates the effect of confounding bias. By observing
qualitatively the difference between the baseline and synthesised images, we
see that ageing and Alzheimer’s disease have similar effects on the
brain333See Xia et al. (2021) for quantitative results confirming this
hypothesis.. That is, that both variables change the volume of brain when
intervened on independently.

Throughout the paper, we will further add variables and causal links to this
example to illustrate how healthcare problems can become more complex and how
a causal approach might mitigate some of the main challenges. In particular,
we will build on this example by explaining some consequences of causal
modelling for dealing with high-dimensional and unstructured data,
generalisation and temporal information.

Figure 2: Causal graph (left) and illustration of how the brain changes in MR
images in response to interventions on “Age” or “Alzheimer’s disease status”.
The images are axial slices of a brain MR scan. The middle image used as a
baseline is from a patient aged 64 years old who is classified an cognitively
normal (CN) within the Alzheimer’s Disease Neuroimaging Initiative (ADNI)
database. All other images are synthesised with a conditional generative model
(Xia et al., 2021). The images with gray background are difference images
obtained by subtracting the synthesised image from the baseline. The upper
sequence of images is generated by fixing Alzheimer’s status at CN and
increasing age by 3 years. The bottom images are generated by fixing the age
at 64 and increasing Alzheimer’s status to MCI and AD, as discussed in the
main text.

###  3.2 Modeling the Data Generation Process

The Alzheimer’s disease example illustrates the importance of considering
causal relationships in a machine learning scenario. Namely, causality gives
the ability to model and identify types and sources of bias444we refer to
https://catalogofbias.org/biases for a catalogue of bias types. To correctly
identify which variables to control for (as means to mitigate confounding
bias), causal diagrams (Pearl, 2009) offer a direct means of visual
exploration and consequently explanation (Brookhart et al., 2010; Lederer et
al., 2019).

Castro et al. (2020) details further how understanding the causal generating
process can be useful in medical imaging. By representing the variables of a
particular problem and their causal relationships as a causal graph, one can
model _domain shifts_ such as population shift (different cohorts),
acquisition shift (different sites or scanners) and annotation shift
(different annotators), and data scarcity (imbalanced classes).

In the Alzheimer’s disease setting above, a classifier naively trained to
perform diagnosis from MR images of the brain might focus on the brain atrophy
alone. This classifier may show reduced performance in younger adults with
Alzheimer’s disease or for cognitively normal older adults, leading to
potentially incorrect diagnosis. To illustrate this, we report the results of
a convolutional neural network (CNN) classifier trained and tested on the ADNI
dataset following the same setting as Xia et al. (2022)555Although we
replicate results from Xia et al. (2022), this work does not constitute an
extension of the original paper. Rather, we use Xia et al. (2022) as an
example that illustrates how causality might impact standard machine
learning.. Table 1 shows that as feared, healthy older patients (80-90 years
old) are less accurately predicted because ageing itself causes the brain to
have Alzheimer’s-like patterns.

Table 1: Illustration of how a naively trained classifier (a neural network) fails when the data generation process and causal structure are not identified. We report the precision and recall on the test set when training a classifier for diagnosing AD. We stratify the results by age. We highlight that the group with  worse performance is the older cognitively normal patients due to the confounding bias described in the main text. After training with counterfactually augmented data, the classifier’s precision for the worse performance age group improved. These results were replicated from Xia et al. (2022). Age Range (years) | 60-70 | 70-80 | 80-90
---|---|---|---
| Precision | 87.7 | 91.4 | 75.5
Naive | Recall | 92.5 | 94.2 | 97.1
| Precision | 88.3 | 93.6 | 84.2
Counterfactually Augmented | Recall | 91.5 | 96.5 | 95.7

Indeed, using augmented data based on causal knowledge is a solution discussed
in Xia et al. (2022), whereby the training data are augmented with
counterfactual images of a patient when intervening on age. That is, images of
a patient at different ages (while controlling for Alzheimer’s status) are
synthesised so the classifier learns how to differentiate the effects of
ageing vs Alzheimer’s disease in brain images.

This causal knowledge enables the formulation of best strategies for
mitigating data bias(es) and improving generalisation (further detailed in
Section 4.3). For example, if after modeling the data distribution, an
acquisition shift becomes apparent (e.g. training data were obtained with a
specific MR sequence but the model will be evaluated on data from a different
sequence), then data augmentation strategies can be designed to increase
robustness of the learned representation. The acquisition shift – e.g.
different intensities due to different scanners – might be modeled according
to the physics of the (sensing) systems. Ultimately, creating a diagram of the
data generation process helps rationalise/visualise which are the best
strategies to solve the problem.

###  3.3 Treatment Effect and Precision Medicine

Figure 3: We illustrate the difference between individualised and average
treatment effect (ITE vs ATE). “Feature” represents patient characteristics,
which would be multi-dimensional in reality. “Outcome” is some measure of
response to the treatment, where a more positive value is preferable. The ITE
for each patient is the difference between actual and the counterfactual
outcome. We show an example counterfactual to highlight that ITE for some
patients might differ from the average (ATE). By employing causal inference
methods to estimate individualised treatment effects, we can understand which
patients benefit from certain medication and which patients do not, thus
enabling us to make personalised treatment recommendations. Note that the
patient data points are evenly distributed along the feature axis which would
indicate that this data comes from an RCT (due to lack of bias). The
estimation of treatment affect using observational data is subject to
confounding as patient characteristics effect both the selection of treatment
and outcome. Causal inference methods need to mitigate this.

Beyond diagnosis, a major challenge in healthcare is ascertaining whether a
given treatment influences an outcome. For a binary treatment decision, for
instance, the aim is to estimate the _average treatment effect_ (ATE),
$E[Y^{(1)}-Y^{(0)}]$ where $Y^{(1)}$ is the outcome given the treatment and
$Y^{(0)}$ is the outcome without it (control). As it is impossible to observe
both potential outcomes $Y^{(0)}$ and $Y_{i}^{(1)}$ for a given patient $i$,
this is typically estimated using $E[Y|T=1]-E[Y|T=0]$, where $T$ is the
treatment assignment.

The treatment assignment and outcomes, however, both depend on the patient’s
condition in normal clinical conditions. This results in confounding, which is
best mitigated by the use of an RCT 2.3. Performing an RCT as detailed in
Section 2.3, however, is not always feasible, and causal inference techniques
can be used to estimate the causal effect of treatment from observational data
(Meid et al., 2020). A number of assumptions need to hold in order for the
treatment effect to be identifiable from observational data (Lesko et al.,
2017; Imbens and Rubin, 2015). Conditional exchangeability (ignorability)
assumes there are no unmeasured confounders. Positivity (overlap) is the
assumption that every patient has a chance of receiving each treatment.
Consistency assumes that the treatment is defined unambiguously. Continuing
the Alzheimer’s example, Charpignon et al. (2021) explore drug re-purposing by
emulating an RCT with a target trial (Hernán and Robins, 2016) and find
indications that metformin (a drug classically used for diabetes) might
prevent dementia.

Note that even if the treatment effect is estimated using data from a well-
designed RCT, $E[Y\mid T=1]-E[Y\mid T=0]$ is the _average_ treatment effect
across the study population. However, there is evidence (Bica et al., 2021)
that for any given treatment, it is likely that only a small proportion of
subjects will actually respond in a manner that resembles the “average”
patient, as illustrated in Fig. 3. In other words, the treatment effect can be
highly heterogeneous across a population. The aim of _precision medicine_ is
to determine the best treatment for an _individual_ (Wilkinson et al., 2020),
rather than simply measuring the average response across a population. In
order to answer this question for a binary treatment decision, it is necessary
to estimate $\tau_{i}=Y_{i}(1)-Y_{i}(0)$ for a patient $i$. This is known as
the individualised treatment effect (ITE). As this estimation is performed
using a conditional average, this is also referred to as the conditional
average treatment effect (CATE) (Abrevaya et al., 2015).

A number of approaches have been proposed to learn conditional average
treatment effect from observational data, such as estimating treatment effect
with double machine learning (Chernozhukov et al., 2018; Semenova and
Chernozhukov, 2020). Another trend for estimating CATE are based on meta-
learners (Künzel et al., 2019; Curth and Schaar, 2021). In the meta-learning
setting, traditional (supervised) machine learning is used to predict the
conditional expectations of outcome for units under control and under
treatment separately. Then, CATE is done by taking the difference between the
estimates of these estimates. While most approaches concentrate on estimating
CATE using observational data, it is also possible to do so using data from an
RCT (Hoogland et al., 2021).

A long-term goal of precision medicine (Bica et al., 2021) includes
personalised risk assessment and prevention. Without a causal model to
distinguish these questions from simpler prediction systems, interpretational
mistakes will arise. In order to design more robust and effective machine
learning methods for personalised treatment recommendations, it is vital that
we gain a deeper theoretical understanding of the challenges and limitations
of modeling multiple treatment options, combinations, and treatment dosages
from observational data.

##  4 Causal machine learning for complex data

In Section 3, we focused on causal reasoning in situations where the causal
models are known (at least partially) and variables are well demarcated. We
refer the reader to Bica et al. (2021) for a comprehensive review on these
methods. Most healthcare problems, however, have challenges that are upstream
of causal reasoning. In this section, we highlight the need to deal with high-
dimensional and multimodal data as well as with temporal information and
discuss generalisation in out-of-distribution settings when learning from
unstructured data.

###  4.1 Multimodal Data

Alzheimer’s disease, in common with other major diseases such as diabetes and
cancer, has multiple causes arising from complex interactions between genetic
and environmental factors. Indeed, a recent attempt (Shen et al., 2020) to
build causal graphs for describing Alzheimer’s disease takes into account data
derived from several data sources and modalities, including patient
demographics, clinical measurements, genetic data, and imaging exams. Uleman
et al. (2020), in particular, creates a causal graph 666Interestingly, Uleman
et al. (2020) gather expert knowledge using a group model-building technique
(Vennix and Forrester, 1999) where multiple experts with complementary skills
create a graph based on their combined mental models and assumptions. with
clusters of nodes related to brain health, physical health, and psychosocial
health, illustrating the complexity of AD.

The above example illustrates that modern healthcare is multimodal. New ways
of measuring biomarkers are increasingly accessible and affordable, but
integrating this information is not trivial. Information from different
sources needs to be transformed to a space where information can be combined,
and the common information across modalities needs to be disentangled from the
unique information within each modality (Braman et al., 2021). This is
critical for developing CDS systems capable of integrating images, text and
genomics data.

On the other hand, the availability of more variables might mean that some
assumptions which are made in classical causal inference are more realistic.
In particular, most methods consider the assumption of _conditional
exchangeability_ (or causal _sufficiency_ (Spirtes et al., 2000)), as in
section 3 3.3. In practice, the conditional exchangeability assumption may
often not be true due to the presence of unmeasured confounders. However,
observing more variables might reduce the probability of this, rendering the
assumption more plausible.

###  4.2 Temporal Data

It is well known that a gene called apolipoprotein E (APOE) is associated with
an increased risk of AD (Zlokovic, 2013; Mishra et al., 2018). However,
environmental factors, such as education (Stern et al., 1994; Larsson et al.,
2017; Anderson et al., 2020), also have an impact on dementia. In other words,
environmental factors over time contribute to different disease trajectories
in Alzheimer’s disease. In addition, there are possible loops in the causal
diagram (Uleman et al., 2020). Wang and Holtzman (2019) illustrate, for
instance, a positive feedback loop between sleep and AD. That is, poor sleep
quality aggravates amyloid-beta and tau pathology concentrations, potentially
leading to neuronal dysfunction which, in turn, leads to worse sleep quality.
It is, therefore, important to consider data-driven approaches for
understanding and modeling the progression of disease over time (Oxtoby and
Alexander, 2017).

At the same time, using temporal information for inferring causation can be
traced back to one of the first definitions of causality by Hume (1904).
Quoting Hume: “we may define a cause to be an object followed by another, and
where all the objects, similar to the first, are followed by objects similar
to the second”. There are many strategies for incorporating time into causal
models since using SCMs with directed acyclic graphs (as defined in Section 2
2.1) is not enough in this context. A classical model of causality for time-
series was developed by Granger (1969). Granger considers $X\rightarrow Y$ if
past $X$ is predictive of future $Y$. Therefore, inferring causality from time
series data is at the core of CML. Bongers et al. (2021) shows that SCMs can
be defined with latent variables and cycles, allowing temporal relationships.
Early work has used temporal causal inference in neuroscience (Friston et al.,
2003), but the application of temporal causal inference in combination with
machine learning for understanding and dealing with complex disease remains
largely unexplored.

Managing diseases such as Alzheimer’s disease can be challenging due to the
heterogeneity of symptoms and their trajectory over time across the
population. A pathology might evolve differently for patients with different
covariates. For treatment decisions in a longitudinal setting, causal
inference methods need to model patient history and treatment timing
(Soleimani et al., 2017). Estimating trajectories under different possible
future treatment plans (interventions) is extremely important (Bica et al.,
2020). CDS systems need to take into account the current health state of the
patient, to make predictions about the potential outcomes for hypothetical
future treatment plans, to enable decision-makers to choose the sequence and
timing of treatments that will lead to the best patient outcome (Lim, 2018b;
Bica et al., 2020; Li et al., 2021).

###  4.3 Out-of-Distribution Generalisation with Unstructured and High-
Dimensional Data

The challenge of integrating different modalities and temporal information
increases when unstructured data is used. Most causality theory was originally
developed in the context of epidemiology, econometrics, social sciences, and
other fields wherein the variables of interest tend to be scalars (Pearl,
2009; Imbens and Rubin, 2015). In healthcare, however, the use of imaging
exams and free-text reports poses significant challenges for consistent and
robust extraction of meaningful information. The processing of unstructured
data is mostly tackled with machine learning, and _generalisation_ is one of
the biggest challenges for learning algorithms.

In its most basic form, generalisation is the ability to correctly categorise
new samples that differ from those used for training (Bishop and Nasrabadi,
2006). However, when learning from data, the notion of generalisation has many
facets. Here, we are interested in a realistic setting where the test data
distribution might be different from the training data distribution. This
setting is often referred as out-of-distribution (OOD) generalisation.
Distribution shifts are often caused by a change in environment (e.g.
different hospitals). We wish to present a causal perspective (Gong et al.,
2016; Rojas-Carulla et al., 2018; Meinshausen, 2018) on generalisation which
unifies many machine learning settings. Causal relationships are stable across
different environments (Cui and Athey, 2022). In a causal learning, the
prediction should be invariant to distribution shifts (Peters et al., 2016a).

As the use of machine learning in high impact domains becomes widespread, the
importance of evaluating safety has increased. A key aspect is evaluating how
robust a model is to changes in environment (or domain), which typically
requires applying the model to multiple independent datasets (Subbaswamy et
al., 2021). Since the cost of collecting such datasets is often prohibitive,
causal inference argues that providing structure (which comes from expert
knowledge) is essential for increasing robustness in real life (Pearl, 2009).

Imagine a prediction problem where the goal is to learn $P(Y|X)$, with the
causal graph illustrated in Fig. 4. We consider an environment variable $Env$
which controls the relationship between $Y$ and $W$. $Env$ is a confounder
$Y\leftarrow Env\rightarrow W$ and $X$ is caused by the two variables
$Y\rightarrow X\leftarrow W$.

Firstly, we consider the view that most prediction problems are in the anti-
causal direction (Schölkopf et al., 2012; Kilbertus et al., 2018; Heinze-Deml
and Meinshausen, 2021; Rosenfeld et al., 2021)777We note that other seminal
works (Peters et al., 2016b; Arjovsky et al., 2019) consider prediction a
causal task because prediction should copy a cognitive human process of
generating labels given the data.. That is, when making a prediction from a
high-dimensional, unstructured variable $X$ (e.g. a brain image) one is
usually interested in extracting and/or categorising one of its true
generating factors $Y$ (e.g. gray matter volume). $P(X|Y)$, which represents
the causal mechanism, $Y\rightarrow X$, is independent of $P(Y|Env)$, however
$P(Y|X)$ is not as $P(Y|X)=P(X|Y)P(Y|env)/P(X)$. Thus $P(Y|X)$ changes as the
environment changes.

Secondly, another (or many others) generating factor $W$ is often correlated
with $Y$, which might cause the predictor to learn the relationship between
$X$ and $W$ instead of the $P(Y|X)$. This is known as shortcut learning
(Geirhos et al., 2020) as it may be easier to learn the spurious correlation
than the required relationship. For example, suppose an imaging dataset $X$ is
collected from two hospitals, $Env_{1}$ and $Env_{2}$. Hospital $Env_{1}$ has
a large neurological disorder unit, hence a higher prevalence of AD status
(denoted by $Y$), and uses a 3T MRI scanner (scanner type denoted by $W$).
Hospital $Env_{2}$ with no specialist unit, hence a lower prevalence of AD,
happens to use a more common 1.5T MRI scanner. The model will learn the
spurious correlation between $W$ (scanner type) and $Y$ (AD status).

Figure 4: Reasoning about generalisation of a prediction task with a causal
graph. Anti-causal prediction and a spurious association that may lead to
shortcut learning are illustrated.

We can now describe several machine learning settings based on this causal
perspective by comparing data availability at train and test time. Classical
_supervised learning_ (or empirical risk minimisation (ERM) (Vapnik, 1999))
uses the strong assumption that the data from train and test sets are
_independent and identically distributed (i.i.d.)_ , therefore we assign the
same environment for both sets. _Semi-supervised learning_ (Chapelle et al.,
2009) is a case where part of the training samples are not paired to
annotations. _Continual (or Lifelong) learning_ considers the case where data
from different environments are added after training, and the challenge is to
learn new environments without forgetting what has initially been learned. In
domain adaptation, only unpaired data from the test environment is available
during training. Domain generalisation aims at learning how to become
invariant to changes of environment, such that a new (unseen in training data)
environment can be used for the test set. Enforcing fairness is important when
$W$ is a sensitive variable and the train set has $Y$ and $W$ spuriously888We
use the term spurious for features that correlate but do not have a causal
relationship between each other. correlated due to a choice of environment.
Finally, learning from imbalanced datasets can be seen under this causal
framework when a specific $Y=y$ have different numbers of samples because of
the environment, but the test environment might contain the same bias towards
a specific value of $Y$.

##  5 Research Directions in Causal Machine Learning

Having discussed the utility of CML for healthcare including complex
multimodal, temporal and unstructured data, the final section of this paper
discusses some future research directions. We discuss CML according to the
three categories defined in Section 1:  (i) Causal Representation Learning;
(ii) Causal Discovery; and  (iii) Causal Reasoning.

###  5.1 Causal Representations

Representation learning (Bengio et al., 2013) refers to a compositional view
of machine learning. Instead of a mapping between input and output domains, we
consider an intermediate representation that captures concepts about the
world. This notion is essential when considering learning and reasoning with
real healthcare data. High-dimensional and unstructured data, as considered in
Section 4 4.3, are not organised in units that can be directly used in current
causal models. In most situations, the variable of interest is not, for
instance, the image itself, but one of its generating factors, for instance
gray matter volume in the AD example.

_Causal_ representation learning (Schölkopf et al., 2021) extends the notion
of learning factors about the world to modelling the relationships between
variables with causal models. In other words, the goal is to model the
representation domain $\mathcal{Z}$ as an SCM as in Section 2 2.1. Causal
representation learning builds on top of the _disentangled_ representation
learning literature (Higgins et al., 2017; Chen et al., 2016; Liu et al.,
2021) towards enforcing stronger inductive bias as opposed to assumptions of
factor independence commonly pursued by disentangled representations. The idea
is to reinforce a hierarchy of latent variables following the causal model,
which in turn should follow the real data generation process.

###  5.2 Causal Discovery

Performing RCTs is very expensive and sometimes unethical or even impossible.
For instance, to understand the impact of smoking in lung cancer, it would be
necessary to force random individuals to smoke or not smoke. Most real data
are observational and discovering causal relationships between the variables
is more challenging. Considering a setting where the causal variables are
known, causal discovery is the task of learning the direction of causal
relationships between the variables. In some settings, we have many input
variables and the goal is to construct the graph structure that best describes
the data generation process.

Extensive background has been developed over the last 3 decades around
discovering causal structures from observational data, as described in recent
reviews of the subject (Peters et al., 2017; Glymour et al., 2019; Nogueira et
al., 2021; Vowels et al., 2021). Most methods rely on conditional independence
tests, combinatorial exploration over possible DAGs and/or assumptions about
the data generation process’ function class and noise distribution ( e.g. the
true causal relationships assumed to be linear, with additive noise or that
the exogenous noise has a Gaussian distribution) for finding the causal
relations of given causal variables.

Causal discovery is still an open area of research and some of the major
challenges in discovering causal effects Peters et al. (2017); Prosperi et al.
(2020) from observational data are the inability to  (i) identify all
potential sources of bias (unobserved confounders);  (ii) select an
appropriate functional form for all variables (model misspecification); and
(iii) model temporal causal relationships.

###  5.3 Causal Reasoning

It has been conjectured that humans internally build generative causal models
for imagining approximate physical mechanisms through intuitive theories
(Kilbertus et al., 2018). Similarly, the development of models that leverage
the power of causal models around interventions would be useful. The causal
models from Sections 2 2.1 and 2.2 can be formally manipulated for measuring
the effects of interventions. Using causal models for quantifying the effect
of interventions and pondering about the best decision is known as causal
reasoning.

Causal reasoning also refers to the ability to answer counterfactual queries
about historical situations, such as“What would have happened if the patient
had received alternative treatment X?”. We elaborated at length on the
benefits of counterfactuals in the healthcare context in Section 3 3.3.

One of the key benefits of reasoning causally about a problem domain is
transparency, by offering a clear and precise language to communicate
assumptions about the collected data (Chou et al., 2021; Rudin, 2019; Castro
et al., 2020) as detailed in Section 3 3.2. In a similar vein, models whose
architecture mirrors an assumed causal graph can be desirable in applications
where interpretability is important (Moraffah et al., 2020).

The main challenges in causal reasoning with ML relate to performing
interventions with complex data representations and functions. Strategies for
counterfactual prediction are simpler with scalar variables and linear
functions. Interventions can have qualitatively distinct behaviours and should
be understood as acting on high-level features rather than purely on the raw
data. However, estimating counterfactuals in image features (Pawlowski et al.,
2020; Sanchez and Tsaftaris, 2022), for example, requires invertible
mechanisms such as normalising flows (Papamakarios et al., 2019) and/or
methods for variational inference (Kingma and Welling, 2014) which have their
own complexities. Another open problem is how to deal with multimodal data
e.g. images, text, age, sex and genetic data in a healthcare scenario as
detailed in Section 4 4.1.

##  6 Conclusion

We have described the importance of considering causal machine learning in
healthcare systems. We highlighted the need to design systems that take into
account the data generation process. A causal perspective on machine learning
contributes to the goal of building systems that are not just performing
better (e.g. achiever higher accuracy), but are able to reason about potential
effects of interventions at population and individual levels, closing the gap
towards realising precision medicine.

We have discussed key pressing challenges in precision medicine and
healthcare, namely, utilising multi-modal, high-dimensional and unstructured
data to make decisions that are generalisable across environments and take
into account temporal information. We finally proposed opportunities drawing
inspiration from causal representation learning, causal discovery and causal
reasoning towards addressing these challenges.

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