Causal Machine Learning for Healthcare and Precision Medicine

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.

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.

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)

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

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 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.

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.

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.

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 ageAge 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)We 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 brainSee 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.

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 biaswe 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)Although 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.

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 Treatment Effect and Precision Medicine

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.

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.

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 Interestingly, 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.

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).

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)We 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).

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 $W$ spuriouslyWe 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 $Y$.

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.

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.

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.

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.

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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