van der Schaar Lab

Time series in healthcare: challenges and solutions

The transformation of healthcare through machine learning depends heavily on the successful application of time series data to model longitudinal trajectories for health and disease. As explained below, this is an extremely challenging undertaking that has arguably received insufficient consideration to date.

This page showcases our lab’s work in developing machine learning models for a wide range of purposes across the time series setting. It is a living document, the content of which will evolve as we continue to develop approaches and build a vision for this new research area.

This page is authored and maintained by Mihaela van der Schaar and Nick Maxfield.


On July 24, 2021, Mihaela van der Schaar gave an invited talk entitled “Time-series in healthcare: challenges and solutions” as part of the ICML 2021 Time Series Workshop.

The full talk can be found below, and is highly recommended viewing for anyone who would like to know more about building models for time series in machine learning for healthcare.

Time series: the backbone of bespoke medicine

Time series datasets such as electronic health records (EHR) and registries represent valuable (but imperfect) sources of information spanning a patient’s entire lifetime of care. Whether intentionally or not, they capture genetic and lifestyle risks, signal the onset of diseases, show the advent of new morbidities and comorbidities, indicate the time and stage of diagnosis, and document the development of treatment plans, as well as their efficacy.

Using patient data generated at each of these points in the pathway of care, we can develop machine learning models that give us a much deeper and more interconnected understanding of individual trajectories of health and disease—including the number of states needed to provide an accurate representation of a disease, how to infer a patient’s current state, what triggers transitions from one state to another, and much more.

Our own lab, for example, has used time series datasets to produce new discoveries and a develop understanding of progression and clinical trajectories across a wide range of diseases, including cancer, cystic fibrosis, Alzheimer’s, cardiovascular disease and COVID-19, as well as within specific settings such as intensive care.

Armed with a fully quantitative and scientific understanding of the progression of multiple diseases over time, we can unlock the full capabilities of machine learning to create long-term comprehensive patient management programs that evolve with each individual’s changing context and history and consider not only a single risk but multiple risks (and the evolution of such risks over time).

This kind of truly personalized end-to-end medical care is what our lab refers to as bespoke medicine. Whereas current approaches to precision or personalized medicine tend to fit the patient to a pattern (based, for example, on genetic information), bespoke medicine seeks to recognize and adapt to changes in patterns caused by age, lifestyle changes, onset of new conditions, and progress in the course of treatment.

The multi-faceted nature of time series

The development of models for time series is a complex, hard-to-define research task that touches every other area of machine learning for healthcare—including dynamic forecasting, survival analysis, clustering and phenotyping, screening and monitoring, early diagnosis, and treatment effect estimation.

Navigate directly to one of these areas:

It may be tempting to try to simplify this complexity by positioning time series as merely a dimension of all other areas within machine learning for healthcare, rather than as a research domain in its own right. Such a prospect would perhaps make sense if static models for healthcare could be readily and uniformly “upgraded” to dynamic versions capable of meaningfully incorporating time series data, regardless of the clinical problem at hand. In reality, as the many examples given below will demonstrate, this is not the case.

Static and dynamic models are fundamentally different animals, and the problems we aim to solve in healthcare are so diverse that there is no single approach to making them all work with time series data. We cannot, therefore, treat time series as a dimension of all kinds of healthcare problems.

Additionally, there are some model development challenges that are unique to the time series setting, and these further justify the treatment of time series as a domain of research in its own right. These challenges (some of which which are shown at the bottom of the figure below and explored on this page) are generally related to the need to ensure that the outputs of models are actionable, informative, and reliable.

Navigate directly to one of these areas:

Tailoring development of time series models to healthcare challenges

In the section below, we will introduce a number of problems in healthcare, and highlight the distinct challenges they present when developing machine learning models for time series.

Forecasting disease trajectories

Chronic diseases such as cardiovascular disease, cancer, and diabetes progress slowly throughout a patient’s lifetime. This progression can be segmented into “stages” that that manifest through clinical observations. A growing area in precision medicine is the forecasting of personalized disease trajectories using patterns in temporal correlations and associations between related diseases.

Our aim here is to build disease progression models from electronic health records and other informative datasets, to learn the model parameters at training time, and then to issue personalized dynamic forecasts. In addition to providing accurate forecasts for the patient at hand, we should be able to make new discoveries regarding disease progression mechanisms at the population level, at the sub-group level, and at the personalized level.

Dynamic forecasting in the time series setting presents an array of unique challenges. For example, we must work with multiple streams of measurement that are often sparse and irregularly (and informatively) sampled. It is also necessary to forecast multiple outcomes rather than a single outcome, and these outcomes themselves may change over time since patients with one chronic disease typically develop other long-term conditions. An additional challenge lies in the fact that true clinical states tend to be inherently unobservable—the timing of diagnosis, for example, may not reliably indicate the timing of disease onset. Furthermore, it is important to factor in the heterogeneity of patients, which may lead to many possible patterns from which to learn.

The figure above illustrates how understandng of disease stages and progression can be used to predict likelihood of onset of comorbidities. This example shows a machine learning model’s learned representation of 3 progression stages for cystic fibrosis. The left-hand side shows the estimated mean of the emission distribution for the forced expiratory volume (FEV1) biomarker in each stage. The right-hand side plots the risks of various comorbidities (diabetes, asthma, ABPA, hypertension and depression) for patients in the 3 progression stages.

One of our lab’s approaches aiming to overcome such limitations is attentive state-space modeling (ASSM), first introduced in a paper published at NeurIPS 2019. ASSM was developed to learn accurate and interpretable structured representations for disease trajectories, and offers a deep probabilistic model of disease progression that capitalizes on both the interpretable structured representations of probabilistic models and the predictive strength of deep learning methods.

Unlike conventional Markovian state-space models, ASSM uses recurrent neural networks (RNNs) to capture more complex state dynamics. Since it learns hidden disease states from observational data in an unsupervised fashion, ASSM is well-suited to EHR data, where a patient’s record is seldom annotated with “labels” indicating their true health state.

As implied by the name, ASSM captures state dynamics through an attention mechanism, which observes the patient’s clinical history and maps it to attention weights that determine how much influence previous disease states have on future state transitions. In that sense, attention weights generated for an individual patient explain the causative and associative relationships between the hidden disease states and the past clinical events for that patient.

ASSM also features a structured inference network trained to predict posterior state distributions by mimicking the attentive structure of our model. The inference network shares attention weights with the generative model, and uses those weights to create summary statistics needed for posterior state inference.

To the best of our knowledge, ASSM is the first deep probabilistic model that provides clinically meaningful latent representations, with non-Markovian state dynamics that can be made arbitrarily complex while remaining interpretable.

Attentive state-space modeling of disease progression

Ahmed Alaa, Mihaela van der Schaar

NeurIPS 2019

Models of disease progression are instrumental for predicting patient outcomes and understanding disease dynamics. Existing models provide the patient with pragmatic (supervised) predictions of risk, but do not provide the clinician with intelligible (unsupervised) representations of disease pathophysiology.

In this paper, we develop the attentive state-space model, a deep probabilistic model that learns accurate and interpretable structured representations for disease trajectories. Unlike Markovian state-space models, in which the dynamics are memoryless, our model uses an attention mechanism to create “memoryful” dynamics, whereby attention weights determine the dependence of future disease states on past medical history.

To learn the model parameters from medical records, we develop an infer ence algorithm that simultaneously learns a compiled inference network and the model parameters, leveraging the attentive state-space representation to construct a “Rao-Blackwellized” variational approximation of the posterior state distribution.

Experiments on data from the UK Cystic Fibrosis registry show that our model demonstrates superior predictive accuracy and provides insights into the progression of chronic disease.

Time-to-event and survival analysis

Survival analysis (often referred to as time-to-event analysis) refers to the study of the duration until one or more events occur. This is vital to a great many predictive tasks across numerous fields of application, including economics, finance, and engineering—and, of course, healthcare.

In the medical setting, survival analysis is often applied to the discovery of risk factors affecting survival, comparison among risks of different subjects at a certain time of interest, and decisions related to cost-efficient acquisition of information (e.g. screening for cancer). Specifically, our goal is to dynamically estimate the probability of occurrence of various types of future events happening at a particular time in the future, while taking competing risks into account.

To do this, it is essential to incorporate longitudinal measurements of biomarkers and risk factors into a model. Rather than discarding valuable information recorded over time, this allows us to make better risk assessments on the clinical events. This is why our lab developed Dynamic-DeepHit, a novel architecture presented in IEEE Transactions on Biomedical Engineering in 2019.

While inheriting the neural network structure of its predecessor DeepHit (introduced in a paper published at AAAI 2018) and maintaining the ability to handle competing risks, Dynamic-DeepHit learns, on the basis of the available longitudinal measurements, a data-driven distribution of first event times of competing events. This completely removes the need for explicit model specifications (i.e., no assumptions about the form of the underlying stochastic processes are made) and enables us to learn the complex relationships between trajectories and survival probabilities.

As shown above, Dynamic-DeepHit updates its survival predictions (presented as cumulative incidence functions) as new observations are collected over time.

Gray solid lines, yellow dotted lines, and stars indicate times at which measurement are taken, the time at which a patient is censored, and the time at which an event occurred, respectively.

A temporal attention mechanism is employed in the hidden states of the RNN structure when constructing the context vector. This allows Dynamic-DeepHit to access the necessary information, which has progressed along with the trajectory of the past longitudinal measurements, by paying attention to relevant hidden states across different time stamps. The cause-specific subnetworks then take the context vector and the last measurements as an input, and estimate the joint distribution of the first event time and competing events, which are used for further risk predictions.

Dynamic-DeepHit: a deep learning approach for dynamic survival analysis with competing risks
based on longitudinal data

Changhee Lee, Jinsung Yoon, Mihaela van der Schaar

IEEE Transactions on Biomedical Engineering, 2019

Currently available risk prediction methods are limited in their ability to deal with complex, heterogeneous, and longitudinal data such as that available in primary care records, or in their ability to deal with multiple competing risks.

This paper develops a novel deep learning approach that is able to successfully address current limitations of standard statistical approaches such as land marking and joint modeling. Our approach, which we call Dynamic-DeepHit, flexibly incorporates the available longitudinal data comprising various repeated measurements (rather than only the last available measurements) in order to issue dynamically updated survival predictions for one or multiple competing risk(s).

Dynamic-DeepHit learns the time-to-event distributions without the need to make any assumptions about the underlying stochastic models for the longitudinal and the time-to-event processes. Thus, unlike existing works in statistics, our method is able to learn data-driven associations between the longitudinal data and the various associated risks without underlying model specifications.

We demonstrate the power of our approach by applying it to a real-world longitudinal dataset from the U.K. Cystic Fibrosis Registry, which includes a heterogeneous cohort of 5883 adult patients with annual follow-ups between 2009 to 2015. The results show that Dynamic-DeepHit provides a drastic improvement in discriminating individual risks of different forms of failures due to cystic fibrosis.

Furthermore, our analysis utilizes post-processing statistics that provide clinical insight by measuring the influence of each covariate on risk predictions and the temporal importance of longitudinal measurements, thereby enabling us to identify covariates that are influential for different competing risks.

Additionally, on a paper published in ACM Transactions on Computing for Healthcare in 2020, our lab presented Bayesian nonparametric dynamic survival (BNDS), a model capable of 1) quantifying the uncertainty around model predictions in a principled manner at the individual level while 2) avoiding making assumptions on the data generating process and adapting model complexity to the structure of the data. Both contributions are particularly important for personalizing health care decisions, as predictions may be uncertain due to lack of data, whereas we can expect the underlying heterogeneous physiological time series to vary wildly across patients.

BNDS can use sparse longitudinal data to give personalized survival predictions that are updated as new information is recorded. Our approach has the advantage of not imposing any constraints on the data generating process, which, together with novel postprocessing statistics, expands the capabilities of current methods.

Flexible modelling of longitudinal medical data: a Bayesian nonparametric approach

Alexis Bellot, Mihaela van der Schaar

ACM Transactions on Computing for Healthcare, 2020

Using electronic medical records to learn personalized risk trajectories poses significant challenges because often very few samples are available in a patient’s history, and, when available, their information content is highly diverse.

In this article, we consider how to integrate sparsely sampled longitudinal data, missing measurements informative of the underlying health status, and static information to estimate (dynamically, as new information becomes available) personalized survival distributions.

We achieve this by developing a nonparametric probabilistic model that generates survival trajectories, and corresponding uncertainty estimates, from an ensemble of Bayesian trees in which time is incorporated explicitly to learn variable interactions over time, without needing to specify the longitudinal process beforehand. As such, the changing influence on survival of variables over time is inferred from the data directly, which we analyze with post-processing statistics derived from our model.

We study the problem of personalizing survival estimates of patients in heterogeneous populations for clinical decision support. The desiderata are to improve predictions by making them personalized to the patient-at-hand, to better understand diseases and their risk factors, and to provide interpretable model outputs to clinicians.

To enable accurate survival prognosis in heterogeneous populations we propose a novel probabilistic survival model which flexibly captures individual traits through a hierarchical latent variable formulation. Survival paths are estimated by jointly sampling the location and shape of the individual survival distribution resulting in patient-specific curves with quantifiable uncertainty estimates. An understanding of model predictions is paramount in medical practice where decisions have major social consequences.

We develop a personalized interpreter that can be used to test the effect of covariates on each individual patient, in contrast to traditional methods that focus on population average effects.

We extensively validated the proposed approach in various clinical settings, with a special focus on cardiovascular disease.

To learn more about our lab’s research in the area of survival analysis, competing risks, and comorbidities, click here.

Clustering and phenotyping

Phenotyping and identifying subgroups of patients are important challenges that become particularly complicated in a dynamic setting where longitudinal datasets are in use. At present, the conventional notion of clustering and phenotyping examines similarities in time series observations, clustering patients together based on the observations about them to date.

However, this type of clustering yields information that is of relatively limited use to clinicians and patients—after all, chronic diseases such as cystic fibrosis and dementia are heterogeneous in nature, with widely differing outcomes, even in narrow patient subgroups.

What clinicians and patients actually need to know is what types of events (including events related to competing risks) will likely occur in the future. We are, therefore, interested in a type of clustering or phenotyping over time in which patients are grouped based on similarity of future outcomes, rather than on similarity of observations.

Identifying patient subgroups with similar progression patterns can be advantageous for understanding such heterogeneous diseases. This allows clinicians to anticipate patients’ prognoses by comparing them to “similar” patients, and to design treatment guidelines tailored to homogeneous subgroups.

Our lab has developed a method for temporal phenotyping in this manner using deep predictive clustering of disease progression, as presented at ICML 2020. This provides a notion of temporal phenotyping that is predictive of similar future outcomes, on the basis of which doctors and patients can actively plan. The focus here is on learning discrete representations of past observations that best describe and predict future events and outcomes of interest.

Temporal phenotyping using deep predictive clustering of disease progression

Changhee Lee, Mihaela van der Schaar

ICML 2020

Due to the wider availability of modern electronic health records, patient care data is often being stored in the form of time-series. Clustering such time-series data is crucial for patient phenotyping, anticipating patients’ prognoses by identifying “similar” patients, and designing treatment guidelines that are tailored to homogeneous patient subgroups.

In this paper, we develop a deep learning approach for clustering time-series data, where each cluster comprises patients who share similar future outcomes of interest (e.g., adverse events, the onset of comorbidities). To encourage each cluster to have homogeneous future outcomes, the clustering is carried out by learning discrete representations that best describe the future outcome distribution based on novel loss functions.

Experiments on two real-world datasets show that our model achieves superior clustering performance over state-of-the-art benchmarks and identifies meaningful clusters that can be translated into actionable information for clinical decision-making.

Chronic diseases evolve slowly throughout a patient’s lifetime creating heterogeneous progression patterns that make clinical outcomes remarkably varied across individual patients. A tool capable of identifying temporal phenotypes based on the patients’ different progression patterns and clinical outcomes would allow clinicians to better forecast disease progression by recognizing a group of similar past patients, and to better design treatment guidelines that are tailored to specific phenotypes.

To build such a tool, we propose a deep learning approach, which we refer to as outcome-oriented deep temporal phenotyping (ODTP), to identify temporal phenotypes of disease progression considering what type of clinical outcomes will occur and when based on the longitudinal observations. More specifically, we model clinical outcomes throughout a patient’s longitudinal observations via time-to-event (TTE) processes whose conditional intensity functions are estimated as non-linear functions using a recurrent neural network. Temporal phenotyping of disease progression is carried out by our novel loss function that is specifically designed to learn discrete latent representations that best characterize the underlying TTE processes.

The key insight here is that learning such discrete representations groups progression patterns considering the similarity in expected clinical outcomes, and thus naturally provides outcome-oriented temporal phenotypes.

We demonstrate the power of ODTP by applying it to a real-world heterogeneous cohort of 11,779 stage III breast cancer patients from the UK National Cancer Registration and Analysis Service. The experiments show that ODTP identifies temporal phenotypes that are strongly associated with the future clinical outcomes and achieves significant gain on the homogeneity and heterogeneity measures over existing methods.

Furthermore, we are able to identify the key driving factors that lead to transitions between phenotypes which can be translated into actionable information to support better clinical decision-making.

Screening and monitoring

At the core of the problem of screening and monitoring are multiple questions related to determining, for each individual, what kind of clinical information to acquire, when to begin acquiring it, how frequently to do so, and the means by which this information should be acquired.

Our objective here is to move from a one-size-fits-all screening and monitoring setting into a personalized setting. We must consider that monitoring and screening are costly, both from a monetary perspective and from the perspective of the patient (as certain forms of screening may be incur detrimental side-effects). Accordingly, we require tools that can optimally balance the benefit of acquiring specific information for each individual at a particular time against the cost of acquiring that information.

This is a challenging undertaking, however, since the value of information is unknown and changes dynamically when we are working in the time series setting; this needs to be learned on the basis of the available data.

To solve this problem, our lab developed a deep learning architecture called Deep Sensing, which was first introduced in a paper for ICLR 2018. At training time, Deep Sensing uses a neural network to learn how to build predictions at various cost-performance points. In doing so, we can create multiple representations associated with different measurements and costs. These are learned recursively and adaptively by introducing missing data at different points in time, letting us model the different cost-benefit trade-offs for different classes of patients and (by extension) the value of information over time as the patient progresses. At runtime, the operator prescribes a performance level or a cost constraint, and Deep Sensing determines what measurements to take and what to infer from those measurements, and then issues predictions.

Deep Sensing: Active Sensing using Multi-directional Recurrent Neural Networks

Jinsung Yoon, William R. Zame, Mihaela van der Schaar

ICLR 2018

For every prediction we might wish to make, we must decide what to observe (what source of information) and when to observe it. Because making observations is costly, this decision must trade off the value of information against the cost of observation. Making observations (sensing) should be an active choice.

To solve the problem of active sensing we develop a novel deep learning architecture: Deep Sensing. At training time, Deep Sensing learns how to issue predictions at various cost-performance points. To do this, it creates multiple representations at various performance levels associated with different measurement rates (costs). This requires learning how to estimate the value of real measurements vs. inferred measurements, which in turn requires learning how to infer missing (unobserved) measurements.

To infer missing measurements, we develop a Multi-directional Recurrent Neural Network (M-RNN). An M-RNN differs from a bi-directional RNN in that it sequentially operates across streams in addition to within streams, and because the timing of inputs into the hidden layers is both lagged and advanced. At runtime, the operator prescribes a performance level or a cost constraint, and Deep Sensing determines what measurements to take and what to infer from those measurements, and then issues predictions.

To demonstrate the power of our method, we apply it to two real-world medical datasets with significantly improved performance.

A number of other papers to consider in this area are listed below.

ASAC: Active Sensing using Actor-Critic models

Jinsung Yoon, James Jordon, Mihaela van der Schaar

Machine Learning for Healthcare (MLHC) 2019

Deciding what and when to observe is critical when making observations is costly. In a medical setting where observations can be made sequentially , making these observations (or not) should be an active choice. We refer to this as the active sensing problem.

In this paper, we propose a novel deep learning framework, which we call ASAC (Active Sensing using Actor-Critic models) to address this problem. ASAC consists of two networks: a selector network and a predictor network. The selector network uses previously selected observations to determine what should be observed in the future. The predictor network uses the observations selected by the selector network to predict a label, providing feedback to the selector network (well-selected variables should be predictive of the label). The goal of the selector network is then to select variables that balance the cost of observing the selected variables with their predictive power; we wish to preserve the conditional label distribution.

During training, we use the actor-critic models to allow the loss of the selector to be “back-propagated” through the sampling process. The selector network “acts” by selecting future observations to make. The predictor network acts as a “critic” by feeding predictive errors for the selected variables back to the selector network.

In our experiments, we show that ASAC significantly outperforms state-of-the-arts in two real-world medical datasets.

ConfidentCare: A Clinical Decision Support System for Personalized Breast Cancer Screening

Ahmed Alaa, Kyeong Moon, William Hsu, Mihaela van der Schaar

IEEE Transactions on Multimedia, 2016

Breast cancer screening policies attempt to achieve timely diagnosis by regularly screening healthy women via various imaging tests. Various clinical decisions are needed to manage the screening process: selecting initial screening tests, interpreting test results, and deciding if further diagnostic tests are required.

Current screening policies are guided by clinical practice guidelines (CPGs), which represent a “one-size-fits-all” approach, designed to work well (on average) for a population, and can only offer coarse expert-based patient stratification that is not rigorously validated through data. Since the risks and benefits of screening tests are functions of each patient’s features,personalized screening policies tailored to the features of individuals are desirable.

To address this issue, we developed ConfidentCare: a computer-aided clinical decision support system that learns a personalized screening policy from electronic health record (EHR) data. By a “personalized screening policy,” we mean a clustering of women’s features, and a set of customized screening guidelines for each cluster. ConfidentCare operates by computing clusters of patients with similar features, then learning the “best” screening procedure for each cluster using a supervised learning algorithm. The algorithm ensures that the learned screening policy satisfies a predefined accuracy requirement with a high level of confidence for every cluster.

By applying ConfidentCare to real-world data, we show that it outperforms the current CPGs in terms of cost efficiency and false positive rates: a reduction of 31% in the false positive rate can be achieved.

Disease-Atlas: Navigating Disease Trajectories using Deep Learning

Bryan Lim, Mihaela van der Schaar

MLHC 2018

Joint models for longitudinal and time-to-event data are commonly used in longitudinal studies to forecast disease trajectories over time. While there are many advantages to joint modeling, the standard forms suffer from limitations that arise from a fixed model specification, and computational difficulties when applied to high-dimensional datasets.

In this paper, we propose a deep learning approach to address these limitations, enhancing existing methods with the inherent flexibility and scalability of deep neural networks, while retaining the benefits of joint modeling.

Using longitudinal data from a real-world medical dataset, we demonstrate improvements in performance and scalability, as well as robustness in the presence of irregularly sampled data.

Early diagnosis

The ability to identify a disease such as breast cancer early in a patient can lead to better and more effective treatment, potentially saving lives. Since diagnosis is the practice of inferring a patient’s current disease state, diagnosing any disease early requires us to correctly understand and characterize the staging and likely trajectory of that disease.

This is only possible, however, if we already possess a thorough understanding of disease trajectories gained from time series data. It is crucial, for example, to determine how many stages of disease exist per disease, how individuals may progress through disease stages differently, the triggers for transitions between stages, and how long individuals may stay in stages. Armed with such understanding, we can successfully predict and diagnose disease early on the basis of changing patient characteristics, symptoms, and morbidities.

Using approaches such as the attentive state-space model (ASSM) introduced above, we can learn the trajectories of diseases, as well as the symptoms and morbidities that are likely to precede diagnosis. This can then be used to build dynamic forecasting models that are personalized and interpretable, and provide more accurate and effective screening and diagnosis. Another relevant approach in this regard is the hidden absorbing semi-Markov model, introduced by our lab in a paper published in the Journal of Machine Learning Research in 2018.

A Hidden Absorbing Semi-Markov Model for Informatively Censored Temporal Data: Learning and Inference

Ahmed Alaa, Mihaela van der Schaar

JMLR, 2018

Modeling continuous-time physiological processes that manifest a patient’s evolving clinical states is a key step in approaching many problems in healthcare.

In this paper, we develop the Hidden Absorbing Semi-Markov Model (HASMM): a versatile probabilistic model that is capable of capturing the modern electronic health record (EHR) data. Unlike existing models, the HASMM accommodates irregularly sampled, temporally correlated, and informatively censored physiological data, and can describe non-stationary clinical state transitions.

Learning the HASMM parameters from the EHR data is achieved via a novel forward-filtering backward-sampling Monte-Carlo EM algorithm that exploits the knowledge of the end-point clinical outcomes (informative censoring) in the EHR data, and implements the E-step by sequentially sampling the patients’ clinical states in the reverse-time direction while conditioning on the future states. Real-time inferences are drawn via a forward-filtering algorithm that operates on a virtually constructed discrete-time embedded Markov chain that mirrors the patient’s continuous-time state trajectory.

We demonstrate the prognostic utility of the HASMM in a critical care prognosis setting using a real-world dataset for patients admitted to the Ronald Reagan UCLA Medical Center. In particular, we show that using HASMMs, a patient’s clinical deterioration can be predicted 8-9 hours prior to intensive care unit admission, with a 22%% AUC gain compared to the Rothman index, which is the state-of-the-art critical care risk scoring technology.

Treatment effects

A major challenge in the domain of healthcare is ascertaining whether a given treatment influences or determines an outcome—for instance, whether there is a survival benefit to prescribing a certain medication, such as the ability of a statin to lower the risk of cardiovascular disease.

Our goal is to use machine learning to estimate the effect of a treatment on an individual using observational data. Observational datasets contain valuable information on complex time-dependent treatment scenarios, such as where the efficacy of treatments changes over time (for example, drug resistance in cancer patients), or where patients receive multiple interventions administered at different points in time (such as joint prescriptions of chemotherapy and radiotherapy)

Estimating the effects of treatments over time therefore offers unique opportunities, such as understanding how diseases evolve under different treatment plans, how individual patients respond to medication over time, and which timings may be optimal for assigning treatments, thus providing new tools to improve clinical decision support systems.

This is very challenging in the time series setting, due to the need to deal with time-dependent confounders (i.e., patient covariates that affect the treatment assignments and are themselves affected by past treatments) which bias the treatment assignment in the observational dataset.

In a NeurIPS 2018 paper entitled “Forecasting Treatment Responses Over Time Using Recurrent Marginal Structural Networks,” we proposed a new deep learning model, which we refer to as recurrent marginal structural networks (RMSN). Drawing inspiration from marginal structural models, a class of methods in epidemiology which use propensity weighting to adjust for time dependent confounders, RMSN adopts a sequence to-sequence architecture to directly learn time-dependent treatment responses from observational data.

We used two sets of deep neural networks to build our RMSN: 1) a set propensity network to compute treatment probabilities for inverse probability of treatment weighting, and 2) a prediction network used to determine the treatment response for a given set of planned interventions.

Using simulations of a state-of-the-art pharmacokinetic pharmacodynamic (PK-PD) model of tumor growth, we demonstrated the ability of our network to accurately learn unbiased treatment responses from observational data—even under changes in the policy of treatment assignments—and performance gains over benchmarks.

Forecasting Treatment Responses Over Time Using Recurrent Marginal Structural Networks

Bryan Lim, Ahmed Alaa, Mihaela van der Schaar

NeurIPS 2018

Electronic health records provide a rich source of data for machine learning methods to learn dynamic treatment responses over time. However, any direct estimation is hampered by the presence of time-dependent confounding, where actions taken are dependent on time-varying variables related to the outcome of interest.

Drawing inspiration from marginal structural models, a class of methods in epidemiology which use propensity weighting to adjust for time-dependent confounders, we introduce the Recurrent Marginal Structural Network – a sequence-to-sequence architecture for forecasting a patient’s expected response to a series of planned treatments.

Using simulations of a state-of-the-art pharmacokinetic-pharmacodynamic (PK-PD) model of tumor growth, we demonstrate the ability of our network to accurately learn unbiased treatment responses from observational data – even under changes in the policy of treatment assignments – and performance gains over benchmarks.

In an ICLR 2020 paper entitled “Estimating counterfactual treatment outcomes over time through adversarially balanced representations,” we introduced the Counterfactual Recurrent Network (CRN), a novel sequence-to-sequence model that leverages the increasing availability of patient observational data, as well as recent advances in representation learning and domain adversarial training, to estimate treatment effects over time.

To handle the bias from time varying confounders, CRN uses domain adversarial training to build balancing representations of the patient history. At each timestep, CRN constructs a treatment invariant representation which removes the association between patient history and treatment assignments and thus can be reliably used for making counterfactual predictions.

Using a model of tumor growth, we validated CRN in realistic medical scenarios, demonstrating that, when compared with existing state-of-the-art methods, CRN achieves lower error in estimating counterfactuals and in choosing the correct treatment and timing of treatment.

Estimating Counterfactual Treatment Outcomes over Time through Adversarially Balanced Representations

Ioana Bica, Ahmed Alaa, James Jordon, Mihaela van der Schaar

ICLR 2020

Identifying when to give treatments to patients and how to select among multiple treatments over time are important medical problems with a few existing solutions.

In this paper, we introduce the Counterfactual Recurrent Network (CRN), a novel sequence-to-sequence model that leverages the increasingly available patient observational data to estimate treatment effects over time and answer such medical questions.

To handle the bias from time-varying confounders, covariates affecting the treatment assignment policy in the observational data, CRN uses domain adversarial training to build balancing representations of the patient history. At each timestep, CRN constructs a treatment invariant representation which removes the association between patient history and treatment assignments and thus can be reliably used for making counterfactual predictions.

On a simulated model of tumour growth, with varying degree of time-dependent confounding, we show how our model achieves lower error in estimating counterfactuals and in choosing the correct treatment and timing of treatment than current state-of-the-art methods.

To learn more about our lab’s research in the area of individualized treatment effect inference, click here. We have also produced a video tutorial series on this topic, which is available here.

Unlocking the full potential of time series models

The following section will explore a range of features and attributes that are necessary in order to make AI and machine learning models as useful as possible in the clinical setting. While these features, such as interpretability, are common across the static and dynamic settings alike, the time series setting presents some unique and substantially more complex challenges, as outlined below.

AutoML

For any given prediction or forecasting problem in the clinical setting, we are likely to be able to choose from a range of time series models. However, it is extremely difficult to attempt to manually identify the best model for a particular problem at a particular moment in time, as the effectiveness of any algorithm at any stage will depend on a number of factors, including temporal distribution shifts and changing risk factors over time.

AutoML frameworks are well-suited to this kind of problem, as they are designed to provide optimal model selection. This formed the basis of our lab’s work on Stepwise Model Selection for Sequence Prediction via Deep Kernel Learning (SMS-DKL), which was introduced in an AISTATS 2020 paper.

SMS-DKL is a hyperparameter optimization tool for sequence modeling, and uses a novel Bayesian optimization algorithm to tackle the challenge of model selection in the time series. This is accomplished by treating the performance at each time step as its own black-box function. In order to solve the resulting multiple black-box function optimization problems jointly and efficiently, we exploit potential correlations among black-box functions using deep kernel learning (DKL).

Stepwise Model Selection for Sequence Prediction via Deep Kernel Learning

Yao Zhang, Daniel Jarrett, Mihaela Schaar

AISTATS 2020

An essential problem in automated machine learning (AutoML) is that of model selection. A unique challenge in the sequential setting is the fact that the optimal model itself may vary over time, depending on the distribution of features and labels available up to each point in time.

In this paper, we propose a novel Bayesian optimization (BO) algorithm to tackle the challenge of model selection in this setting. This is accomplished by treating the performance at each time step as its own black-box function. In order to solve the resulting multiple black-box function optimization problem jointly and efficiently, we exploit potential correlations among black-box functions using deep kernel learning (DKL).

To the best of our knowledge, we are the first to formulate the problem of stepwise model selection (SMS) for sequence prediction, and to design and demonstrate an efficient joint-learning algorithm for this purpose.

Using multiple real-world datasets, we verify that our proposed method outperforms both standard BO and multi-objective BO algorithms on a variety of sequence prediction tasks.

To learn more about our lab’s research in the area of automated machine learning (AutoML), click here.

Interpretability

There are several reasons to make a “black box” machine learning model for healthcare interpretable. First, an interpretable output can be more readily understood and trusted by its users (for example, clinicians deciding whether to prescribe a treatment), making its outputs more actionable. Second, a model’s outputs often need to be explained by its users to the subjects of its outputs (for example, patients deciding whether to accept a proposed treatment course) . Third, by uncovering valuable information that otherwise would have remained hidden within the model’s opaque inner workings, an interpretable output can empower users such as researchers with powerful new insights.

To date, the vast majority of the existing work on interpretability (including our own lab’s work) has focused on the static setting, with very little research having explored interpretability in the time series setting.

At ICML 2021, our lab presented a first model for explaining time series predictions in healthcare. Our method, DynaMask, is specifically designed for multivariate time series and uses saliency masks to identify and highlight important features at each time step.

Dynamask produces instance-wise importance scores for each feature at each time step by fitting a perturbation mask to the input sequence.

Explaining Time Series Predictions With Dynamic Masks

Jonathan Crabbé, Mihaela van der Schaar

ICML 2021

How can we explain the predictions of a machine learning model?

When the data is structured as a multivariate time series, this question induces additional difficulties such as the necessity for the explanation to embody the time dependency and the large number of inputs.

To address these challenges, we propose dynamic masks (Dynamask). This method produces instance-wise importance scores for each feature at each time step by fitting a perturbation mask to the input sequence. In order to incorporate the time dependency of the data, Dynamask studies the effects of dynamic perturbation operators. In order to tackle the large number of inputs, we propose a scheme to make the feature selection parsimonious (to select no more feature than necessary) and legible (a notion that we detail by making a parallel with information theory).

With synthetic and real-world data, we demonstrate that the dynamic underpinning of Dynamask, together with its parsimony, offer a neat improvement in the identification of feature importance over time. The modularity of Dynamask makes it ideal as a plug-in to increase the transparency of a wide range of machine learning models in areas such as medicine and finance, where time series are abundant.

To learn more about our lab’s research in the area of interpretable machine learning, click here.

Discovery and understanding of event data

It is also important to use time series datasets and models to make discoveries and understand event data.

One example of this is the development of personalized morbidity and comorbidity networks that enable us to understand how particular morbidities may trigger other morbidities over time.

Current state-of-the-art morbidity and comorbidity networks in healthcare are only capable of mapping the relationships between different diseases in a static manner at the population level. There is much to be gained from creating models that are both personalized (i.e., they depend on the unique characteristics, such as genetic information, of each specific individual) and dynamic (i.e., they depend on the order in which morbidities occur).

This is what our lab achieved through an approach we call deep diffusion processes (DDP), which allows us to model the temporal relationships between comorbid disease onsets expressed through a dynamic graph. Our work in this area is showcased in a paper published at AISTATS 2020.

DDP offers a deep probabilistic model for diffusion over comorbidity networks based on mutually-interacting point processes. We modeled DDP’s intensity function as a combination of contextualized background risk and networked disease interaction, using a deep neural network to (dynamically) update the disease’s influence on future events. This enables principled predictions based on clinically interpretable parameters which map patient history on to personalized comorbidity networks.

The dynamic comorbidity network learned by DDP for an individual patient at three time steps, together with the corresponding intensity function. Nodes for diseases that have not occurred are colored in gray, and diseases already diagnosed are assigned a distinct color. Edge thickness corresponds to the disease likelihood at the given time step. In the upper left panel, we plot the Jaccard distance of the patient’s network with respect to the average population as a function of time (on a logarithmic scale). The static comorbidity network obtained by counting disease co-occurrences and using the counts as graph edges is depicted on the right panel.

Learning Dynamic and Personalized Comorbidity Networks from Event Data using Deep Diffusion Processes

Zhaozhi Qian, Ahmed Alaa, Alexis Bellot, Jem Rashbass, Mihaela van der Schaar

AISTATS 2020

Comorbid diseases co-occur and progress via complex temporal patterns that vary among individuals. In electronic medical records, we only observe onsets of diseases, but not their triggering comorbidities — i.e., the mechanisms underlying temporal relations between diseases need to be inferred.

Learning such temporal patterns from event data is crucial for understanding disease pathology and predicting prognoses. To this end, we develop deep diffusion processes (DDP) to model ’dynamic comorbidity networks’, i.e., the temporal relationships between comorbid disease onsets expressed through a dynamic graph.

A DDP comprises events modelled as a multi-dimensional point process, with an intensity function parameterized by the edges of a dynamic weighted graph. The graph structure is modulated by a neural network that maps patient history to edge weights, enabling rich temporal representations for disease trajectories. The DDP parameters decouple into clinically meaningful components, which enables serving the dual purpose of accurate risk prediction and intelligible representation of disease pathology.

We illustrate these features in experiments using cancer registry data.

Uncertainty estimation

For the outputs of a model to be trustworthy and actionable, the model must offer reliable uncertainty estimates. Estimation of the uncertainty of a healthcare associated inference is often as important as the prediction itself, as it allows the clinician to know how much weight to give it.

This is important for both static and dynamic models, but again the latter category presents an array of unique challenges; however, such challenges are not accounted for by commonly used approaches. For example, RNNs typically only produce single point forecasts, whereas we would ideally have sequential confidence intervals. This is why our lab developed an approach based on frequentist uncertainty in recurrent neural networks via blockwise influence functions, which we introduced in a paper published at at ICML 2020.

In this setting, we are computing uncertainty estimates by measuring the variability in the resampled RNN outputs. This is achieved by perturbing the model parameters through iterative deletion of blocks of data and retraining the model on the remaining data.

This approach is particularly well-suited to healthcare as it yields post-hoc uncertainty estimates that do not affect model accuracy or interfere with model training. It is also highly versatile, and can be applied to a wide range of sequence prediction settings without requiring changes to model architecture. Importantly, we can also provide frequentist coverage guarantees, which require formal frequentist procedures.

Frequentist Uncertainty in Recurrent Neural Networks via Blockwise Influence Functions

Ahmed Alaa, Mihaela van der Schaar

ICML 2020

Recurrent neural networks (RNNs) are instrumental in modelling sequential and time-series data. Yet, when using RNNs to inform decision-making, predictions by themselves are not sufficient {—} we also need estimates of predictive uncertainty. Existing approaches for uncertainty quantification in RNNs are based predominantly on Bayesian methods; these are computationally prohibitive, and require major alterations to the RNN architecture and training.

Capitalizing on ideas from classical jackknife resampling, we develop a frequentist alternative that: (a) does not interfere with model training or compromise its accuracy, (b) applies to any RNN architecture, and (c) provides theoretical coverage guarantees on the estimated uncertainty intervals.

Our method derives predictive uncertainty from the variability of the (jackknife) sampling distribution of the RNN outputs, which is estimated by repeatedly deleting “blocks” of (temporally-correlated) training data, and collecting the predictions of the RNN re-trained on the remaining data. To avoid exhaustive re-training, we utilize influence functions to estimate the effect of removing training data blocks on the learned RNN parameters.

Using data from a critical care setting, we demonstrate the utility of uncertainty quantification in sequential decision-making.

(Informatively) missing data

Missing data (inclusively informatively missing data) is another important area in time series.

Some of our lab’s earlier work in this area involved development of multi-directional recurrent neural networks (M-RNN) that enable us to interpolate features over time as well as across features. In other words, the M-RNN approach provides for simultaneous imputation across different medical time series streams and across time. Unlike bidirectional recurrent neural networks, we can use M-RNNs to perform imputation in a causal manner, since we do not need to consider the future: we simply use information that has been made available so far for imputation.

Estimating Missing Data in Temporal Data Streams Using Multi-Directional Recurrent Neural Networks

Jinsung Yoon, William Zame, Mihaela van der Schaar

IEEE Transactions on Biomedical Engineering, 2018

Missing data is a ubiquitous problem. It is especially challenging in medical settings because many streams of measurements are collected at different-and often irregular-times.

Accurate estimation of the missing measurements is critical for many reasons, including diagnosis, prognosis, and treatment. Existing methods address this estimation problem by interpolating within data streams or imputing across data streams (both of which ignore important information) or ignoring the temporal aspect of the data and imposing strong assumptions about the nature of the data-generating process and/or the pattern of missing data (both of which are especially problematic for medical data).

We propose a new approach, based on a novel deep learning architecture that we call a Multi-directional Recurrent Neural Network that interpolates within data streams and imputes across data streams. We demonstrate the power of our approach by applying it to five real-world medical datasets.

We show that it provides dramatically improved estimation of missing measurements in comparison to 11 state-of-the-art benchmarks (including Spline and Cubic Interpolations, MICE, MissForest, matrix completion, and several RNN methods); typical improvements in Root Mean Squared Error are between 35%-50%. Additional experiments based on the same five datasets demonstrate that the improvements provided by our method are extremely robust.

It is also important, however, to bear in mind that clinical data is generally not missing at random: its missingness is often informative. We can learn about (and from) the underlying clinical judgements by building probabilistic models for learning not only from the value of clinical data, but also from its presence and absence.

Our lab achieved this in an approach presented in a paper published at ICML 2017, where we modeled a patient trajectory as a marked point process modulated by the health state. This model captures informatively sampled patient episodes: the clinicians’ decisions on when to observe a hospitalized patient’s vital signs and lab tests over time are represented by a marked Hawkes process, with intensity parameters modulated by the patient’s latent clinical states, and with observable physiological data (mark process) modeled as a switching multitask Gaussian process. In addition, our model captures informatively censored patient episodes by representing the patient’s latent clinical states as an absorbing semi-Markov jump process.

Learning from Clinical Judgments: Semi-Markov-Modulated Marked Hawkes Processes for Risk Prognosis

Ahmed Alaa, Scott Hu, Mihaela van der Schaar

ICML 2017

Critically ill patients in regular wards are vulnerable to unanticipated adverse events which require prompt transfer to the intensive care unit (ICU).

To allow for accurate prognosis of deteriorating patients, we develop a novel continuous-time probabilistic model for a monitored patient’s temporal sequence of physiological data.

Our model captures “informatively sampled” patient episodes: the clinicians’ decisions on when to observe a hospitalized patient’s vital signs and lab tests over time are represented by a marked Hawkes process, with intensity parameters that are modulated by the patient’s latent clinical states, and with observable physiological data (mark process) modeled as a switching multi-task Gaussian process. In addition, our model captures “informatively censored” patient episodes by representing the patient’s latent clinical states as an absorbing semi-Markov jump process. The model parameters are learned from offline patient episodes in the electronic health records via an EM-based algorithm.

Experiments conducted on a cohort of patients admitted to a major medical center over a 3-year period show that risk prognosis based on our model significantly outperforms the currently deployed medical risk scores and other baseline machine learning algorithms.

Synthetic data generation

Machine learning has the potential to catalyze a complete transformation in healthcare, but researchers in our field are still hamstrung by a lack of access to high-quality data, which is the result of perfectly valid concerns regarding privacy.

If the purpose of sharing a dataset is to develop and validate machine learning methods for a particular task (e.g. prognostic risk scoring), real data is not necessary; it would suffice to have a synthetic dataset that is sufficiently like the real data. Generating synthetic patient records based on real patient records can, therefore, be an alternative way of providing machine learning researchers with the data that they need to be able to develop appropriate methods for the task at hand, while avoiding sharing sensitive patient information. This could dramatically swing the balance between risks and benefits in favor of the latter.

Synthetic data can also provide researchers with datasets that have been tailored to specific needs, while still based on real data. Varying types of synthetic datasets could, for instance, be created specifically for ICU admission prediction, for clinical trials, for estimating treatment effects, and for time series datasets (to name a few examples).

Generating realistic synthetic time series datasets that preserve the temporal dynamics of real datasets is challenging: we must capture the distribution of features within each time point as well as the complex dynamics of variables across time points.

Existing methods do not adequately attend to the temporal correlations unique to time series data. At the same time, supervised models for sequence prediction—which allow finer control over network dynamics—are inherently deterministic. This led our lab to develop TimeGAN, a generative model for time series data, which we presented in a paper for NeurIPS 2019. TimeGAN straddles the intersection of multiple strands of research, combining themes from autoregressive models for sequence prediction, GAN-based methods for sequence generation, and time series representation learning.

Since TimeGAN is trained adversarially and jointly via a learned embedding space with both supervised and unsupervised losses, it offers both the flexibility of unsupervised GAN frameworks and the control afforded by supervised training in autoregressive models. 

Importantly, TimeGAN handles mixed-data settings, where both static and time series data can be generated at the same time.

Time-series Generative Adversarial Networks

Jinsung Yoon, Daniel Jarrett, Mihaela van der Schaar

NeurIPS 2019

A good generative model for time-series data should preserve temporal dynamics, in the sense that new sequences respect the original relationships between variables across time.

Existing methods that bring generative adversarial networks (GANs) into the sequential setting do not adequately attend to the temporal correlations unique to time-series data. At the same time, supervised models for sequence prediction – which allow finer control over network dynamics – are inherently deterministic.

We propose a novel framework for generating realistic time-series data that combines the flexibility of the unsupervised paradigm with the control afforded by supervised training. Through a learned embedding space jointly optimized with both supervised and adversarial objectives, we encourage the network to adhere to the dynamics of the training data during sampling.

Empirically, we evaluate the ability of our method to generate realistic samples using a variety of real and synthetic time-series datasets. Qualitatively and quantitatively, we find that the proposed framework consistently and significantly outperforms state-of-the-art benchmarks with respect to measures of similarity and predictive ability.

TimeGAN does, however, have a number of limitations. It is hard to train (especially for time series data) and difficult to evaluate quantitatively due to the absence of a computable likelihood function. It is also vulnerable to training data memorization. This is why our lab more recently developed an approach to generative time series modeling based on Fourier flows, as presented in an ICLR 2021 paper.

In this case, our focus was to develop a generative model that can sample synthetic time series data while providing explicit likelihood models that are easy to optimize and evaluate.

Generative Time-series Modeling with Fourier Flows

Ahmed Alaa, Alex Chan, Mihaela van der Schaar

ICLR 2021

Generating synthetic time-series data is crucial in various application domains, such as medical prognosis, wherein research is hamstrung by the lack of access to data due to concerns over privacy. Most of the recently proposed methods for generating synthetic time-series rely on implicit likelihood modeling using generative adversarial networks (GANs)—but such models can be difficult to train, and may jeopardize privacy by “memorizing” temporal patterns in training data.

In this paper, we propose an explicit likelihood model based on a novel class of normalizing flows that view time-series data in the frequency-domain rather than the time-domain. The proposed flow, dubbed a Fourier flow, uses a discrete Fourier transform (DFT) to convert variable-length time-series with arbitrary sampling periods into fixed-length spectral representations, then applies a (data-dependent) spectral filter to the frequency-transformed time-series.

We show that, by virtue of the DFT analytic properties, the Jacobian determinants and inverse mapping for the Fourier flow can be computed efficiently in linearithmic time, without imposing explicit structural constraints as in existing flows such as NICE (Dinh et al. (2014)), RealNVP (Dinh et al. (2016)) and GLOW (Kingma & Dhariwal (2018)).

Experiments show that Fourier flows perform competitively compared to state-of-the-art baselines.

To learn more about our lab’s research in the area of synthetic data generation, assessment, and evaluation, click here.

Reproducibility and visualization

Reproducibility is another essential attribute of any successful AI or machine learning model for healthcare—whether static or dynamic.

One example of a reproducible model developed by our lab for the time series setting is Clairvoyance, a unified, end-to-end pipeline for clinical decision support. Clairvoyance is capable of predictions, forecasts, monitoring and personalized treatment planning over time. Since reproducibility is the focus of Clairvoyance, all the code is available and can be freely tested, augmented, and benchmarked. Additionally, we are currently developing a comprehensive visualization tool for time series models that will be usable by both clinicians and patients.

Clairvoyance: A Pipeline Toolkit for Medical Time Series

Daniel Jarrett, Jinsung Yoon, Ioana Bica, Zhaozhi Qian, Ari Ercole, Mihaela van der Schaar

ICLR 2021

Time-series learning is the bread and butter of data-driven clinical decision support, and the recent explosion in ML research has demonstrated great potential in various healthcare settings. At the same time, medical time-series problems in the wild are challenging due to their highly composite nature: They entail design choices and interactions among components that preprocess data, impute missing values, select features, issue predictions, estimate uncertainty, and interpret models.

Despite exponential growth in electronic patient data, there is a remarkable gap between the potential and realized utilization of ML for clinical research and decision support. In particular, orchestrating a real-world project lifecycle poses challenges in engineering (i.e. hard to build), evaluation (i.e. hard to assess), and efficiency (i.e. hard to optimize).

Designed to address these issues simultaneously, Clairvoyance proposes a unified, end-to-end, autoML-friendly pipeline that serves as a (i) software toolkit, (ii) empirical standard, and (iii) interface for optimization. Our ultimate goal lies in facilitating transparent and reproducible experimentation with complex inference workflows, providing integrated pathways for (1) personalized prediction, (2) treatment-effect estimation, and (3) information acquisition.

Through illustrative examples on real-world data in outpatient, general wards, and intensive-care settings, we illustrate the applicability of the pipeline paradigm on core tasks in the healthcare journey. To the best of our knowledge, Clairvoyance is the first to demonstrate viability of a comprehensive and automatable pipeline for clinical time-series ML.

The code for Clairvoyance can be found here on our lab’s GitHub.

Find out more and get involved

This page has served as an introduction to a range of challenges and solutions unique to the time series setting—from the perspective of both healthcare and machine learning.

We have demonstrated the importance of understanding the nature and drivers of disease progression, as well as the value of insight into how individuals transition between disease states and how multiple morbidities may interact.

Machine learning tools such as those introduced above can enable us to build a comprehensive view of patient health that incorporates the past, present, and future and can factor in the evolving interactions and causal relationships between multiple competing risks and comorbidities. This is the key to accelerating the advent of bespoke medicine and truly moving beyond one-size-fits-all approaches.

We would also encourage you to stay abreast of ongoing developments in this and other areas of machine learning for healthcare by signing up to take part in one of our two streams of online engagement sessions.

If you are a practicing clinician, please sign up for Revolutionizing Healthcare, which is a forum for members of the clinical community to share ideas and discuss topics that will define the future of machine learning in healthcare (no machine learning experience required).

If you are a machine learning student, you can join our Inspiration Exchange engagement sessions, in which we introduce and discuss new ideas and development of new methods, approaches, and techniques in machine learning for healthcare.

A full list of our papers on this and related topics can be found here.