van der Schaar Lab

Demonstrator: Survival Analysis


Survival Analysis


Survival analysis, also known as time-to-event analysis, refers to the study of the duration until an event (or events) occur(s).  In healthcare, the objective is typically to model the probability of a certain (often adverse) event occurring, based on the patient’s covariates.  It is worth noting that time-to-event analysis applies beyond the medical setting, and is also useful in economics, finance, and engineering.

In this demonstrator, we focus on (i) the dynamic time-to-event analysis, that is, the case where a patient’s longitudinal covariates are made use of; and (ii) temporal clustering (phenotyping) of patients based on their relative risk.

Watch the Video: Dynamic Survival Analysis and Temporal Phenotyping in Prostate Cancer Active Surveillance by Prof. Vincent Gnanapragasam

On 26 October, 2021, we ran the eleventh Revolutionizing Healthcare engagement sessions of the van der Schaar Lab and its audience of practicing clinicians.  As part of the session, Prof. Vincent Gnanapragasam discussed the power of dynamic survival analysis and temporal phenotyping when applied to prostate cancer active surveillance (21:04), and went over an interactive demonstrator (38:25), designed at the lab, which you can watch here.

What are the Healthcare Applications?

Survival analysis has numerous applications, as long as the problem can be formulated to have an event/events of interest that may occur at some time in the future.  Here are just a few illustrative scenarios:

  • Probability of death from a certain type of cancer (breast, prostate, etc.),
  • Probability of an ICU patient being put on a mechanical ventilator,
  • Probability of organ transplant rejection.

In our demonstrator, the setting is that of prostate cancer active surveillance, or monitoring of prostate cancer patients over time, with the target adverse event being the elevation of a patient to Cambridge Prognostic Group 3 (CPG3).

What are the Clinical Use Cases?

The following use cases are the focus of our demonstrator:

  • Bespoke Medicine: ML time-to-event models are a perfect tool for personalized medicine, able to leverage the entirety of the individual’s health records, and making personalized predictions.
  • Dynamic Risk Scoring: evaluating a risk score of an adverse event, given the static and longitudinal patient data.
  • Temporal Clustering: allocating a patient to a risk group (cluster), and monitoring the patient’s trajectory across the different clusters over time.

Use Case: Bespoke Medicine

The demonstrator is designed to focus on one individual patient at a time, displaying their static covariates (e.g., ethnicity, family history), temporal covariates (e.g. repeat PSA measurements), and the personalized predictions: dynamic risk scores and risk cluster allocations over time.  Furthermore, the clinician is able to enter new measurements and observe the change in the model predictions in real time, providing an opportunity for bespoke analysis and personalized treatment decisions.  This represents a significant step forward from the current decision-making process, which is often done on the basis of an “average” patient or low-resolution patient stratification.

Use Case: Dynamic Risk Scoring

As healthcare data becomes more ubiquitous, more longitudinal (temporal) data is collected per patient – that is, data points associated with a time, e.g., MRI scores taken over multiple MRI scans.  These rich data carry additional information, which can improve patient risk scoring, as well as providing an infrastructure where a patient’s predictions can be continuously updated as more information is collected. 

The demonstrator illustrates the power of such dynamic risk scoring in two ways:

  1. the real time updating of the patient’s risk score and risk cluster assignment as the user enters a new set of observations, and
  2. the “Historic Risk” tab, which visualizes the risk curves as would have been evaluated by the model as each subsequent temporal set of observations was collected.
Survival analysis demonstrator screenshot: "Historic Risk" tab.

The “Historic Risk” chart of the demonstrator, showing the evolution of the risk score as more data is gathered over time.  Vertical grey lines indicate the time points where new observations were made.

The underlying model powering the demonstrator is a variation on the Dynamic DeepHit method [1] developed at our lab.  In the static setting where longitudinal covariates are not available, our earlier method, DeepHit [2], can be used.

Use Case: Temporal Clustering

Identifying patient strata that reflect similar trajectories in terms of patient outcome (for a particular event) is another useful tool in survival analysis, which we term outcome-oriented clustering.  Where longitudinal data are involved, it is likely that a patient may move between the allocated clusters as their disease progresses, meaning that the cluster assignments are temporal.  The knowledge this cluster allocation can serve as an important input to the clinician’s decision-making process, especially in the setting of active monitoring.  Our demonstrator visualizes this concept by tracking a patient’s cluster assignment over time on the “Cluster” line plots, and also by providing an intuitive “Cluster Space” visualization of the patient’s trajectory.

The “Cluster Space” visualization leverages PCA to display a patient’s cluster assignment over time in two dimensions.

The method used to perform temporal clustering in this demonstrator is AC-TPC ([3], [4]), developed at our lab.


[1] C. Lee, J. Yoon, M. van der Schaar, “Dynamic-DeepHit: A Deep Learning Approach for Dynamic Survival Analysis with Competing Risks based on Longitudinal Data”, IEEE Transactions on Biomedical Engineering 67.1, 2019.

[2] C. Lee, W. R. Zame, J. Yoon, M. van der Schaar, “DeepHit: A Deep Learning Approach to Survival Analysis with Competing Risks”, Proceedings of the AAAI conference on artificial intelligence. 32.1. 2018.

[3] C. Lee, J. Rashbass, M. van der Schaar, “Outcome-Oriented Deep Temporal Phenotyping of Disease Progression”, IEEE Transactions on Biomedical Engineering 68.8, 2021.

[4] C. Lee, M. van der Schaar, “Temporal Phenotyping using Deep Predictive Clustering of Disease Progression”, International Conference on Machine Learning (ICML), 2020.