What is survival analysis?

Survival analysis is a statistical method used to analyse the time until an event of interest occurs. The key feature of survival analysis is that the outcome has two dimensions:

– an event indicator (yes/no), and

– the time spent at risk for the event

All survival analyses require precise definitions of start and end of follow-up, and a relevant time-scale (e.g., time since diagnosis of a disease).

The two main ingredients in any survival analysis are:

  • the hazard function, which tells us the rate (speed) at which the event is occurring, and
  • the survival function, which quantifies the probability of survival (or the probability of the event not occurring) over time

Survival analysis is commonly used in medical research, engineering, finance, and other fields where the time of event is of interest, in fact, it is also known as the analysis of time-to-event data.

The hazard function can be estimated non-parametrically or modelled. The most commonly used model is the Cox proportional hazards model. The survival function can be calculated using, e.g., the Kaplan-Meier method.

What tends to make survival analysis special is censoring. Censoring occurs when the information on the survival time is incomplete or partially observed. Learn more about censoring here.


State-of-the-art statistical models for modern HTA

At @RedDoorAnalytics, we develop methodology and software for efficient modelling of biomarkers, measured repeatedly over time, jointly with survival outcomes, which are being increasingly used in cancer settings. We have also developed methods and software for general non-Markov multi-state survival analysis, allowing for the development of more plausible natural history models, where patient history can […]
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Multilevel (hierarchical) survival models: Estimation, prediction, interpretation

Hierarchical time-to-event data is common across various research domains. In the medical field, for instance, patients are often nested within hospitals and regions, while in education, students are nested within schools. In these settings, the outcome is typically measured at the individual level, with covariates recorded at any level of the hierarchy. This hierarchical structure […]
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Statistical Primers

What are competing risks?

Competing risks In survival analysis, competing risks refer to the situation when an individual is at risk of experiencing an event that precludes the event under study to occur. Competing risks commonly occur in studies of cause-specific mortality, as all other causes of death than the one under study might happen before the individuals “have […]
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