Survival Analysis

What is survival data?

Time-to-event data consist of an exact start time and end time.

Examples from cardiac surgery

  • Time from Surgery to Death

  • Time from first Surgery to Second surgery (reoperation)

  • Time from RV-PA Conduit surgery to RV-PA Conduit failure event

  • Time from Systemic-to-Pulmonary Shunt operation to Shunt Thrombosis event

  • Time from Biological Valve Replacement to Biological Valve ReReplacement

Survival analysis, also known as time-to-event analysis, is a statistical method used to analyze the time until an event of interest occurs. The event of interest could be death, failure, or a specific outcome, and the time could be measured in days, months, or years. The main idea behind survival analysis is to model the probability that the event of interest has not occurred at a specific time, called the survival function.

There are several statistical models used in survival analysis, including:

  1. Kaplan-Meier estimator: This is a non-parametric method that estimates the survival function based on the observed data. It is commonly used to estimate the survival function for a single group of subjects.

  2. Cox proportional hazards model: This is a semi-parametric method that estimates the relative risk of an event occurring for different groups of subjects. It allows for the modeling of time-dependent covariates and is commonly used to compare the survival between groups.

  3. Aalen's additive model: This is a semi-parametric method that estimates the cumulative hazard function for different groups of subjects. It allows for the modeling of time-dependent covariates and is particularly useful for modeling non-proportional hazards.

  4. Accelerated failure time models (AFT): This is a parametric method that assumes that the time to failure follows a particular distribution and estimates the parameters of the distribution.

The choice of model depends on the research question and the assumptions that can be made about the data. In general, non-parametric methods such as Kaplan-Meier are less powerful but more flexible, while parametric methods such as AFT models are more powerful but require more assumptions about the data.

Kaplan-meier curve

The standard graph of the cumulative survival probability during a defined time is the Kaplan–Meier plot. It is based on the non-parametric product-limit estimator. All information is usually clearly displayed to the reader.


cox-regression or proportional hazard model

is a method for investigating the effect of several variables upon the time a specified event takes to happen. Kaplan–Meier estimates of survival curves and Cox proportional hazard models are widely used to describe survival trends and identify significant prognostic factors. All these statistical analyses deal with only one type of event, for example death, independently of its cause.


Competing Risk Analysis

is a type of survival analysis that aims to correctly estimate the marginal probability of an event in the presence of competing events. Competing risks occur when subjects can experience one or more events or outcomes which ‘compete’ with the outcome of interest.