Clinical research & EBM · Reference
What is a Kaplan–Meier curve?
A Kaplan–Meier curve is a step-shaped graph that estimates the probability of surviving — or remaining event-free — over time from time-to-event data. It accounts for censored observations and is a foundational tool of survival analysis.
How the curve is built
The Kaplan–Meier estimator calculates the probability of surviving past each successive time at which an event occurs, multiplying these conditional probabilities together to produce a cumulative survival estimate. Plotted over time, this yields a characteristic step function that drops at each event and stays flat between events. The vertical axis shows the estimated proportion still event-free; the horizontal axis shows time since a defined starting point such as randomisation. Because it makes no assumption about the shape of the underlying survival distribution, it is described as non-parametric.
Censoring
A defining strength of the Kaplan–Meier method is its handling of censoring. A participant is censored when their event has not occurred by the time their data end — for example because the study finished or they were lost to follow-up — so all that is known is that they were event-free up to that point. Rather than discard these partial observations, the estimator uses each participant’s information up to the moment they are censored. Censored observations are often marked as small ticks on the curve. Properly accounting for censoring is what allows survival to be estimated without waiting for every participant to have an event.
Comparing groups and the log-rank test
Kaplan–Meier curves are commonly drawn for two or more groups on the same axes — for example an intervention group and a control group — so their survival experience can be compared visually. To test whether the difference between curves is statistically significant, researchers use the log-rank test, which compares observed and expected events across the groups over time. The magnitude of any difference is usually quantified separately with a hazard ratio from a Cox model, since the curve and log-rank test show whether groups differ but not by how much in a single number.
Key facts
At a glance
- Definition: Step-function estimate of survival over time
- Type: Non-parametric (no assumed distribution)
- Handles: Censored (incomplete) observations
- Axes: Survival probability versus time
- Compared by: The log-rank test
- Quantified by: A hazard ratio from a Cox model
Common questions
FAQ
What does a Kaplan–Meier curve show?+
It shows the estimated probability of remaining event-free over time as a descending step function, dropping at each point an event occurs. It is used to display and compare survival or time-to-event experience between groups.
What is censoring in a Kaplan–Meier analysis?+
Censoring occurs when a participant’s event has not happened by the time their data end, so it is only known they were event-free up to that point. The Kaplan–Meier method uses each participant’s information up to censoring rather than discarding it.
What is the log-rank test used for?+
The log-rank test assesses whether the difference between two or more Kaplan–Meier survival curves is statistically significant by comparing observed and expected events over time. It indicates whether groups differ but not the size of the difference, which a hazard ratio quantifies.
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