Reading a Kaplan-Meier Curve

Last updated October 30, 2026·4 min read

A Kaplan-Meier curve estimates the share of a population still free of an event as time passes: patients still alive, subscribers still subscribed, components still running. It starts at one, steps down at each observed event time, and stays flat between events. Its distinguishing virtue is honesty about incomplete follow-up: cases leave observation for reasons other than the event, and the estimator uses them while they are present and releases them when they go, instead of pretending the study ended for everyone at once.

Censoring: the marks on the curve

A censored case was event-free when last seen and then left: the study ended, the patient moved, the subscription record stops. Censoring times are usually drawn as small ticks on the curve. Two reading rules follow. A stretch of curve with many ticks and few steps is a stretch where information is draining away even though the line looks calm. And the estimator trusts that censored cases would have fared like those who stayed; when censoring tracks prognosis, sicker patients leaving early, the curve flatters the population, and no feature of the plot itself will warn you. The warning has to come from knowing how follow-up worked.

The worked curve

Eight cases. Events at months 3, 6, 8, 12, and 18; censoring at months 5, 10, and 15.

• Month 3: 8 at risk, one event, survival 0.875
• Month 6: 6 at risk, one event, survival 0.729
• Month 8: 5 at risk, one event, survival 0.583
• Month 12: 3 at risk, one event, survival 0.389
• Month 18: 1 at risk, one event, survival 0

Each step multiplies the running survival by the share of the risk set that survived that time. Between months 8 and 12 the curve is flat, not because nothing happened, but because the only departure in between was a censoring at month 10, which shrinks the risk set without stepping the curve.

The number at risk: the most important row under the plot

At month 12, three cases remain at risk. At month 18, one. The final step to zero rests on a single case, and in a large study the tail of the curve routinely rests on a small, selected remainder of the original cohort: the cases with the longest follow-up, who differ from the rest by the accident of enrollment date. Read the right-hand end of any Kaplan-Meier curve against its risk table before believing it, prefer curves that print the table, and grow suspicious of tails drawn long past the point where the risk set thins to a handful. Many analysts truncate interpretation where fewer than ten or twenty remain at risk, and say where they truncated.

Median survival and the other summaries

Median survival is the time at which the curve crosses one half: month 12 in the worked curve, the first step at or below 0.5. It is the most quoted summary because it needs no extrapolation and survives in plain language. When the curve never reaches one half, median survival is not reached, and the correct report says exactly that, with the follow-up window named, rather than projecting a crossing nobody observed. Means are treacherous in this setting because the tail is censored; where a mean is needed, the restricted mean up to a stated horizon is the defensible version.

Comparing curves: the log-rank test and its limits

The log-rank test compares whole curves, accumulating at each event time the difference between observed events in a group and the events expected if the groups shared one survival experience. It is the right default when the curves separate steadily. It loses power when curves cross, because early and late differences cancel in the accumulation, and crossing curves are themselves the finding in such cases: the report should describe the crossing and consider whether a single hazard ratio can summarize it honestly. Often it cannot, which is the bridge to the Cox model and its proportional hazards check.

A reading checklist

• Find the censoring ticks. Are departures spread evenly, or draining one group faster?
• Read the number at risk at the times the report quotes. Thin risk sets, thin claims.
• Locate the median and its interval, or confirm it was not reached.
• Check where the curves separate, and whether they cross.
• Ask what happened to the censored, and whether the answer could track the outcome.

Draw one

Module 16 of Analysis Studio draws the curve with its risk table, Greenwood intervals, median survival, and the log-rank test, and checks the Cox assumption on the same screen when a model follows:

Module 16: Survival AnalysisOpen in Analysis Studio →

Sources and method notes

Estimator and interval forms follow Kaplan and Meier (1958) with Greenwood variance and log-log transformed intervals, as implemented in the Studio module. The worked curve is shared with the calculator page and re-verified at build.