What is a Kaplan-Meier curve?

How the estimate is built

Kaplan and Meier published the method in 1958. Follow up is split at every time an event occurs. At each of those times the chance of getting through that moment is the number who did not have the event divided by the number still at risk just before it. The curve at any time is the product of all those conditional probabilities so far. People who leave the study, move away or reach the end of follow up without the event are censored: they count in the denominator while observed and then drop out of it, which is why the method can use incomplete follow up without pretending everyone had the same length of observation. Goel and colleagues set out the arithmetic with a worked table in their tutorial.

Reading two curves against each other

Look first at the y axis, which should start at 1 or 100 percent, and at the x axis units, which should match the follow up time. Then compare the curves at clinically meaningful landmarks such as one year and five years, not only at the far right. A log rank test gives the p value for the difference across the whole curve, and a Cox model gives the hazard ratio, but neither replaces the picture: curves that run together and separate late tell a different story from curves that separate at once. Rich and colleagues recommend always printing the numbers at risk beneath the time axis so readers can judge how much data supports each part of the curve.

Why the right end misleads

As follow up lengthens, fewer people remain at risk, so each event causes a larger step. A curve that drops sharply at year eight may reflect one death among four remaining patients. Bland and Altman note that the estimate becomes less precise as the numbers shrink, so the right end of a curve deserves the least weight. Stop the plot where only a handful of people remain at risk, or at least print the numbers at risk so readers see the thin data for themselves, and describe the tail in words rather than drawing conclusions from its last few steps.

Common mistakes

Joining the points with sloping lines instead of steps, which invents survival between events. Omitting the censoring ticks or the numbers at risk. Reporting the median survival when the curve never falls below 0.5, which means the median was not reached. Treating one minus the Kaplan-Meier estimate as the cumulative incidence when a competing event, such as death from another cause, stops people from having the event of interest. And starting the y axis above zero without saying so, which makes small gaps look large.

Putting a survival result on a poster board

The poster builder draws chart figures from numbers in ten kinds: vertical and horizontal bars, stacked columns, line, area, pie, donut, radar, waterfall and waffle. None is a step plot and none draws censoring ticks, so a true Kaplan-Meier figure has to come from statistics software. Inside the builder, survival at fixed landmarks as a bar or line chart with the numbers at risk in a table or a key number block is the honest substitute, with the median survival and the log rank result written in the section text. Name the landmarks and the values in the brief, since the generator does not invent figures.

Questions people ask