Kaplan-Meier and the log-rank test
What question does this help answer?
It answers "what proportion are still event-free at six months", and, with the log-rank test, "do these two groups differ over the whole follow-up period". It does this without assuming any shape for the underlying risk.
How censoring works
Someone who leaves the study, or reaches the end of it, without the outcome contributes information up to that moment and then stops. The estimator uses that partial information rather than discarding the person, which is what makes it usable when follow-up varies.
What censored follow-up looks like
What a Kaplan-Meier plot looks like
When to use it
Use it to describe time-to-event data before modelling it, to present survival visually, and to compare groups when no adjustment is needed. A Kaplan-Meier plot with numbers at risk beneath it is usually the most informative single figure in a survival paper.
When not to use it
It cannot adjust for covariates, so it is descriptive rather than a substitute for a model. It should not be used where a COMPETING EVENT exists, because it treats the competing death as though the patient could still have the outcome later. And a log-rank test is the wrong test when curves cross, because it averages an effect that changes direction into one number and can report no difference where a large one exists.
Why Mallard may recommend it
Mallard offers a Kaplan-Meier exhibit when the estimand's measure is a hazard ratio and nothing in the plan contradicts a survival presentation. Where the estimand records a competing event, it does NOT: the figure is withheld rather than printed with a caveat.
Key assumptions and design requirements
- Censoring is uninformative: leaving the study is unrelated to the risk of the outcome.
- Time zero is defined the same way for everyone, and follow-up begins there.
- Numbers at risk are shown beneath the curve, because the tail is where the estimate is least stable.
- A median survival is not reported when the curve has not reached 50 percent.
- Where a competing event exists, cumulative incidence is used instead.
What to watch out for
The curve assumes censoring is uninformative: that people lost to follow-up were no more and no less likely to have the outcome than those who stayed. Where a competing event exists the complement of the curve OVERSTATES cumulative incidence, and a log-rank test can miss a real difference entirely when curves cross, because it averages a changing effect into a single comparison.
Clinical example
Question: Do patients discharged on a new anticoagulant remain free of readmission longer? Analysis: Plot Kaplan-Meier curves by drug with numbers at risk, compare with a log-rank test, and inspect whether the curves cross before trusting that single p-value.
- The logrank test (opens in a new tab) · BMJ · doi 10.1136/bmj.328.7447.1073
- Kaplan-Meier Curves, Log-Rank Tests, and Cox Regression for Time-to-Event Data (opens in a new tab) · Anesth Analg · doi 10.1213/ANE.0000000000005358