Kaplan-Meier curve
- Concept
A step curve showing what share of people remain free of the event as time passes. It drops one step at each event.
What it is
The Kaplan-Meier (product-limit) estimator calculates the probability of remaining free of the event over time. At each time an event occurs, the probability of getting past it is (at risk − events) / at risk, and cumulative survival is the product of those probabilities. Censored people leave the at-risk group without lowering the curve and are usually shown as small tick marks.
Worked example
- Data: 10 patients. Deaths at 2, 4, 5, 8 and 11 months; censored at 3, 6, 9, 12 and 12 months.
- Month 2: 10 at risk, 1 death: S = 9/10 = 0.900.
- Month 3: one censored (no step); 8 remain. Month 4: 1 death: S = 0.900 × 7/8 = 0.788.
- Month 5: 7 at risk, 1 death: S = 0.788 × 6/7 = 0.675.
- Month 6: one censored; 5 remain. Month 8: 1 death: S = 0.675 × 4/5 = 0.540.
- Month 9: one censored; 3 remain. Month 11: 1 death: S = 0.540 × 2/3 = 0.360.
- Median: first time with S ≤ 0.5, that is 11 months. Estimated survival at 10 months = 54%.
- If another group had 75% at 10 months, its curve would run above; the log-rank test would say whether the gap exceeds chance.
- Reading: each step reflects one death among those still at risk; the last steps rest on very few patients.
Markers
- S(t)
- product limit
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Common pitfalls
- Reading the right-hand end of the curve as precise when only two or three people remain at risk.
- Comparing curves at a single time point chosen after looking at them.
- Dropping the curve at a censoring time (censoring is not an event).
Test yourself
Think of the answer, then tap the question to see it.
How is Kaplan-Meier cumulative survival calculated?
By multiplying, at each event time, the probability of getting past it: (at risk − events) / at risk.
What happens to the curve when a patient is censored?
It does not drop; the patient leaves the at-risk group and is usually marked with a small vertical tick.
How is median survival read from the curve?
It is the first time at which the curve reaches or drops below 50%.
Why is the right-hand end of a Kaplan-Meier curve unreliable?
Because few people remain at risk and each event makes a large step with a wide confidence interval.
Connections
Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.
Sources: Empirical model fitting - distribution free (Kaplan-Meier) approach (NIST/SEMATECH e-Handbook of Statistical Methods, National Institute of Standards and Technology, 2012); Censoring (NIST/SEMATECH e-Handbook of Statistical Methods, National Institute of Standards and Technology, 2012); How do you compare reliability between two or more populations? (NIST/SEMATECH e-Handbook of Statistical Methods, National Institute of Standards and Technology, 2012).
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Representative model, for educational purposes only.