Survival analysis and censoring
- Concept
It studies how long it takes until an event, making use of people whose follow-up ends before it is known whether the event happened.
What it is
Survival analysis studies the time until an event (death, relapse, cure, discharge), not only whether the event happened. Its central feature is censoring: people leave follow-up before the event because the study ended, they were lost or they withdrew. Survival methods use each person’s information for as long as they were observed, rather than discarding it or counting it as if no event had occurred.
Worked example
- Data: 6 patients. Deaths at 4, 9 and 15 months; lost at 6 and 10 months; one is alive at 24 months when the study closes.
- Error 1: dropping the 2 lost patients gives 3 deaths out of 4 = 75%; it throws away months of survival information.
- Error 2: counting them as alive gives 3 of 6 = 50%; it assumes they survived longer than is known.
- Correct: at 4 months, 6 at risk and 1 death: 5/6 = 0.833.
- At 6 months one is censored; at 9 months 4 remain at risk and 1 dies: 0.833 × 3/4 = 0.625.
- At 10 months another is censored; at 15 months 2 remain and 1 dies: 0.625 × 1/2 = 0.3125 (rounded, 31%).
- The curve drops below 50% at 15 months: median survival = 15 months.
- Reading: with censoring, survival is estimated step by step from those still at risk, not from simple counts.
Markers
- censoring
- median
- S(t)
Common pitfalls
- Dropping censored patients or counting them as event-free.
- Ignoring informative censoring: if the sickest drop out, survival is overestimated.
- Reporting mean survival instead of the median with censored data.
Test yourself
Think of the answer, then tap the question to see it.
What is a censored observation?
One from a person whose follow-up ended without the event: they are known to be event-free until then, but not what happened afterwards.
What does survival analysis assume about censoring?
That it is non-informative: those leaving follow-up have the same risk as those who stay.
What is median survival?
The time at which the survival curve falls to 50%: half the people have had the event.
Why are censored patients not discarded?
Because they carry useful information (they survived until censoring); dropping them biases the estimate and wastes data.
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: Censoring (NIST/SEMATECH e-Handbook of Statistical Methods, National Institute of Standards and Technology, 2012); Empirical model fitting - distribution free (Kaplan-Meier) approach (NIST/SEMATECH e-Handbook of Statistical Methods, National Institute of Standards and Technology, 2012); Chapter 6: Choosing effect measures and computing estimates of effect (Cochrane, 2024).
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Representative model, for educational purposes only.