The ICU clock that never stops
You check the monitor at 06:00. Patient 1 is still alive, MAP 70, ventilator on. At 10:00, Patient 2 is extubated and transferred out of the ICU. At 14:00, Patient 3 dies. At 16:00, Patient 4 is transferred to a ward and is censored (still alive, but no longer in the study). At 18:00, Patient 5 is still alive, still in the ICU.
When you read a paper that says “Kaplan‑Meier curve shows median survival 12 days,” it means the analysis counted only the time each patient was at risk — from enrollment until death, transfer out, or the end of follow‑up. The curve drops only at the exact times when an event (death) occurs; censored points are not counted as events.
In the ICU, censoring is common: patients are transferred, die, or become lost to follow‑up. The Kaplan‑Meier estimator handles this gracefully, but only if the paper explicitly states how censoring was handled and how the curve was built.
The two faces of censoring
Censoring type | Definition | Typical ICU example |
Right censoring | Patient is still alive (or event‑free) at the last time point measured. | Patient transferred to another unit on day 12, still alive; follow‑up ends. |
Left censoring | Event occurred before the start of observation (rare in ICU). | Patient died before ICU admission was recorded. |
Interval censoring | Exact time of event unknown, only a time window is known. | Patient died sometime between day 10 and day 12; exact time unknown. |
In most ICU RCTs and cohort studies, right censoring is the only type used. If a paper mentions “censored at 28 days” or “censored at discharge,” that is right censoring.
The Kaplan‑Meier estimator in plain language
- Order all patients by the time of the first event (death) or censoring.
- At each event time, compute the proportion of patients still at risk just before that time.
- Multiply the survival probabilities (1 − events/total at risk) across all event times to get the survival curve.
Mathematically, the Kaplan‑Meier estimate for survival at time t is
[ (t) = _{t_i t} (1 - ) ]
where (d_i) is the number of events at time (t_i) and (n_i) is the number at risk just before (t_i).
If you plot the curve, the y‑axis is survival probability (0–1) and the x‑axis is time (days, hours, etc.). The curve steps down only at event times; it is flat during periods with no events.
Why Kaplan‑Meier matters in the ICU
- Mortality curves are the most common survival outcome in sepsis, trauma, and cardiac arrest trials.
- Ventilator‑free days, ICU‑free days, and time to discharge are also time‑to‑event outcomes.
- Censoring is inevitable: patients may be transferred, die, or become lost; Kaplan‑Meier accommodates this without discarding data.
If a paper reports a Kaplan‑Meier curve but omits how censoring was handled, or if it treats censored patients as events, the survival curve is biased and the median survival estimate is unreliable.
Common pitfalls in Kaplan‑Meier curves
- Incorrect censoring definition – Some papers treat “transfer out” as an event, artificially inflating mortality.
- Failure to report censoring numbers – You cannot assess the risk of bias if you cannot see how many patients were censored and when.
- Improper handling of ties – If multiple events occur at the same time, the Kaplan‑Meier method averages the risk set; the paper should state how this was done.
- Using Kaplan‑Meier for non‑time‑to‑event outcomes – Applying it to a binary outcome (e.g., mortality at 30 days) without converting to time‑to‑event is invalid.
How to read a Kaplan‑Meier curve
- Identify the axes – X = time, Y = survival probability.
- Locate the median – The time point where the curve crosses 0.5.
- Check the number at risk – A table or line on the plot shows how many patients are at risk at several time points. A rapid drop in “at risk” indicates many censored patients early, which may bias the curve.
- Examine the confidence limits – Most Kaplan‑Meier plots include 95% CI bands; if they are very wide, the estimate is imprecise.
Appraisal checklist for Kaplan‑Meier
- Is the curve based on right censoring only?
- Are the numbers at risk reported (e.g., a table or line on the plot)?
- Are the 95% confidence limits shown?
- Are censoring events clearly defined (e.g., “censored at discharge”) and not treated as events?
- Is the median survival reported with its CI? (Often omitted in short reports.)
- Is the analysis pre‑specified (i.e., the survival analysis was part of the protocol, not an ad‑hoc add‑on)?
Open‑access resources
- StatPearls – “Survival analysis” (NBK551995): free, step‑by‑step description of Kaplan‑Meier, censoring, and interpretation. https://www.ncbi.nlm.nih.gov/books/NBK551995/
- OpenIntro Statistics – Chapter 7 “Survival analysis” (free PDF): clear derivation of Kaplan‑Meier, handling of ties, and confidence limits. https://www.openintro.org/stat/textbook.php
- PMC3122736 – “The significance of significance testing” (free full text): includes a concise discussion of survival analysis and Kaplan‑Meier in clinical trials. https://doi.org/10.1016/j.jclinepi.2009.08.001 (PMCID: PMC2765276)
- PMC10457100 – “Doubly robust estimators for generalizing treatment effects on survival outcomes” (free): shows how to combine Kaplan‑Meier with regression for target‑population analysis. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10457100/
Next: Chapter 11 — Survival analysis II: Cox proportional hazards