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Reporting Survival Analysis: Kaplan-Meier Curves and Hazard Ratios

DE By Directive Editorial Team, Directive Publications ·27 Sep 2026 ·7 min read
Reporting Survival Analysis: Kaplan-Meier Curves and Hazard Ratios

To report Kaplan-Meier survival analysis, define time zero and the event, state how and why data were censored, and show the curves with numbers at risk and confidence intervals. Give median survival with its interval, or say it was not reached. Pair the log-rank p-value with a hazard ratio and its confidence interval, after checking proportional hazards.

Survival analysis is the analysis of time until a defined event, and it allows for participants who have not had the event by the end of follow-up. The event need not be death. Which test to run is covered in our decision guide to choosing a statistical test; this guide covers what to write once the analysis is done.

The Statistical Analyses and Methods in the Published Literature (SAMPL) guidelines, listed by the EQUATOR Network, name the basics: the events that start and end the time analysed, the censoring rules, the methods used and a check of their assumptions.

Define time zero, the event and the data cut-off in the Methods

Time zero is the moment each participant's clock starts. In a randomised trial it is typically the date of randomisation; in a cohort it might be the date of diagnosis or surgery. Every survival time is measured from it, so name it exactly.

Then define the event. Death from any cause and death from the disease are different endpoints, and a composite endpoint needs every component listed. Finally, give the data cut-off: the last date on which events were counted.

Say who was censored, when and why

A survival time is censored when observation stops before the event is seen, so its true length is unknown. Three situations produce it: the study closes while the participant is still event-free, the participant is lost to follow-up, or some other event rules out further observation.

Standard survival methods rely on non-informative censoring: someone censored at month 10 should face the same later risk as someone still followed then. That fails when leaving is tied to prognosis, for example withdrawal because of treatment side effects or declining health. State the censoring rule for each reason in the Methods. Give the numbers censored for each reason, by group, in the Results.

Never drop participants lost to follow-up, or count them as event-free until the end of the study, without saying so. The STROBE explanation and elaboration paper accepts either shortcut only when few patients are lost. It asks authors to report how many were lost and the censoring strategy used.

Draw Kaplan-Meier curves with numbers at risk

The Kaplan-Meier, or product-limit, estimate is a step curve of the proportion still event-free, and censored participants count in the risk set until they leave. SAMPL asks for each group's estimated survival probability at chosen time points, with a confidence interval (CI), and for the number at risk at each time.

In the KMunicate stakeholder survey, published in 2019, respondents favoured plots with a CI around each curve and a table beneath it. That table gave the numbers at risk, censored and with an event at regular time points. Its authors make no explicit recommendations, but encourage researchers to consider these formats.

  • Do not over-read the right-hand tail. Few participants remain at risk there, so late separation between curves is more likely to be chance.
  • Never truncate the y-axis of a downward survival plot to magnify a difference. Ending the time axis before the last follow-up can be reasonable, as confidence limits balloon there.
  • When events are uncommon, consider a rising cumulative incidence curve (one minus the survival estimate). The STROBE explanation and elaboration paper suggests this may be preferable when the event rate is below about 30%.

Legends, resolution and other figure rules are in preparing figures and tables for publication.

Give median survival with its interval, or write "not reached"

Median survival is the time at which the Kaplan-Meier curve first drops to 0.5. Because survival times tend to be skewed, the median, not the mean, is the usual summary. Report each group's median with its 95% CI for comparison with other studies.

If estimated survival stays above 50% at the end of follow-up, the median cannot be calculated. Write "median not reached" and give survival probabilities at fixed time points instead; never substitute the last follow-up time. A median also cannot describe a long plateau at the end of the curve.

Do not compare groups by checking whether their median intervals overlap. Use the log-rank test or a hazard ratio with its CI; the British Journal of Cancer survival analysis tutorial advises against comparing the intervals.

Estimate median follow-up with the reverse Kaplan-Meier method

Median follow-up tells readers how mature the data are. Taking the median observation time, whether across all participants or only those censored, usually gives too low a figure. Early deaths, for example, cut observation short.

The reverse Kaplan-Meier method, described in Controlled Clinical Trials in 1996, is more robust. It swaps the roles: being censored counts as the event, and a death as a censored time. Name the method whenever you report median follow-up. For cohort studies, STROBE item 14(c) also asks you to summarise follow-up time, for example as the average and the total amount.

Pair the log-rank p-value with a checked hazard ratio

The log-rank test compares two or more survival curves. With two groups, its null hypothesis is a hazard ratio of 1: equal event rates throughout follow-up. It gives a p-value but no effect size, so report a hazard ratio with its CI beside it. The CONSORT 2025 explanation and elaboration paper accepts the hazard ratio or the difference in median survival as the effect size, each with a CI.

A Cox proportional hazards model assumes that the hazard in one group is a constant multiple of the hazard in the other. A hazard ratio above 1 means a higher event hazard and shorter survival. It is a ratio of hazards, not of median survival times or of risks at a fixed time. SAMPL asks you to name the model and give each explanatory variable's hazard ratio with a CI. In an observational study, STROBE item 16(a) asks for unadjusted and, if applicable, confounder-adjusted estimates, and for which confounders were adjusted for and why; adjustment does not establish causation. What to print beside a hazard ratio is set out in reporting p-values, confidence intervals and effect sizes.

Check the proportional hazards assumption and say how. Accepted checks, each shown in a tutorial on checking proportional hazards, are log(-log(survival)) plotted against log(time), where the lines should be parallel, and formal tests such as the scaled Schoenfeld residuals test. Crossing curves suggest the hazards are not proportional, so do not report a single hazard ratio without this check. Options then include time-dependent covariates, a stratified model or a model without the assumption. Stratifying on a variable removes its hazard ratio from the output, so reserve stratification for a variable whose effect you do not need to report. The log-rank test shares the proportional hazards assumption, though it tolerates minor deviations.

A copyable checklist for reporting Kaplan-Meier survival analysis

Copy the table and replace the last column with your own study. The study below is invented to illustrate the structure; its numbers are not real data. It is a retrospective cohort of 235 adults treated with approach A (n = 120) or approach B (n = 115), and the event is death from any cause.

ItemWhereWhat to stateInvented example
Time zeroMethodsWhen each participant's clock startsDate of first treatment
EventMethodsExact definition; every part of a composite endpointDeath from any cause
Data cut-offMethodsLast date on which events were counted30 June 2025
Censoring rulesMethodsEach reason for censoring and the date usedAlive at cut-off: censored at cut-off. Lost: censored at last contact
Censoring countsResultsNumber censored for each reason, by groupLost to follow-up 7 (A), 5 (B); alive at cut-off 68 (A), 47 (B)
Methods namedMethodsSurvival estimate, test, model and softwareKaplan-Meier estimate, log-rank test, Cox model
Assumption checkMethods and ResultsHow proportional hazards was checked, and the resultScaled Schoenfeld residuals test p = 0.41; log(-log) curves parallel
Follow-upResultsMedian follow-up and the method52.6 months by reverse Kaplan-Meier (median observation time 39.1 months)
Survival at fixed timesResultsProbability with 95% CI, by group3-year: 71% (95% CI 61 to 79) with A; 55% (95% CI 45 to 65) with B
Median survivalResultsMedian with 95% CI, or not reachedA: not reached. B: 42.4 months (95% CI 35.6 to 50.8)
ComparisonResultsEvents per group, log-rank p-value, hazard ratio with 95% CI, unadjusted and adjustedDeaths 45 (A), 63 (B); log-rank p = 0.005; hazard ratio, B versus A, 1.72 (95% CI 1.17 to 2.52) unadjusted and 1.58 (95% CI 1.06 to 2.35) adjusted for age, sex and comorbidity score

Show the numbers at risk beneath the plot, aligned with the time axis.

Months since treatment01224364860
Approach A, number at risk12010491745021
Approach B, number at risk1159275553413

A Results paragraph can then follow this template. Write "not reached" where a group's curve never fell to 0.5.

Over a median follow-up of [months] months (reverse Kaplan-Meier), [n/N] participants in [group A] and [n/N] in [group B] had [the event]; [n] and [n] were lost to follow-up. Median [endpoint] was [months] (95% CI [lower] to [upper]) in [group A] and [months] (95% CI [lower] to [upper]) in [group B]. The hazard ratio for [group B] versus [group A] was [estimate] (95% CI [lower] to [upper]; log-rank p = [exact value]). After adjustment for [covariates], the hazard ratio was [estimate] (95% CI [lower] to [upper]). Proportional hazards were checked with [method].

Our author guidelines ask you to match the manuscript to the relevant EQUATOR checklist. For a survival study, that means STROBE for an observational cohort and CONSORT 2025 for a randomised trial. Oncology papers that report response and toxicity beside survival should also follow RECIST and CTCAE reporting. If you spot an error in this guide, please report the problem to us.

For a binary outcome analysed without time-to-event methods, odds ratio vs relative risk explains which ratio to report and how to word it.

Frequently Asked Questions

What should I write when median survival is not reached?
Write that the median was not reached and give survival probabilities with 95% confidence intervals at fixed time points, such as one and three years. The median cannot be calculated when estimated survival stays above 50% at the end of follow-up. Do not replace it with the longest follow-up time, which is not a median.
Why is the reverse Kaplan-Meier method used to estimate median follow-up?
The median observation time of all participants is shortened by early deaths, so it understates how long the study followed people. The reverse Kaplan-Meier method treats censoring as the event and deaths as censored times, which gives a more robust estimate. Name the method whenever you report median follow-up.
Is a log-rank p-value enough to compare two survival curves?
No. The log-rank test gives a p-value but no measure of how large the difference is. Report a hazard ratio with its 95% confidence interval beside it, for example from a Cox proportional hazards model, and state how the proportional hazards assumption was checked.
Does a Kaplan-Meier plot need numbers at risk and confidence intervals?
Yes. The Statistical Analyses and Methods in the Published Literature (SAMPL) guidelines ask for survival probabilities with confidence intervals and the number at risk at each time point, for each group. Numbers at risk show how few participants support the right-hand end of the curve, where the estimate is least certain.
DE
Directive Editorial Team
Directive Publications

The editorial team at Directive Publications — an international open-access publisher of peer-reviewed medical and scientific journals.

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