Kaplan-Meier analysis is a non-parametric method for estimating a survival function from time-to-event data. It shows for each time point the estimated probability of remaining event-free until then, taking censored observations into account. In clinical trials, it is frequently used for endpoints such as overall survival, progression-free survival or time to the first defined event.
Basic principle of stepwise estimation
The Kaplan-Meier curve changes stepwise with each observed event. At each event time point, the conditional probability of remaining event-free is determined from the number of individuals still observed at that time point and the number of events. The successive conditional probabilities are multiplied. This creates an estimate of the survival function over time.
The curve not only depicts the proportion with an event, but the temporal distribution of the events. As a result, trials with the same number of events at the end of follow-up can show different courses. Indications of the number of participants still under observation, confidence intervals and the predefined analysis population are common. A median can only be estimated if the curve reaches the 50 percent mark.
An observation is censored if no event is documented for a participating individual up to a specified time point, but the further event time is not known. Reasons can be the end of follow-up, withdrawal or loss to follow-up. The individual contributes information to the risk set until the time of censoring, but not thereafter. Censoring is not synonymous with an event-free completion.
For its usual interpretation, the analysis assumes that censoring is not informative in the given context, i.e., based on the considered information, it is not systematically related to the future event time. Different follow-up or incomplete recording can jeopardize this assumption. Event definition, censoring rules, handling of subsequent therapies and data cuts must therefore be clearly defined in the protocol and statistical analysis plan.
Comparison of treatment groups
Kaplan-Meier curves allow for the graphical comparison of groups, but on their own do not provide a complete analysis of the effect. A log-rank test can test a predefined test hypothesis for different survival curves. A hazard ratio from a suitable model supplements the presentation with a relative measure of event rates. Both methods answer related but not identical questions and are based on assumptions that should be tested and transparently reported.
In the case of crossing curves or a treatment effect changing over time, a single hazard ratio can be difficult to interpret. Then, depending on the clinical question, predefined additional key figures or analyses may be necessary. With competing risks, it must be chosen particularly carefully which event probability or which effect is to be estimated; a standard Kaplan-Meier curve does not treat a competing event as the event of interest.
Differentiation from survival analysis
Survival analysis refers to the entire methodological field for data where the time period until an event is of interest and observations can be censored. This includes, in addition to Kaplan-Meier estimation, for example regression models, tests for group comparisons, models with time-dependent covariates and methods for competing risks.
Kaplan-Meier analysis is thus a concrete method within survival analysis. It estimates and visualizes the survival function, but does not automatically model the influence of multiple covariates and does not solve every question regarding time-to-event data. The term survival analysis must therefore not be used as a synonym for the Kaplan-Meier curve.
Relevance for clinical trials
Consistent event assessments and careful follow-up are crucial for the validity of a Kaplan-Meier analysis. The data review must clarify whether data on event date, censoring date and status are available completely and plausibly. In confirmatory trials, the primary analysis should be specified in advance; supplementary presentations and sensitivity analyses serve the transparent classification of the results.
Full-service CROs such as Mediconomics support the definition of time-dependent endpoints, the creation of the statistical analysis plan and the programming of Kaplan-Meier tables and graphs. They coordinate data management, medical evaluation and biostatistics, verify the consistency of event and follow-up data and prepare the analyses for the clinical study report.
Frequently Asked Questions (FAQ)
Does every mark on the curve show an event?
No. Marks frequently indicate censored observations; downward steps result from observations defined as an event.
Can a Kaplan-Meier curve automatically compensate for missing data?
No. It considers censoring under certain assumptions. Informative dropouts or incorrect data can bias the estimation.
Is the median always the most important value?
No. It is only one possible summary. The entire course of the curve and the clinical question can be more important. Additionally, it must be considered whether the follow-up in both groups was sufficiently long and equivalent. The curve shows an estimation from the observed data, no guarantee for a course outside the observation period.
Regulatory references
- ICH E9, Statistical Principles for Clinical Trials — requires pre-planned, comprehensible analyses of clinical endpoints.
- ICH E9(R1), Addendum on Estimands and Sensitivity Analysis in Clinical Trials — addresses time-to-event data within the framework of clear estimands.
- ICH E6(R3), Guideline for Good Clinical Practice — requires a documented handling of data, evaluations and analysis sets.
- Cochrane Handbook, Chapter 6 — explains time-to-event data and effect measures used for them.