Kaplan-Meier Survival Analysis

Estimate and compare survival functions over time — for time-to-event data with censored observations.

Kaplan-Meier Survival Analysis estimates the probability of surviving (or remaining event-free) beyond each observed time point in a sample that includes censored observations — cases where the event had not yet occurred at the last follow-up. The product-limit estimator handles censoring correctly; standard descriptive statistics cannot.

The method is used in clinical trials (time to death, relapse, or recovery), engineering (time to equipment failure), and social sciences (time to employment, marriage, or re-offending). When comparing two or more groups, the log-rank test assesses whether survival curves differ significantly.

StatRyx computes Kaplan-Meier curves for each group, median survival times with 95% CIs, and the log-rank chi-square test — all plotted with step-function curves and censoring marks, formatted in APA 7 style.

Kaplan-Meier analysis estimates the probability of remaining event-free over time while correctly handling censored cases — participants who left the study or had not had the event when it ended. The survival curve drops at each event; censored cases are marked but do not count as events. The log-rank test compares whole curves between groups, and the median survival time is where a curve crosses 50%.

When to use the Kaplan-Meier Survival Analysis

You have time-to-event data where some participants did not experience the event by the end of follow-up (censored)
You want to estimate the probability of surviving to each time point
You want to compare survival between two or more groups
You compare time to dropout, relapse or graduation between two programmes
You need a survival curve figure for a clinical or educational follow-up study

When not to use it

You want to control for multiple covariates simultaneously — use Cox Proportional Hazards Regression instead
Your outcome is continuous, not time-to-event — use Linear regression or ANOVA instead
The hazard ratio between groups changes over time (curves cross) — use Report restricted mean survival time or a time-varying model instead

Worked example

Group	n	Events	Censored	Median Survival	95% CI
CBT	65	42	23	18.4 mo	[14.2, 22.6]
Pharmacotherapy	63	51	12	12.1 mo	[9.4, 14.8]

How to report it (APA 7)

Kaplan-Meier survival analysis was conducted to compare time to relapse between CBT and pharmacotherapy groups. The log-rank test indicated a significant difference in survival curves, χ²(1) = 7.43, p = .006. Median survival was 18.4 months for CBT (95% CI [14.2, 22.6]) vs. 12.1 months for pharmacotherapy (95% CI [9.4, 14.8]).

Frequently asked questions

Is Kaplan-Meier analysis free on StatRyx?

Yes. You can run it without an account (3 free analyses), and a free account adds 10 more — a one-time allowance, no payment needed. Every result includes the APA 7 write-up. Paid plans (Student from $9/month) add more analyses and Word, PDF and Excel export.

What is censoring?

A censored observation is one where the event had not occurred by the end of follow-up. The participant was last known to be event-free at that time. Kaplan-Meier handles censoring correctly; simply dropping censored cases would bias results.

What is median survival?

Median survival is the time at which the estimated survival probability falls to 0.50 — i.e., when half the group has experienced the event. It is preferred over mean survival because survival distributions are typically right-skewed.

How do I report a Kaplan-Meier analysis in APA 7?

Give the number of events and censored cases, the median survival per group, and the log-rank test: "Median time to relapse was 14 months in the CBT group and 8 months in the medication group, log-rank χ²(1) = 6.21, p = .013." Include the survival curve as a figure.

What is the difference between Kaplan-Meier and Cox regression?

Kaplan-Meier describes and compares survival curves for groups without adjusting for anything else. Cox proportional hazards regression estimates hazard ratios while controlling for several covariates at once. A typical paper shows Kaplan-Meier curves and then a Cox model.

Run a Kaplan-Meier Survival Analysis on your data →