Log-Rank Test for Comparing Survival Curves
Also known as: Mantel log-rank test, Mantel-Cox test, log-rank sağkalım testi, Log-Rank Testi
The log-rank test, developed by Nathan Mantel in 1966, is a non-parametric hypothesis test that compares the overall survival experience of two or more groups throughout the entire follow-up period. It is the standard companion to Kaplan-Meier curves and determines whether observed differences between curves are statistically meaningful.
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When to use it
Use the log-rank test when you have right-censored time-to-event data from two or more independent groups and you want to test whether their overall survival distributions differ. The key assumption is proportional hazards: the hazard ratio between groups must remain approximately constant over time, meaning the survival curves should not cross. Censoring must be non-informative — subjects who are censored should carry the same future risk as those who remain under observation. Each group should have at least ten events to give the test adequate power.
Strengths & limitations
- Makes no parametric assumptions about the shape of the survival distribution — only the order of event times matters.
- Handles right-censored observations correctly, retaining the information they provide rather than discarding them.
- The standard and widely recognised test for comparing Kaplan-Meier curves, accepted by reviewers in health, social, and engineering sciences.
- Sensitive only to a specific alternative — a constant proportional difference in hazard. When the hazard ratio changes over time (non-proportional hazards), the test loses power.
- Does not produce an effect-size estimate; a separate Cox regression is needed to obtain a hazard ratio with confidence interval.
- Cannot adjust for confounding variables. If groups differ on baseline characteristics, stratified log-rank or Cox regression is required.
Frequently asked
What does the log-rank test actually compare?
It compares the entire survival experience of groups over the full follow-up period, not just survival at a single time point. At each event time it asks whether the observed number of events in each group matches what would be expected if all groups shared the same survival distribution. The accumulated discrepancy produces the chi-square test statistic.
What is the proportional-hazards assumption, and how do I check it?
The proportional-hazards assumption requires that the hazard ratio between groups remains constant over time, which in practice means the Kaplan-Meier curves should not cross. The standard graphical check is a log-log plot: plot log(−log(S(t))) against log(t) for each group and inspect whether the resulting curves are approximately parallel. Crossing lines are a warning that the log-rank test may give misleading results.
What should I do after a significant log-rank result?
Report the chi-square statistic with its degrees of freedom and p-value, then follow up with Cox regression to obtain a hazard ratio and 95% confidence interval — the log-rank test alone does not quantify the size of the difference. If covariates need to be controlled, use the Cox model directly. If a confounding variable is suspected, a stratified log-rank test can adjust for it while remaining non-parametric.
How does the log-rank test differ from the Wilcoxon (Breslow) test for survival data?
Both compare survival curves, but they weight event times differently. The log-rank test weights all event times equally, giving it the best power when the proportional-hazards assumption holds. The Wilcoxon-Breslow-Gehan test weights by the number at risk at each event time, so it emphasises early differences. When curves diverge early and then converge, Wilcoxon-Breslow may be more sensitive; when differences are constant or emerge later, log-rank is preferred.
Sources
- Mantel, N. (1966). Evaluation of Survival Data and Two New Rank Order Statistics Arising in Its Consideration. Cancer Chemotherapy Reports, 50(3), 163–170. link ↗
- Kleinbaum, D. G. & Klein, M. (2012). Survival Analysis: A Self-Learning Text (3rd ed.). Springer. ISBN: 978-1441966452
How to cite this page
ScholarGate. (2026, June 1). Log-Rank Test for Comparing Survival Curves. ScholarGate. https://scholargate.app/en/survival/log-rank-test
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Kaplan-MeierSurvival↔ compare
- Nelson-Aalen EstimatorSurvival↔ compare