Log-Rank Test Calculator
Enter event times and censoring indicators for two groups to compare their survival curves. The log-rank test (also called the Mantel-Cox test) determines whether the two groups have statistically different survival experiences.
What is the Log-Rank Test?
The log-rank test is the most widely used method for comparing survival curves between two or more groups. It is a non-parametric test that works well even with censored data, which is common in clinical trials and time-to-event studies.
How it works:
- At each distinct event time, count observed events and subjects at risk in each group
- Calculate expected events for each group under the null hypothesis (equal survival)
- Sum the observed-minus-expected differences across all event times
- Compute the test statistic: χ² = [Σ(O - E)]² / Σ Variance
Key features:
- Handles right-censored data (subjects lost to follow-up or still event-free at study end)
- Non-parametric: no assumption about the shape of the survival distribution
- Tests the null hypothesis that both groups have the same survival function
- Most powerful when the hazard ratio is constant over time (proportional hazards)
Interpreting results:
A significant result (p < 0.05) means the survival experiences of the two groups are statistically different. It does not tell you which group survives longer; compare the observed vs. expected events to determine direction.
Common applications:
- Clinical trials comparing treatments
- Oncology studies comparing cancer therapies
- Engineering reliability testing
- Any study measuring time until an event