Survival Sample Size Calculator
Sizes a time-to-event (survival) trial by first determining the number of events required to detect a target hazard ratio with a log-rank test, then converting events into the total number of participants given the control median, accrual, and follow-up. Supports superiority and non-inferiority designs with equal or unequal allocation.
How it works
The required number of events is computed with the Schoenfeld (1983) formula, with the Freedman (1982) formula reported alongside as a more conservative comparison. Because power in a survival trial is driven by events rather than patients, the calculator translates the event target into a patient count using an event-probability model, and reports the study duration. You can solve for sample size, achieved power, or the minimum detectable hazard ratio.
When to use it
- Your primary endpoint is time-to-event (e.g., overall survival, progression-free survival, time to a clinical event).
- You expect an approximately constant hazard ratio between arms over the follow-up period.
- You need to justify events, patient count, and study duration together for a protocol or statistical analysis plan.
Assumptions & limitations
- The log-rank/Schoenfeld approach assumes proportional hazards; under non-proportional hazards (e.g., delayed or crossing effects) the event count is only illustrative and simulation of operating characteristics is recommended.
- The event-to-patient conversion assumes exponential survival with uniform accrual; non-exponential survival will misestimate the patient count more than the event count.
- Freedman and Schoenfeld can differ, especially for hazard ratios far from 1; the two are shown side by side rather than averaged.
- This dedicated tool honors one- vs two-sided testing and both formulas — it is distinct from the free sample-size calculator's survival tab, which is Schoenfeld-only and two-sided.
For the full methodology, derivation, and worked examples, read the complete guide.