Calculator Inputs
Example Data Table
This example illustrates a balanced design under exponential survival assumptions.
| Scenario | Alpha | Hazard ratio | Control median | Accrual | Follow-up | Dropout | Total sample | Illustrative power |
|---|---|---|---|---|---|---|---|---|
| Balanced superiority design | 0.05 two-sided | 0.65 | 18 months | 12 months | 12 months | 8% yearly | 420 | About 80.1% |
| More modest treatment effect | 0.05 two-sided | 0.75 | 18 months | 12 months | 12 months | 8% yearly | 800 | About 75.5% |
| Stronger effect, shorter follow-up | 0.05 two-sided | 0.60 | 18 months | 12 months | 9 months | 5% yearly | 350 | About 79% to 83% |
Formula Used
1) Convert median survival to hazard.
λcontrol = ln(2) / Mediancontrol
λtreatment = HR × λcontrol
2) Convert annual dropout to a monthly hazard.
δ = -ln(1 - d) / 12
3) Average observed event probability under uniform accrual.
qg = (λg / (λg + δ)) × [1 - (e-(λg+δ)F - e-(λg+δ)(F+A)) / ((λg+δ)A)]
4) Overall expected event fraction.
q = pcontrolqcontrol + ptreatmentqtreatment
5) Expected observed events.
D = N × q
6) Log-rank information formulas.
Required events: Dreq = (z1-α/s + z1-β)² / [(ln(HR))² p(1-p)]
Power: Φ[√(D × (ln(HR))² × p(1-p)) - z1-α/s]
Here, A is accrual months, F is additional follow-up months, d is annual dropout proportion, p is the treatment allocation proportion, and Φ is the standard normal cumulative distribution.
How to Use This Calculator
- Choose whether you want to estimate achieved power or required sample size.
- Enter alpha and select one-sided or two-sided testing.
- Provide the hazard ratio for treatment relative to control.
- Enter the control median survival in months.
- Add accrual duration, additional follow-up, annual dropout, and treatment-control allocation ratio.
- If estimating power, enter the total sample size.
- If estimating sample size, enter the target power.
- Submit the form to view the result summary, event estimates, and the survival curve plot.
FAQs
1) What does this calculator estimate?
It estimates study power from a planned sample size or estimates required sample size from a target power. It also shows expected event fractions, observed events, implied treatment median survival, and a visual survival curve comparison.
2) Which statistical method is being approximated?
The calculator uses a log-rank style approximation under proportional hazards. Sample size and power are driven by expected information events rather than only by enrolled participants.
3) Why do accrual and follow-up change power?
Longer observation produces more events, and more events increase information. Uniform accrual means late enrollees contribute less follow-up time than early enrollees, so the event fraction depends strongly on both timings.
4) How is dropout handled here?
Annual dropout is converted into an independent censoring hazard. Higher dropout lowers the observed event fraction, which usually raises the required sample size or reduces achieved power.
5) Can I use a hazard ratio greater than 1?
Yes. A value above 1 means higher hazard in treatment than control. Power is driven by the absolute distance of the hazard ratio from 1, not only by whether treatment is beneficial.
6) When is a one-sided alpha appropriate?
A one-sided test may be justified when only one direction is scientifically meaningful and that choice is pre-specified in the protocol. Many confirmatory trials still prefer two-sided testing.
7) Are exponential survival curves always realistic?
No. Exponential curves assume a constant hazard over time. They are useful for rapid planning, but complex settings may require more flexible survival shapes, simulation, or piecewise hazards.
8) What should I do after getting a result?
Use the result as a planning benchmark, then stress-test assumptions. Try alternative hazard ratios, dropout rates, and follow-up periods to see how sensitive your design is before finalizing the protocol.