Advanced Survival Power Calculator

Calculator inputs

Alpha level

Typical choice is 0.05.

Test sidedness

Choose the testing direction.

Total sample size

Total participants across both arms.

Treatment:control ratio

Use 1 for equal allocation.

Hazard ratio

Below 1 suggests benefit.

Control median survival (months)

Assumes exponential survival.

Accrual period (months)

Uniform entry is assumed.

Additional follow-up (months)

Added after accrual ends.

Annual dropout rate (%)

Converted into a censoring hazard.

Target power (%)

Used for event and sample targets.

Reset

Formula used

This calculator uses the log-rank test approximation with an exponential survival model, uniform accrual, and exponential dropout censoring.

1) Convert median survival to hazard.

λ_control = ln(2) / Median_control

λ_treatment = HR × λ_control

2) Convert annual dropout to censoring hazard.

μ = -ln(1 - dropout rate) / 12

3) Average event probability under uniform accrual.

P(event) = [λ / (λ + μ)] × [1 - exp(-(λ + μ)F) × (1 - exp(-(λ + μ)A)) / ((λ + μ)A)]

Here, A is accrual and F is additional follow-up.

4) Expected events.

D = n_controlP_control + n_treatmentP_treatment

5) Log-rank power and required events.

Power = Φ( √(D × p × (1-p)) × |ln(HR)| - z_α )

D_required = (z_α + z_β)² / [p(1-p)(ln(HR))²]

The method is approximate and most useful during study planning.

How to use this calculator

Enter the significance level and choose one-sided or two-sided testing.
Provide the total sample size and the treatment-to-control allocation ratio.
Enter the hazard ratio you want to evaluate.
Add the control median survival in months.
Set the accrual period and additional follow-up.
Include the expected annual dropout percentage.
Choose a target power percentage for planning outputs.
Click the button to view power, expected events, sample targets, downloadable tables, and graphs.

Example data table

Scenario	Total N	Allocation	HR	Control Median	Accrual	Follow-up	Dropout
Balanced oncology study	300	1:1	0.75	18 months	12 months	12 months	5%
Smaller signal-seeking study	180	1:1	0.70	14 months	10 months	10 months	6%
Unequal allocation design	360	2:1	0.80	20 months	15 months	12 months	4%
Longer follow-up design	420	1:1	0.78	22 months	18 months	18 months	3%

FAQs

1) What does this calculator estimate?

It estimates approximate log-rank power, expected event counts, required events, and an approximate sample size for time-to-event studies.

2) What survival model is assumed?

It assumes exponential survival in both arms, which means each arm has a constant hazard rate over time.

3) Why is median survival required?

The control median converts into a baseline hazard. The hazard ratio then scales that baseline to create the treatment hazard.

4) Why does dropout matter?

Dropout creates censoring, which reduces the average event probability and usually lowers expected information and power.

5) Why is power driven by events?

For log-rank testing, the informative quantity is usually the number of observed events, not just the enrolled sample size.

6) What does the detectable hazard ratio mean?

It is the smallest effect size approximately detectable at the selected alpha and target power with the current event information.

7) Is this enough for a final protocol?

It is best for planning and quick comparisons. Final protocol work often needs simulation or dedicated survival design software.

8) Can I use unequal allocation?

Yes. Enter the treatment-to-control ratio, such as 2 for a 2:1 design or 0.5 for a 1:2 design.