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Survival Analysis · SURV-1S

Sample Size for Testing One Survival Probability

Plan a one-sided single-arm test of a Kaplan–Meier survival probability at one prespecified landmark time.

1. Planning setup

Use the same unit for the landmark time, accrual, and follow-up.

2. Information obtained from previous study / literature

3. Information decided by the researcher

Enter probabilities as percentages. The method assumes uniform accrual, independent administrative censoring, and exponential survival under the alternative.

4. Results

Enter the study assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A researcher tests whether five-year disease-free survival after a new treatment exceeds a historical benchmark while accounting for censoring.

Formula and methodological note

Uses the Nagashima–Noma–Sato–Gosho one-sample Kaplan–Meier arcsine square-root method. It is a directional, one-sided fixed-time survival-probability calculation.

Administrative censoring is included in the variance calculation. Random loss to follow-up is not modelled there and is handled only through the separate recruitment inflation. This calculator supports planning and does not replace statistical consultation.

It does not cover median survival, complete survival-curve tests, one-sample log-rank tests, two-sided designs, competing risks, recurrent events, cluster designs, interim monitoring, or arbitrary non-exponential survival planning.

Method references

  1. Nagashima K, Noma H, Sato Y, Gosho M. Sample size calculations for single-arm survival studies using transformations of the Kaplan–Meier estimator. Pharm Stat. 2021;20:499–511.
  2. Kaplan EL, Meier P. Nonparametric estimation from incomplete observations. J Am Stat Assoc. 1958;53:457–481.
  3. Breslow N, Crowley J. A large sample study of the life table and product-limit estimates under random censorship. Ann Stat. 1974;2:437–453.
  4. Thomas DR, Grunkemeier GL. Confidence interval estimation of survival probabilities for censored data. J Am Stat Assoc. 1975;70:865–871.
  5. Greenwood M. A Report on the Natural Duration of Cancer. London: HMSO; 1926.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Testing One Survival Probability (SURV-1S).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. https://najibmy.netlify.app/tools/sample-size/survival-analysis/testing-one-survival-probability/.