## Brief description

This web application is an implementation of sample size calculation methods for one sample non-parametric survival test/confidence interval (based on the Kaplan–Meier estimator) in JavaScript.

A large sample approximation to the variance of the Kaplan–Meier estimator, an exponential survival distribution, and a uniform entry over [0, accural time] are assumed.
For theoretical background, see Fleming & Harrington (1991) and Andersen, Borgan, Gill & Keiding (1993).
Moreover, various transformations for the Kaplan–Meier estimator are supported in this application.
Log-minus-log, logit, and arcsine square-root transformed confidence intervals have better performance than linear and log transformed confidence intervals (Bie et al., 1987; Borgan & Liestøl, 1990).
The required sample size and the performance depend on the method of the transformation.
The well known SWOG's calculator (One Sample Nonparametric Survival) use the log transformation, but a sample size formula different form this application is used.
We submitted a research paper to a journal about this results with numerical evaluations via simulations.
As a result, empirical power of the sample size formula with the arcsine square-root transformation is close to the nominal power than the other transformations.
Therefore, this application uses the arcsine square-root transformation as default.
When performing analysis, it is reccomended to use the arcsine square-root transformation or more conservative (i.e., log-minus-log or logit) transformation.

## Application

## References

- Fleming TR, Harrington DP. Counting Processes and Survival Analysis. New York: Wiley, 1991, 236–237, Example 6.3.1.
- Andersen PK, Borgan Ø, Gill RD, Keiding N. Statistical Models Based on Counting Processes. New York: Springer-Verlag, 1993, 176–287, Section IV.1–3.
- Bie O, Borgan Ø, Liestøl K. Confidence intervals and confidence bands for the cumulative hazard rate function and their small sample properties. Scandinavian Journal of Statistics 1987; 14(3): 221–233.
- Borgan Ø, Liestøl K. A note on confidence intervals and bands for the survival function based on transformations. Scandinavian Journal of Statistics 1990; 17(1): 35–41.

## Update history

- 2018/10/11 Update due to a manuscript revision
- 2016/04/06 Translated to English
- 2016/03/21 Test release

## To cite this page

- Nagashima K. A sample size estimation tool for one sample non-parametric tests for a median survival time [Internet]. 2016 Mar 21 [cited 20XX YYY ZZ]; Available from: http://nshi.jp/en/js/onesurvmst/.