# Sample size calculation for one sample non-parametric survival (survival proportion)

## 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. Our paper (Nagashima et al., 2020) discussed 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) transformation.

## References

1. Fleming TR, Harrington DP. Counting Processes and Survival Analysis. New York: Wiley, 1991, 236–237, Example 6.3.1.
2. 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.
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.
4. 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.
5. Nagashima K, Noma H, Sato Y, Gosho M. Sample size calculations for single-arm survival studies using transformations of the Kaplan–Meier estimator. Pharmaceutical Statistics 2020. In press. DOI: 10.1002/pst.2090. [arXiv:2012.03355]

## Update history

• 2020/12/22 Fixed the selection box of transformation
• 2020/12/8 Added a citation
• 2018/10/11 Update due to a manuscript revision
• 2016/4/6 Translated to English
• 2016/3/21 Test release