Sample size determination for the log-rank test of non-inferiority (annual survival probabilities)

Brief description

This web application is an implementation of sample size determination method for the log-rank test of non-inferiority (Jung & Chow, 2012), assuming the proportional hazards assumption holds. This app is implemented in JavaScript, and it does not collect any information from user input.

Survival time, Accural time, Follow-up time: You should unify time unit (year or month).

Allcation ratio: When the ratio, $r \gt 1$, sample size of test group is larger than of standard group ($n_{\mathrm{test}} = r n_{\mathrm{std}}$). For instance, when $r = 2$, $n_{\mathrm{test}} = 2 n_{\mathrm{std}}$.

Non-inferiority margin: $\Delta_0$ is a hazard ratio for null hypothesis. You may input $HR \lt \Delta_0$.

Of course, only one-sided test is supported.






  1. Jung SH, Chow SC. On sample size calculation for comparing survival curves under general hypothesis testing. Journal of Biopharmaceutical Statistics 2012;22(3):485–495. [Web Site]

Update history

  • 2019/7/31 Fixed: almost exact sample sizes according to the allocation ratio can be calculated (Thanks to Dr. Masayuki Yamada)
  • 2017/12/1 Added: English translation
  • 2015/5/27 Added: test release

To cite this page

  • Nagashima K. A sample size determination tool for the log-rank test of non-inferiority [Internet]. 2015 May 27 [cited 20XX YYY ZZ]; Available from: