Simon's two-stage design

Brief description

This web application is an implementation of sample size determination method for Simon's two stage designs (Simon, 1989). This app is implemented in JavaScript, and it does not collect any information from user input. This app is licensed under GPLv3, because the "nTwoStageDesign" function in this app is a modification and translation from the "ph2simon" function in the clinfun package.

Input parameters

  • $p_0$: the response probability of uninteresting level (poor drug)
  • $p_1$: the response probability of desirable level (good drug)
  • $\alpha$: one-sided type I error rate
  • $1 - \beta$: power
  • Upper limit of $n$: maximum total sample size (it is recommended to set $n \lt 500$; CPU-intensive!)


  • $n$: the total sample size
  • $n_1$: the sample size for stage 1
  • $r_1$: the futility boundary for stage 1; if the observed number of response is equal to or smaller than $r_1$, the study will be stopped early
  • $r$: the decision threshold: if the total number of response is equal to or larger than $r+1$, the null hypothesis will be rejected
  • $EN_{p_0}$: the expected total sample size under response rate $p_0$
  • $PET_{p_0}$: the probability of early stopping






  1. Simon R. Optimal two-stage designs for phase II clinical trials. Controlled Clinical Trials 1989; 10(1): 1–10.

Update history

  • 2021/4/29 Fixed: Notation fixed (Thanks to Dr. Wonsuk Yoo)
  • 2017/12/25 Added: English translation
  • 2016/9/15 Fixed: Captions for $r_1$ and $r$ have been revised
  • 2016/6/23 Added: test release

To cite this page

  • Nagashima K. A sample size determination tool for Simon's two stage designs [Internet]. 2016 Jun 23 [cited 20XX YYY ZZ]; Available from: