TwoStageInference < Main < Vanderbilt Biostatistics Wiki

---+ Proper inference from Simon's two-stage designs
     by [[TatsukiKoyama][Tatsuki Koyama]]

<!-- ---+++ Introduction --> 

There are many software available for constructing a Simon's design.  These software usually give sample sizes and critical values for stages 1 and 2, therefore, hypothesis testing is simple to conduct.  Analyzing the data beyond hypothesis testing, however, is not straightforward when a Simon's design is used.  When the actual stage 2 sample size is different from the one originally planned, data analysis is even more complicated.  Many previously published clinical trials do not correctly account for such mid-course changes.

We present a simple R function for inference from Simon's two stage design: 
[[https://biostat.app.vumc.org/wiki/pub/Main/TatsukiRcode/twostage2020Web.R][twostage2020Web.R]]

The method is based on "Proper inference from Simon's two-stage designs" by Koyama and Chen (Statistics in Medicine [2008]).
   * Koyama T, Chen H. Proper inference from Simon's two-stage designs. Stat Med. 2008 Jul 20;27(16):3145-54. doi: 10.1002/sim.3123. PMID: 17960777; PMCID: PMC6047527.

<!--
---++++ Notation

---+++++ Response Rate
   * %$p_0 \, \cdots$% Response rate under the null hypothesis
   * %$p_1 \, \cdots$% Response rate under the alternative hypothesis

---+++++ Stage 1
   * %$n_1 \, \cdots$% Planned sample size for stage 1.
   * %$R_1 \, \cdots$% Critical value for stage 1.  Note if there are %$R_1$% or more ''successes'' in stage 1, the trial continues to stage 2.  

---+++++ Stage 2 (planned)
   * %$n_2 \, \cdots$% Planned sample size for stage 2.
   * %$R_t \, \cdots$% Planned critical value at the end of stage 2.  Note if there are %$R_t$% or more ''successes'' in stage 1 and 2 combined, the null hyopthesis is rejected.  

---+++++ Stage 2 (actual)
   * %$n^*_2 \, \cdots$% Actual sample size for stage 2.  

---+++++ Data 
   * %$X_1 \, \cdots$% Number of successes in stage 1.
   * %$X_2 \, \cdots$% Number of successes in stage 2 (out of %$n_2$% or %$n^*_2$%).

---+++ [[http://data.vanderbilt.edu/~graywh/brew/twostage.html][>> Inference from a Simon's Design]]
-->

This topic: Main > TWikiUsers > TatsukiKoyama > TwoStageInference
Topic revision: 05 Aug 2021, TatsukiKoyama (raw view)

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