R Functions

Custom Figures Misc Functions Two-Stage Designs Randomization

Inference from Two-Stage Designs

Download twoStage2025.R (GitHub)
These functions are based on:
Koyama T, Chen H (2008). "Proper inference from Simon's two‐stage designs." Statistics in Medicine.

This function displays the design parameters and calculates key design characteristics, including the Type I error rate, power (POWER), probabilities of early termination (PET), and expected sample sizes (EN) under both the null and alternative hypotheses.
- Note R1=r1+1 and RT=r+1, where r1 and r are the conventional parameters used.
- Power under the null hypothesis is the type I error rate.
Example
```
TwoStageInf.prob(p0=0.1, p1=0.3, n1=10, R1=2, nT=29, RT=6)


[[1]]
   p0  p1 n1 R1 nT RT
1 0.1 0.3 10  2 29  6

[[2]]
      POWER   PET   EN
NULL 0.0471 0.736 15.0
ALT  0.8051 0.149 26.2
        
```
This function computes the proper p-value, a confidence interval, and a median estimate based on a two-stage design and observed data. The design is specified using the same parameters as in TwoStageInf.prob: p0, p1, n1, R1, nT, RT.
- Stage 1 data are provided in x1. If the actual stage 2 sample size differs from the planned value, it can be specified using m2.
- Stage 2 data are provided in x2.
Example
```
TwoStageInf(p0=0.3, p1=0.5, n1=19, R1=7, nT=39, RT=17, x1=7, m2=23, x2=10)


$parameter
   p0  p1 n1 R1 nT RT
1 0.3 0.5 19  7 39 17

$character
      POWER    PET   EN
NULL 0.0455 0.6655 25.7
ALT  0.8036 0.0835 37.3

$data
  x1 n2 m2 x2
1  7 20 23 10

$p.value
[1] 0.0828

$conf
[1] 0.282 0.546

$med.esti
[1] 0.405
```