Simon's 2-stage Phase II design

Calculates Optimal and Minimax 2-stage Phase II designs given by Richard Simon

Usage

ph2simon(pu, pa, ep1, ep2, nmax=100)
# S3 method for class 'ph2simon'
print(x, ...)
# S3 method for class 'ph2simon'
plot(x, ...)

Arguments

pu: unacceptable response rate; baseline response rate that needs to be exceeded for treatment to be deemed promising
pa: response rate that is desirable; should be larger than pu
ep1: threshold for the probability of declaring drug desirable under pu (target type 1 error rate); between 0 and 1
ep2: threshold for the probability of rejecting the drug under pa (target type 2 error rate); between 0 and 1
nmax: maximum total sample size (default 100; can be at most 1000)
x: object returned by ph2simon
...: arguments to be passed onto plot and print commands called within

Value

ph2simon returns a list with pu, pa, alpha, beta and nmax as above and:

out

matrix of best 2 stage designs for each value of total sample size n. The 6 columns in the matrix are:

r1	number of responses needed to exceeded in first stage
n1	number of subjects treated in first stage
r	number of responses needed to exceeded at the end of trial
n	total number of subjects to be treated in the trial
EN(pu)	expected number pf patients in the trial under pu
PET(pu)	probability of stopping after the first stage under pu

Trial is stopped early if <= r1 responses are seen in the first stage and treatment is considered desirable only when >r responses seen.

Methods (by generic)

print(ph2simon): formats and returns the minimax, optimal and any admissible designs.
plot(ph2simon): plots the expected sample size against the maximum sample size as in Jung et al., 2001

References

Simon R. (1989). Optimal Two-Stage Designs for Phase II Clinical Trials. Controlled Clinical Trials 10, 1-10.

Jung SH, Carey M and Kim KM. (2001). Graphical Search for Two-Stage Designs for Phase II Clinical Trials. Controlled Clinical Trials 22, 367-372.

Jung SH, Lee T, Kim K, and George, SL. (2004). Admissible two-stage designs for phase II cancer clinical trials. Statistics in medicine 23(4), 561-569.

Examples

  ph2simon(0.2, 0.4, 0.1, 0.1)
#> 
#>  Simon 2-stage Phase II design 
#> 
#> Unacceptable response rate:  0.2 
#> Desirable response rate:  0.4 
#> Error rates: alpha =  0.1 ; beta =  0.1 
#> 
#>         r1 n1  r  n EN(p0) PET(p0)   qLo   qHi
#> Minimax  3 19 10 36  28.26  0.4551 0.691 1.000
#> Optimal  3 17 10 37  26.02  0.5489 0.000 0.691
#> 
  ph2simon(0.2, 0.35, 0.05, 0.05)
#> 
#>  Simon 2-stage Phase II design 
#> 
#> Unacceptable response rate:  0.2 
#> Desirable response rate:  0.35 
#> Error rates: alpha =  0.05 ; beta =  0.05 
#> 
#>         r1 n1  r  n EN(p0) PET(p0)   qLo   qHi
#> Minimax 15 68 25 95  75.44  0.7244 0.582 1.000
#> Optimal 11 53 26 99  69.88  0.6330 0.000 0.582
#> 
#> Warning:   Optimal sample size too close to nmax. 
#>   Try increasing nmax (current value = 100)
  ph2simon(0.2, 0.35, 0.05, 0.05, nmax=150)
#> 
#>  Simon 2-stage Phase II design 
#> 
#> Unacceptable response rate:  0.2 
#> Desirable response rate:  0.35 
#> Error rates: alpha =  0.05 ; beta =  0.05 
#> 
#>            r1 n1  r   n EN(p0) PET(p0)   qLo   qHi
#> Minimax    15 68 25  95  75.44  0.7244 0.582 1.000
#> Admissible 11 53 26  99  69.88  0.6330 0.306 0.582
#> Admissible 11 51 27 104  67.68  0.6852 0.109 0.306
#> Optimal    11 50 28 109  67.07  0.7107 0.000 0.109
#>