Simon's two-stage Phase II design

Calculates the sample size and decision rules for Optimal and Minimax two-stage Phase II designs given by Richard Simon. The trial proceeds to the second stage only if a minimal number of responses is observed at the end of the first stage.

Usage

ph2simon(pu, pa, ep1, ep2, nmax = 100)

# S3 method for ph2simon
print(x, ...)

# S3 method for 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 promising under pu (target type 1 error rate); between 0 and 1

ep2

threshold for the probability of declaring the drug not promising 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

Value

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

out

matrix of best two-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 and optimal designs

• plot(ph2simon): plots the expected sample size against the maximum sample size ass 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.

See also

twostage.inference, oc.twostage.bdry

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)
#> Optimal  3 17 10 37  26.02  0.5489
#> Minimax  3 19 10 36  28.26  0.4551
#> 
  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)
#> Optimal 11 53 26 99  69.88  0.6330
#> Minimax 15 68 25 95  75.44  0.7244
#> 
#> 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)
#> Optimal 11 50 28 109  67.07  0.7107
#> Minimax 15 68 25  95  75.44  0.7244
#>