Simon's Two-Stage Design — simon2stage • lrstat

Obtains Simon's two-stage minimax, admissible, and optimal designs.

Usage

simon2stage(
  alpha = NA_real_,
  beta = NA_real_,
  piH0 = NA_real_,
  pi = NA_real_,
  n_max = 110L
)

Arguments

alpha: Type I error rate (one-sided).
beta: Type II error rate (1-power).
piH0: Response probability under the null hypothesis.
pi: Response probability under the alternative hypothesis.
n_max: Upper limit for sample size, defaults to 110.

Value

A data frame containing the following variables:

piH0: Response probability under the null hypothesis.
pi: Response probability under the alternative hypothesis.
alpha: The specified one-sided significance level.
beta: The specified type II error.
n: Total sample size.
n1: Stage 1 sample size.
r1: Futility boundary for stage 1.
r: Futility boundary for stage 2.
EN0: Expected sample size under the null hypothesis.
attainedAlpha: Attained type 1 error.
power: Attained power.
PET0: Probability of early stopping under the null hypothesis.
w_lower: Lower bound of the interval for w.
w_upper: Upper bound of the interval for w.
design: Description of the design, e.g., minimax, admissible, or optimal.

Here w is the weight in the objective function: w*n + (1-w)*EN0.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples

simon2stage(0.05, 0.2, 0.1, 0.3)
#>   piH0  pi alpha beta  n n1 r1 r      EN0 attainedAlpha attainedPower      PET0
#> 1  0.1 0.3  0.05  0.2 25 15  1 5 19.50957    0.03280867     0.8017006 0.5490430
#> 2  0.1 0.3  0.05  0.2 26 12  1 5 16.77397    0.03596715     0.8047804 0.6590023
#> 3  0.1 0.3  0.05  0.2 27 11  1 5 15.84229    0.03950052     0.8061954 0.6973569
#> 4  0.1 0.3  0.05  0.2 29 10  1 5 15.01412    0.04708631     0.8050629 0.7360989
#>     w_lower   w_upper     design
#> 1 0.7323055 1.0000000    Minimax
#> 2 0.4823155 0.7323055 Admissible
#> 3 0.2928288 0.4823155 Admissible
#> 4 0.0000000 0.2928288    Optimal