simon: Optimal Two-Stage Single-Arm Designs

In raredd/desmon: Functions for design and monitoring of clinical trials

Optimal Two-Stage Single-Arm Designs

Description

For studies with binary endpoints, searches for two-stage sampling designs that minimize the expected number of subjects under the null, subject to various constraints.

Usage

simon(
  p0,
  pa,
  n1max = 0,
  ntmax = 1e+05,
  alpha = 0.1,
  beta = 0.1,
  del = 1,
  minimax = FALSE
)

Arguments

p0	Null hypothesis response probability
pa	Alternative hypothesis response probability
n1max	The maximum number of subjects entered during the first stage. Ignored if <= 0.
ntmax	The maximum total number of subjects.
alpha	Type I error rate
beta	Type II error rate
del	Searches for designs where the expected number of subjects under the null is within del of the minimum possible value
minimax	If TRUE, only searches for designs with the total sample size equal to the minimum possible value

Details

For two-stage phase II designs for studies with binary endpoints, searches over possible two-stage sampling designs to find those that minimize the expected \# of subjects, subject to specified constraints. If the only constraints are the type I and type II errors of the tests, then the designs are the optimal designs of Simon (1989). If a positive value of n1max is specified, then only designs with <= n1max subjects in the first stage are considered. Also, only designs with <= ntmax total subjects are considered. Setting ntmax to a large value (as in the default), effectively allows the search to consider all possible designs.

If minimax=TRUE, then the minimax designs of Simon (1989), which minimize the maximum sample size, are considered. As there are typically multiple designs with the same minimum max sample size, the program still selects among the designs in this class based on the the expected sample size under the null.

Designs which optimize one particular criterion sometimes have other undesirable properties. By specifying a value of del > 0, alternate designs meeting the criteria that have expected sample sizes under the null within del of the optimal design will also be retained.

Value

Returns a list with components

designs	A matrix with a row giving a summary of each design meeting the criteria. The columns are n1, the number of subjects entered in the first stage; r1, the cutoff for stopping at the first stage (continue if \# responses > r1); n2, the additional number of subjects enrolled in the second stage; r2, the cutoff for inactivity after the second stage (reject null if \# responses > r2); Pstop1.H0, the probability of stopping after the first stage under H0; size, the actual type I error; type2, the actual type II error; E.tot.n.H0, the expected \# subjects under H0.
call	The call to simon().
description	A text string giving a brief description of the columns in $designs.

References

Simon R (1989). Optimal two-stage designs for phase II clinical trials. Controlled Clinical Trials 10:1-10.

See Also

twostg; bin1samp; pickwin; rp21

Examples

simon(0.05, 0.20)
simon(0.05, 0.20, minimax = TRUE)

raredd/desmon documentation built on May 7, 2024, 3:46 p.m.