opt.design: Zhong's 2- or 3-stage Phase II design

In tsdf: Two-/Three-Stage Designs for Phase 1&2 Clinical Trials

Zhong's 2- or 3-stage Phase II design

Description

Calculate the optimal 2- or 3-stage design proposed by Bob Zhong.

Usage

opt.design(
  alpha1,
  alpha2,
  beta,
  pc,
  pe,
  stage = 2,
  stop.eff = FALSE,
  frac_n1 = NULL,
  frac_n2 = NULL,
  sf.param = NULL,
  show = FALSE,
  nmax = 100,
  n.choice = 1,
  ...
)

Arguments

alpha1	Left-side overall type I error.
alpha2	right-side overall type I error.
beta	Type II error.
pc	A numeric vector of response rates. It should have length 1 or 2.
pe	Alternative hypothesis response rate.
stage	Either 2 or 3. Defaults to 2.
stop.eff	Logical; if TRUE, the trial may stop early for efficacy at an interim analysis.
frac_n1	Proportion range for n1. For a two-stage design, the default is c(0.3, 0.6). For a three-stage design, the default is c(0.2, 0.3).
frac_n2	Proportion range for n2. Used only for three-stage designs. Defaults to c(0.2, 0.4).
sf.param	A single real value specifying the gamma parameter for the Hwang-Shih-DeCani spending function. The allowable range is [-40, 40]. Larger values spend more error early and leave less for later stages. For two-stage designs, the default is NULL (no alpha-spending). For three-stage designs, the default is 4.
show	Logical; if TRUE, the current total sample size is printed during the search.
nmax	Maximum sample size. Defaults to 100.
n.choice	Stopping criterion for the search over feasible designs. The search stops once the number of designs exceeds n.choice.
...	Unused arguments.

Details

In the two-stage design, n1 patients are treated in the first stage. At the end of stage 1, the trial either continues to stage 2 or stops early for inefficacy, depending on the number of observed responses. If the trial continues, an additional n2 patients are treated. The three-stage design extends the two-stage design by adding one interim stage between stages 1 and 2. The left-side rejection region is defined by response <= r_i for i = 1, 2, 3, and the right-side rejection region is defined by response > s. An alpha-spending method is available for both two- and three-stage designs. opt.design uses the Hwang-Shih-DeCani spending function; you can change the definition of HSD to use a different spending function.

Value

An object of class "opt.design", returned as a list containing:

bdry	The rejection boundaries.
error	The true type I and type II errors.
n	The sample size at each stage.
complete	The complete list of feasible designs.
alpha1	The input left-side type I error.
alpha2	The input right-side type I error.
beta	The input type II error.
pc	The input response-rate vector.
pe	The input alternative response rate.
sf.param	The input alpha-spending parameter.
stage	The number of stages in the selected design.

Author(s)

Wenchuan Guo <[e-mail]>, Jianan Hui <[e-mail]>

References

Zhong. (2012) Single-arm Phase IIA clinical trials with go/no-go decisions. Contemporary Clinical Trials, 33, 1272–1279.

Examples

 alpha1 <- 0.15
 alpha2 <- 0.10
 beta <- 0.15
 pc <- 0.25
 pe <- pc + 0.20
 # calculate optimal two-stage design without using alpha-spending
 opt.design(alpha1, alpha2, beta, pc, pe, stage=2)
 
 # calculate optimal two-stage design with Pocock-like spending function 
 opt.design(alpha1, alpha2, beta, pc, pe, stage = 2, sf.param = 1)
 
 # calculate optimal three-stage design with an O'Brien-Fleming-like spending function
 opt.design(alpha1, alpha2, beta, pc, pe, stage = 3, sf.param = -4)

tsdf documentation built on April 26, 2026, 1:06 a.m.