szgaGAw {graposas}

Sample size optimization using graphical approach in clinical trial design with three hypotheses when the transition matrix is pre-specified

Description

This function computes the optimal design using graphical approach along with the minimum sample size when three hypotheses are considered in a clinical trial. The transition matrix is pre-specified and fixed.

Usage

szgaGAw(
  alpha,
  betaVec,
  deltaVec,
  cVec,
  rhoMat,
  transMat,
  lower = c(1, rep(1e-06, 2)),
  upper = c(10000, rep(1 - 1e-06, 2)),
  gaIter = c(20, 20),
  penPara = 0.1,
  seed = 2022
)

Arguments

alpha

a value of overall type I error rate

betaVec

a vector of one minus marginal powers for testing H1, H2 and H3, respectively

deltaVec

a vector of effect sizes for testing H1, H2 and H3, respectively

cVec

a vector of coefficients. When testing continuous endpoints, these coefficients are exactly one. When testing binary endpoints, the values are roughly one but not exactly one

rhoMat

a matrix of the correlation coefficients among three hypotheses

transMat

a matrix of the fixed transition probabilities among three hypotheses

lower

a vector of lower limit of sample size n, and initial weights w1 and w2, where w3 is computed by 1 - w1 - w2

upper

a vector of upper limit of sample size n, and initial weights w1 and w2, where w3 is computed by 1 - w1 - w2

gaIter

a vector of two numbers. The first one is the parameter maxiter of the ga function, and the second one is the parameter run of the ga function

penPara

a number of penalization parameter for optimization to balance the sample size requirement and the power requirement

seed

a number of the seed of the random number generator

Details

R package GA is used for Genetic Algorithms.

Value

a vector of three numbers: the optimal sample size n, and initial weights w1 and w2

Author(s)

Jiangtao Gou

References

Zhang, F. and Gou, J. (2023). Sample size optimization for clinical trials using graphical approaches for multiplicity adjustment, Technical Report. Gou, J. (2022). Sample size optimization and initial allocation of the significance levels in group sequential trials with multiple endpoints. Biometrical Journal, 64(2), 301-311.

Examples

start <- Sys.time()
szgaGAw(alpha = 0.025, betaVec = c(0.15, 0.20, 0.10),
        deltaVec = c(0.1111952, 0.1037179, 0.1335865),
        cVec = c(1.003086, 1.002686, 1.004451),
        rhoMat = matrix(c(1,0.5,0.8, 0.5,1,0.6, 0.8,0.6,1), nrow = 3, byrow = TRUE),
        transMat = matrix(c(0,0.50,0.50, 0.5,0,0.5, 0.5,0.5,0), nrow = 3, byrow = TRUE),
        lower = c(700, rep(0.05, 2)),
        upper = c(900, rep(0.95, 2)),
        gaIter = c(10, 5),
        penPara = 0.0135,
        seed = 234)
end <- Sys.time()
data.frame(time = end - start)