solveAlphaXsampleSize {triggerstrategy}

Sample size calculation

Description

This function computes the sample size and the error rate pre-assigned to the primary endpoint using methods of trigger, holm, maurer-bretz, bonferroni.

Usage

solveAlphaXsampleSize(
  alpha,
  beta0,
  beta1,
  effsz0,
  effsz1,
  szratio = 1,
  t0 = 1,
  t1 = 1,
  tc0 = t0,
  tc1 = t1,
  rho = 0,
  iuse0 = 1,
  iuse1 = 1,
  phi0 = rep(1, length(alpha)),
  phi1 = rep(1, length(alpha)),
  usingRhoForBoundary = FALSE,
  method = "trigger",
  myinit
)

Arguments

alpha

a number of overall type I error rate

beta0

a number of type II error rate for H0

beta1

a number of type II error rate for H1

effsz0

a number of the effect size of testing H0

effsz1

a number of the effect size of testing H1

szratio

a number of the ratio of sample size of testing H0 to that of testing H1

t0

a vector of information times for H0

t1

a vector of information times for H1

tc0

a vector of calendar times for H0

tc1

a vector of calendar times for H1

rho

a value of correlation coefficient between H0 and H1

iuse0

an integer shows the type of group sequential boundaries used for the primary endpoint

iuse1

an integer shows the type of group sequential boundaries used for the secondary endpoint

phi0

a parameter for the power family or the HSD gamma family for the primary endpoint

phi1

a parameter for the power family or the HSD gamma family for the secondary endpoint

usingRhoForBoundary

an indicator whether using the informaiton of rho to calculate the boundary, default is FALSE (not using)

method

a text of method, including trigger, holm, maurer-bretz, bonferroni

myinit

a vector of two starting points for alpha0 and sample size.

Value

a list of two values, alpha0 and groupsize

References

Gou, J. (2023). Trigger strategy in repeated tests on multiple hypotheses. Statistics in Biopharmaceutical Research, 15(1), 133-140. 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

# Single Stage Example
alpha <- 0.025
effsz0 <- 0.4
effsz1 <- 0.30
szratio <- 1
beta0 <- 0.10
beta1 <- 0.20
solveAlphaXsampleSize(alpha, beta0, beta1,
    effsz0, effsz1, szratio)
# Multi-stage example
alpha <- 0.025
beta0 <- 0.10
beta1 <- 0.20
effsz0 <- 0.33
effsz1 <- 0.30
szratio <- 1
t0 <- c(0.5,0.9,1)
t1 <- c(0.6,1)
tc0 <- c(1,2)
tc1 <- c(1,2,3)
rho <- 0
iuse0 <- 1
iuse1 <- 2
phi0 <- -4
phi1 <- 1
usingRhoForBoundary <- FALSE
myinit <- c(300,alpha/2)
myinit <- c(200,alpha/10)
method="trigger"
method="bonferroni"
method="holm"
method="maurer-bretz"
solveAlphaXsampleSize(alpha=alpha,
    beta0=beta0, beta1=beta1,
    effsz0=effsz0, effsz1=effsz1,
    szratio=szratio,
    t0=t0, t1=t1, tc0=tc0, tc1=tc1,
    rho=rho, iuse0=iuse0, iuse1=iuse1,
    phi0=phi0, phi1=phi1,
    usingRhoForBoundary=usingRhoForBoundary,
    method=method,
    myinit=myinit)