sErrRphInt2 {triggerstrategy}

Type I error rate of the overall null hypothesis using the partial hierarchical design

Description

This function computes the type I error rate of the overall null hypothesis using the partial hierarchical group sequential design.

Usage

sErrRphInt2(cvec0, cvec1, t0, t1, tc0 = t0, tc1 = t1, rho = 0)

Arguments

cvec0

a vector of critical boundaries for testing H0

cvec1

a vector of critical boundaries for 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 the correlation between the test statistics for H0 and H1.

Value

a number shows the type I error rate of testing H0 intersect H1

Author(s)

Jiangtao Gou

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. Tamhane, A. C., Gou, J., Jennison, C., Mehta, C. R., and Curto, T. (2018). A gatekeeping procedure to test a primary and a secondary endpoint in a group sequential design with multiple interim looks. Biometrics, 74(1), 40-48. Tamhane, A. C., & Gou, J. (2022). Chapter 2 - Multiple test procedures based on p-values. In X. Cui, T. Dickhaus, Y. Ding, & J. C. Hsu (Eds.), Handbook of multiple comparisons (Vol. 45, pp. 11–34).

Examples

alpha0 <- 0.03
alpha1 <- 0.02
iuse0 <- 4
iuse1 <- 4
phi0 <- -4
phi1 <- 1
tc0 <- c(3,6,9,12)
tc1 <- c(6,12,18,24)
t0 <- c(0.3,0.6,0.9,1)
t1 <- (1:4)/4
rho <- 0
cvecList0 <- gbounds(t=t0,iuse=iuse0,
    alpha=alpha0,phi=phi0)
cvec0 <- cvecList0$bd
cvecList1 <- gbounds(t=t1,iuse=iuse1,
    alpha=alpha1,phi=phi1)
cvec1 <- cvecList1$bd
result <- sErrRphInt2(cvec0, cvec1,
    t0, t1, tc0, tc1, rho)
print(result)