psPwRbhmb {triggerstrategy}

Powers of testing the primary and secondary hypotheses

Description

This function computes the powers of testing the primary and secondary hypotheses using the holm, maurer-bretz, bonferroni methods.

Usage

psPwRbhmb(
  alpha,
  alpha0,
  t0,
  t1,
  tc0 = t0,
  tc1 = t1,
  rho = 0,
  iuse0 = 1,
  iuse1 = 1,
  phi0 = rep(1, length(alpha)),
  phi1 = rep(1, length(alpha)),
  usingRhoForBoundary = FALSE,
  groupsize,
  szratio = 1,
  effsz0,
  effsz1,
  method = "bonferroni"
)

Arguments

alpha

a number shows the overall error rate

alpha0

a number shows the error rate assigned to the primary endpoint initially

t0

a vector shows the information times of the primary endpoint

t1

a vector shows the information times of the secondary endpoint

tc0

a vector shows the calendar times of the primary endpoint

tc1

a vector shows the calendar times of the secondary endpoint

rho

a number shows the correlation between the primary and secondary endpoints

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)

groupsize

a value of sample size in group 1

szratio

a value of the sample size ratio, n2/n1

effsz0

a value of effect size for hypothesis H0

effsz1

a value of effect size for hypothesis H1

method

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

Details

The methods include holm, maurer-bretz, and bonferroni. Users can decide whether the correlation information is used or not.

Value

a vector of two values of the probability that H0 is rejected, the probability that H1 is rejected, the power, using holm, maurer-bretz, or bonferroni.

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

alpha <-  0.025
alpha0 <- 0.0136
iuse0 <- 1
iuse1 <- 2
phi0 <- -4
phi1 <- 1
tc0 <- c(1,2)
tc1 <- c(1,2,3)
t0 <- c(0.6,1)
t1 <- c(0.5,0.9,1)
rho <- 0
effsz0 <- 0.33
effsz1 <- 0.30
groupsize=226
szratio=1
method="bonferroni"
method = "holm"
method="maurer-bretz"
psPwRbhmb(alpha=alpha, alpha0=alpha0,
    t0=t0, t1=t1, tc0=tc0, tc1=tc1,
    rho=rho, iuse0=1, iuse1=iuse1,
    phi0=phi0, phi1=phi1,
    usingRhoForBoundary=usingRhoForBoundary,
    groupsize=groupsize, szratio=szratio,
    effsz0=effsz0, effsz1=effsz1,
    method=method)