Package 'triggerstrategy' reference manual

Title:	Trigger Strategy in Clinical Trials
Description:	The trigger strategy is a general framework for a multistage statistical design with multiple hypotheses, allowing an adaptive selection of interim analyses. The selection of interim stages can be associated with some prespecified endpoints which serve as the trigger. This selection allows us to refine the critical boundaries in hypotheses testing procedures, and potentially increase the statistical power. This package includes several trial designs using the trigger strategy. See Gou, J. (2023), "Trigger strategy in repeated tests on multiple hypotheses", Statistics in Biopharmaceutical Research, 15(1), 133-140, and 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.
Authors:	Jiangtao Gou [aut, cre], Fengqing (Zoe) Zhang [aut]
Maintainer:	Jiangtao Gou <[email protected]>
License:	GPL-3
Version:	1.2.0
Built:	2024-12-24 06:41:17 UTC
Source:	CRAN

Convert cumulative alpha levels to normal critical boundaries

Description

This function converts cumulative alpha levels into normal critical boundaries.

Usage

alpha2boundary(
  alphas,
  t,
  initIntvl = c(1, 2 * stats::qnorm(p = alphas[1], lower.tail = FALSE))
)
alpha2boundary(
  alphas,
  t,
  initIntvl = c(1, 2 * stats::qnorm(p = alphas[1], lower.tail = FALSE))
)

Arguments

`alphas`	a list of cumulative errors from some error spending functions
`t`	a vector of information times
`initIntvl`	a pair of numbers as the lower and upper bounds of critical boundaries, used for `stats::uniroot` function

Details

The current version of ldbounds::ldBounds may not work for Hwang-Shih-DeCani boundaries.

Value

a vector of critical boundaries

Author(s)

Jiangtao Gou

Examples

library(ldbounds)
tvec <- c(0.5,1)
result <- ldbounds::ldBounds(t=tvec, iuse=1, alpha=0.05, sides=1)
print(result$upper.bounds)
bd <- alpha2boundary(alphas = result$exit.pr, t=tvec)
print(bd)
library(ldbounds)
tvec <- c(0.5,1)
result <- ldbounds::ldBounds(t=tvec, iuse=1, alpha=0.05, sides=1)
print(result$upper.bounds)
bd <- alpha2boundary(alphas = result$exit.pr, t=tvec)
print(bd)

Convert normal critical boundaries to cumulative alpha levels.

Description

This function converts normal critical boundaries to cumulative alpha levels.

Usage

boundary2alpha(cvec, t)
boundary2alpha(cvec, t)

Arguments

`cvec`	a vector of critical boundaries
`t`	a vector of information times

Value

alphas, a vector of cumulative errors

Author(s)

Jiangtao Gou

Fengqing Zhang

Examples

t <- c(0.5,0.8,1)
iuse <- 4
result <- gbounds(t=t, iuse=iuse)
print(result)
boundary2alpha(cvec=result$bd, t=t)
t <- c(0.5,0.8,1)
iuse <- 4
result <- gbounds(t=t, iuse=iuse)
print(result)
boundary2alpha(cvec=result$bd, t=t)

Correlation matrix generator

Description

This function generate the correlation matrix for group sequential trials with two endpoints.

Usage

corrMatGenerator(tp, ts, rhops)
corrMatGenerator(tp, ts, rhops)

Arguments

`tp`	an information fraction vector of Hp
`ts`	an information fraction vector of Hs
`rhops`	a number that shows the correlation coefficient between the test statistics of the primary endpoint and that of the secondary endpoint

Value

the correlation matrix, Hp goes first, and Hs goes second.

Author(s)

Jiangtao Gou

Examples

corrMatGenerator(tp=c(0.64,1),
    ts=c(0.25,0.49,1),
    rhops=1)
corrMatGenerator(tp=c(0.64,1),
    ts=c(0.25,0.49,1),
    rhops=1)

Critical boundary in group sequential trials

Description

This function computes the critical boundaries and the error spent until each stage in group sequential trials

Usage

gbounds(t, iuse = 1, alpha = 0.05, phi = rep(1, length(alpha)))
gbounds(t, iuse = 1, alpha = 0.05, phi = rep(1, length(alpha)))

Arguments

`t`	a vector of information times
`iuse`	a number of the type of the error spending function, from -2, -1, 1, 2, 3, 4
`alpha`	a number of type I error rate
`phi`	a parameter for the power family or the HSD gamma family

Details

If the original Pocock is implemented, we specify iuse=-2. If the original OBrien-Flemming is implemented, we specify iuse=-1.

Value

a list of two vectors: bd critical boundaries, er error spent until each stage

Author(s)

Jiangtao Gou

Examples

t<-c(0.5,0.8,1)
iuse <- 4
gbounds(t=t, iuse=iuse)
gbounds(t=(1:5)/5, iuse=4, alpha=0.01, phi=-4)
gbounds(t=(1:5)/5, iuse=-2, alpha=0.01)
t<-c(0.5,0.8,1)
iuse <- 4
gbounds(t=t, iuse=iuse)
gbounds(t=(1:5)/5, iuse=4, alpha=0.01, phi=-4)
gbounds(t=(1:5)/5, iuse=-2, alpha=0.01)

Marginal Power Rate

Description

This function computes the marginal powers.

Usage

marginalPwR(cvec, t, delta = 0)
marginalPwR(cvec, t, delta = 0)

Arguments

`cvec`	a vector of critical boundaries
`t`	a vector of information times
`delta`	a number shows the drift paramter

Value

a number shows the marginal power (delta isn't equal to zero) or type I error (delta is zero)

Author(s)

Jiangtao Gou

Examples

marginalPwR(c(2.218,2.218),c(0.1,0.5,1),delta=3)
marginalPwR(1.96,t=1,delta=3)
marginalPwR(c(2.218,2.218),c(0.1,0.5,1),delta=3)
marginalPwR(1.96,t=1,delta=3)

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"
)
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)
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)

Powers of testing the primary and secondary hypotheses using trigger strategy

Description

This function computes the powers of testing the primary and secondary hypotheses using trigger strategy.

Usage

psPwRtrigger(
  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
)
psPwRtrigger(
  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
)

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

Value

a vector of two values of the probability that H0 is rejected, and the probability that H1 is rejected, using the trigger strategy

References

Examples

alpha <-  0.0250
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
psPwRtrigger(alpha=alpha, alpha0=alpha0,
    t0=t0, t1=t1, tc0=tc0, tc1=tc1,
    rho=rho, iuse0=1, iuse1=iuse1,
    phi0=phi0, phi1=phi1,
    usingRhoForBoundary=FALSE,
    groupsize=groupsize, szratio=szratio,
    effsz0=effsz0, effsz1=effsz1)
alpha <-  0.0250
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
psPwRtrigger(alpha=alpha, alpha0=alpha0,
    t0=t0, t1=t1, tc0=tc0, tc1=tc1,
    rho=rho, iuse0=1, iuse1=iuse1,
    phi0=phi0, phi1=phi1,
    usingRhoForBoundary=FALSE,
    groupsize=groupsize, szratio=szratio,
    effsz0=effsz0, effsz1=effsz1)

Critical boundaries for the secondary endpoint in the partially hierarchical group sequential design

Description

This function computes the critical boundaries for the secondary endpoint in the partially hierarchical group sequential design.

Usage

sBoundsPh2(
  alpha,
  alpha0,
  t0,
  t1,
  tc0 = t0,
  tc1 = t1,
  rho = 0,
  iuse0 = 1,
  iuse1h = 1,
  iuse1t = 1,
  phi0 = rep(1, length(alpha)),
  phi1h = rep(1, length(alpha)),
  phi1t = rep(1, length(alpha))
)
sBoundsPh2(
  alpha,
  alpha0,
  t0,
  t1,
  tc0 = t0,
  tc1 = t1,
  rho = 0,
  iuse0 = 1,
  iuse1h = 1,
  iuse1t = 1,
  phi0 = rep(1, length(alpha)),
  phi1h = rep(1, length(alpha)),
  phi1t = rep(1, length(alpha))
)

Arguments

`alpha`	a value of overall type I error rate
`alpha0`	a value of the type I error rate for testing H0
`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.
`iuse0`	a value of the type of error spending function for H0, ranging from 1 to 4
`iuse1h`	a value of the type of error spending function for H1 first half, ranging from 1 to 4
`iuse1t`	a value of the type of error spending function for H1 second half, ranging from 1 to 4
`phi0`	a value of the parameter of error spending function for H0
`phi1h`	a value of the parameter of error spending function for H1 first half
`phi1t`	a value of the parameter of error spending function for H1 second half

Value

a list of two vectors: bd critical boundaries, er error spent until each stage

Author(s)

Jiangtao Gou

References

Examples

alpha <- 0.05
alpha0 <- 0.03
iuse0 <- 4
iuse1h <- 4
iuse1t <- 4
phi0 <- -4
phi1h <- 1
phi1t <- 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
sBoundsPh2(alpha, alpha0,
    t0, t1, tc0, tc1,
    rho, iuse0, iuse1h, iuse1t,
    phi0, phi1h, phi1t)
alpha <-  0.025
alpha0 <- 0.01
iuse0 <- 4
iuse1 <- 4
phi0 <- -4
phi1 <- -4
tc0 <- c(3,6,9,12,18)
tc1 <- c(6,12,18,36)
t0 <- (1:5)/5
t1 <- (1:4)/4
rho <- 0.0;
sBoundsPh2(alpha, alpha0,
    t0, t1, tc0, tc1,
    rho, iuse0, iuse1h=iuse1, iuse1t=iuse1,
    phi0, phi1h=phi1, phi1t=phi1)
alpha <- 0.05
alpha0 <- 0.03
iuse0 <- 4
iuse1h <- 4
iuse1t <- 4
phi0 <- -4
phi1h <- 1
phi1t <- 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
sBoundsPh2(alpha, alpha0,
    t0, t1, tc0, tc1,
    rho, iuse0, iuse1h, iuse1t,
    phi0, phi1h, phi1t)
alpha <-  0.025
alpha0 <- 0.01
iuse0 <- 4
iuse1 <- 4
phi0 <- -4
phi1 <- -4
tc0 <- c(3,6,9,12,18)
tc1 <- c(6,12,18,36)
t0 <- (1:5)/5
t1 <- (1:4)/4
rho <- 0.0;
sBoundsPh2(alpha, alpha0,
    t0, t1, tc0, tc1,
    rho, iuse0, iuse1h=iuse1, iuse1t=iuse1,
    phi0, phi1h=phi1, phi1t=phi1)

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)
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

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)
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)

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
)
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

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)
# 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)

Sample size calculation using Genetic Algorithms

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, with Genetic Algorithms.

Usage

solveAlphaXsampleSizeGA(
  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",
  lower = c(1, 1e-04),
  upper = c(10000, alpha - 1e-04),
  maxiter = 20,
  run = 200,
  seed = 1949
)
solveAlphaXsampleSizeGA(
  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",
  lower = c(1, 1e-04),
  upper = c(10000, alpha - 1e-04),
  maxiter = 20,
  run = 200,
  seed = 1949
)

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`
`lower`	a vector of two lower limits for alpha0 and sample size
`upper`	a vector of two upper limits for alpha0 and sample size.
`maxiter`	a number of maximum number of iterations
`run`	a number of maximum number of consecutive generations without any improvement in the best fitness value before the GA is stopped
`seed`	a number of seed of random number generator

Details

R package GA is used for Genetic Algorithms.

Value

a list of two values, alpha0 and groupsize

References

Examples

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
method="trigger"
method="bonferroni"
method="holm"
method="maurer-bretz"
lower = c(180,0.005)
upper = c(240, alpha-0.005)
maxiter = 1 # Increase this number for more precise results
run = 1 # Increase this number for more precise results
seed = 123
result <- solveAlphaXsampleSizeGA(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,
    lower = lower, upper = upper,
    maxiter = maxiter,
    run = run,
    seed = seed)
print(result)
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
method="trigger"
method="bonferroni"
method="holm"
method="maurer-bretz"
lower = c(180,0.005)
upper = c(240, alpha-0.005)
maxiter = 1 # Increase this number for more precise results
run = 1 # Increase this number for more precise results
seed = 123
result <- solveAlphaXsampleSizeGA(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,
    lower = lower, upper = upper,
    maxiter = maxiter,
    run = run,
    seed = seed)
print(result)

Power of testing the secondary hypothesis using Holm

Description

This function computes the power of testing the secondary hypothesis using Holm

Usage

sPwRholm(
  alpha,
  alpha0,
  t0,
  t1,
  delta0,
  delta1,
  rho = 0,
  iuse0 = 1,
  iuse1 = 1,
  phi0 = rep(1, length(alpha)),
  phi1 = rep(1, length(alpha))
)
sPwRholm(
  alpha,
  alpha0,
  t0,
  t1,
  delta0,
  delta1,
  rho = 0,
  iuse0 = 1,
  iuse1 = 1,
  phi0 = rep(1, length(alpha)),
  phi1 = rep(1, length(alpha))
)

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
`delta0`	a value of delta for hypothesis H0
`delta1`	a value of delta for hypothesis H1
`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

Value

a number shows the statistical power of rejecting H1

Examples

alpha <-  0.025
alpha0 <- 0.01
iuse0 <- 4
iuse1 <- 4
phi0 <- -4
phi1 <- -4
t0 <- (1:5)/5
t1 <- (1:4)/4
rho <- 0.5
delta0 <- 1
delta1 <- 3
sPwRholm(alpha=alpha, alpha0=alpha0, 
    t0=t0, t1=t1, 
    delta0=delta0, delta1=delta1, 
    rho=rho, iuse0=iuse0, iuse1=iuse1, 
    phi0=phi0, phi1=phi1)
alpha <-  0.025
alpha0 <- 0.01
iuse0 <- 4
iuse1 <- 4
phi0 <- -4
phi1 <- -4
t0 <- (1:5)/5
t1 <- (1:4)/4
rho <- 0.5
delta0 <- 1
delta1 <- 3
sPwRholm(alpha=alpha, alpha0=alpha0, 
    t0=t0, t1=t1, 
    delta0=delta0, delta1=delta1, 
    rho=rho, iuse0=iuse0, iuse1=iuse1, 
    phi0=phi0, phi1=phi1)

Power of testing the secondary hypothesis using Holm-Ye

Description

This function computes the power of testing the secondary hypothesis using Holm-Ye

Usage

sPwRholmye(
  alpha,
  alpha0,
  t0,
  t1,
  tc0 = t0,
  tc1 = t1,
  delta0,
  delta1,
  rho = 0,
  iuse0 = 1,
  iuse1 = 1,
  phi0 = rep(1, length(alpha)),
  phi1 = rep(1, length(alpha))
)
sPwRholmye(
  alpha,
  alpha0,
  t0,
  t1,
  tc0 = t0,
  tc1 = t1,
  delta0,
  delta1,
  rho = 0,
  iuse0 = 1,
  iuse1 = 1,
  phi0 = rep(1, length(alpha)),
  phi1 = rep(1, length(alpha))
)

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
`delta0`	a value of delta for hypothesis H0
`delta1`	a value of delta for hypothesis H1
`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

Value

a number shows the statistical power of rejecting H1

Examples

alpha <-  0.025
alpha0 <- 0.01
iuse0 <- 4
iuse1 <- 4
phi0 <- -4
phi1 <- -4
tc0 <- c(3,6,9,12,18)
tc1 <- c(6,12,18,36)
t0 <- (1:5)/5
t1 <- (1:4)/4
rho <- 0.5
delta0 <- 1
delta1 <- 3
sPwRholmye(alpha=alpha, alpha0=alpha0, 
    t0=t0, t1=t1, tc0=tc0, tc1=tc1, 
    delta0=delta0, delta1=delta1, 
    rho=rho, iuse0=iuse0, iuse1=iuse1, 
    phi0=phi0, phi1=phi1) 
alpha <-  0.025
alpha0 <- 0.01
iuse0 <- 4
iuse1 <- 4
phi0 <- -4
phi1 <- -4
tc0 <- c(3,6,9,12,18)
tc1 <- c(6,12,18,36)
t0 <- (1:5)/5
t1 <- (1:4)/4
rho <- 0.5
delta0 <- 1
delta1 <- 3
sPwRholmye(alpha=alpha, alpha0=alpha0, 
    t0=t0, t1=t1, tc0=tc0, tc1=tc1, 
    delta0=delta0, delta1=delta1, 
    rho=rho, iuse0=iuse0, iuse1=iuse1, 
    phi0=phi0, phi1=phi1)

Power of testing the secondary hypothesis using Bonferroni

Description

This function computes the power of testing the secondary hypothesis using Bonferroni

Usage

sPwRnaiveBonf(
  alpha,
  alpha0 = alpha/2,
  t1,
  delta1,
  iuse1,
  phi1 = rep(1, length(alpha))
)
sPwRnaiveBonf(
  alpha,
  alpha0 = alpha/2,
  t1,
  delta1,
  iuse1,
  phi1 = rep(1, length(alpha))
)

Arguments

`alpha`	a number shows the overall error rate
`alpha0`	a number shows the error rate assigned to the primary endpoint initially
`t1`	a vector shows the information times of the secondary endpoint
`delta1`	a value of delta for hypothesis H1
`iuse1`	an integer shows the type of group sequential boundaries used for the secondary endpoint
`phi1`	a parameter for the power family or the HSD gamma family for the secondary endpoint

Value

a value of the probability that H1 is rejected, the power, using the naive Bonferroni method

Examples

alpha <-  0.025
alpha0 <- 0.01
iuse0 <- 4
iuse1 <- 4
phi0 <- -4
phi1 <- -4
tc0 <- c(3,6,9,12,18)
tc1 <- c(6,12,18,36)
t0 <- (1:5)/5
t1 <- (1:4)/4
rho <- 0.5
delta0 <- 1
delta1 <- 3
sPwRnaiveBonf(alpha=alpha, 
    alpha0=alpha0, 
    t1=t1, 
    delta1=delta1, 
    iuse1=iuse1, 
    phi1=phi1)
alpha <-  0.025
alpha0 <- 0.01
iuse0 <- 4
iuse1 <- 4
phi0 <- -4
phi1 <- -4
tc0 <- c(3,6,9,12,18)
tc1 <- c(6,12,18,36)
t0 <- (1:5)/5
t1 <- (1:4)/4
rho <- 0.5
delta0 <- 1
delta1 <- 3
sPwRnaiveBonf(alpha=alpha, 
    alpha0=alpha0, 
    t1=t1, 
    delta1=delta1, 
    iuse1=iuse1, 
    phi1=phi1)

Power of testing the secondary hypothesis in partially hierarchical design

Description

This function computes the power of testing the secondary hypothesis in partially hierarchical design.

Usage

sPwRph2(cvec0, cvec1, delta0, delta1, t0, t1, tc0 = t0, tc1 = t1, rho = 0)
sPwRph2(cvec0, cvec1, delta0, delta1, 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
`delta0`	a value of drift parameter for testing H0
`delta1`	a value of drift parameter 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 correlation coefficient between H0 and H1

Value

a value of the probability that H1 is rejected, the power

References

Examples

alpha <- 0.05
alpha0 <- 0.03
iuse0 <- 4
iuse1h <- 4
iuse1t <- 4
phi0 <- -4
phi1h <- 1
phi1t <- 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$bd
cvecList1 <- sBoundsPh2(alpha, alpha0,
    t0, t1, tc0, tc1,
    rho, iuse0, iuse1h, iuse1t,
    phi0, phi1h, phi1t)
cvec1 <- cvecList1$bd
sPwRph2(cvec0, cvec1,
    delta0=2, delta1=3,
    t0, t1, tc0, tc1,
    rho=0)
alpha <- 0.05
alpha0 <- 0.03
iuse0 <- 4
iuse1h <- 4
iuse1t <- 4
phi0 <- -4
phi1h <- 1
phi1t <- 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$bd
cvecList1 <- sBoundsPh2(alpha, alpha0,
    t0, t1, tc0, tc1,
    rho, iuse0, iuse1h, iuse1t,
    phi0, phi1h, phi1t)
cvec1 <- cvecList1$bd
sPwRph2(cvec0, cvec1,
    delta0=2, delta1=3,
    t0, t1, tc0, tc1,
    rho=0)

Power of testing the secondary hypothesis using Trigger strategy

Description

This function computes the power of testing the secondary hypothesis using Trigger strategy

Usage

sPwRtrigger(
  alpha,
  alpha0,
  t0,
  t1,
  tc0 = t0,
  tc1 = t1,
  delta0,
  delta1,
  rho = 0,
  iuse0 = 1,
  iuse1 = 1,
  phi0 = rep(1, length(alpha)),
  phi1 = rep(1, length(alpha)),
  usingRhoForBoundary = FALSE
)
sPwRtrigger(
  alpha,
  alpha0,
  t0,
  t1,
  tc0 = t0,
  tc1 = t1,
  delta0,
  delta1,
  rho = 0,
  iuse0 = 1,
  iuse1 = 1,
  phi0 = rep(1, length(alpha)),
  phi1 = rep(1, length(alpha)),
  usingRhoForBoundary = FALSE
)

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
`delta0`	a value of delta for hypothesis H0
`delta1`	a value of delta for hypothesis H1
`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)

Value

a value of the probability that H1 is rejected, the power, using the trigger strategy

References

Examples

alpha <-  0.025
alpha0 <- 0.01
iuse0 <- 4
iuse1 <- 4
phi0 <- -4
phi1 <- -4
tc0 <- c(3,6,9,12,18)
tc1 <- c(6,12,18,36)
t0 <- (1:5)/5
t1 <- (1:4)/4
rho <- 0.5
delta0 <- 1
delta1 <- 3
sPwRtrigger(alpha=alpha, alpha0=alpha0,
    t0=t0, t1=t1, tc0=tc0, tc1=tc1,
    delta0=delta0, delta1=delta1,
    rho=rho, iuse0=1, iuse1=iuse1,
    phi0=phi0, phi1=phi1,
    usingRhoForBoundary=FALSE)
alpha <-  0.025
alpha0 <- 0.01
iuse0 <- 4
iuse1 <- 4
phi0 <- -4
phi1 <- -4
tc0 <- c(3,6,9,12,18)
tc1 <- c(6,12,18,36)
t0 <- (1:5)/5
t1 <- (1:4)/4
rho <- 0.5
delta0 <- 1
delta1 <- 3
sPwRtrigger(alpha=alpha, alpha0=alpha0,
    t0=t0, t1=t1, tc0=tc0, tc1=tc1,
    delta0=delta0, delta1=delta1,
    rho=rho, iuse0=1, iuse1=iuse1,
    phi0=phi0, phi1=phi1,
    usingRhoForBoundary=FALSE)

Package 'triggerstrategy'

Help Index

Convert cumulative alpha levels to normal critical boundaries

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Convert normal critical boundaries to cumulative alpha levels.

Description

Usage

Arguments

Value

Author(s)

Examples

Correlation matrix generator

Description

Usage

Arguments

Value

Author(s)

Examples

Critical boundary in group sequential trials

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Marginal Power Rate

Description

Usage

Arguments

Value

Author(s)

Examples

Powers of testing the primary and secondary hypotheses

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Powers of testing the primary and secondary hypotheses using trigger strategy

Description

Usage

Arguments

Value

References

Examples

Critical boundaries for the secondary endpoint in the partially hierarchical group sequential design

Description

Usage

Arguments

Value

Author(s)

References

Examples

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

Description

Usage

Arguments

Value

Author(s)

References

Examples

Sample size calculation

Description

Usage

Arguments

Value

References

Examples

Sample size calculation using Genetic Algorithms

Description