Package 'MultiGroupSequential' reference manual

Title:	Group-Sequential Procedures with Multiple Endpoints
Description:	Provides various testing procedures for group-sequential trials with multiple endpoints. Two sets of procedures are provided.
Authors:	Xiaodong Luo [aut, cre], Hui Quan [ctb], Sanofi [cph]
Maintainer:	Xiaodong Luo <[email protected]>
License:	GPL (>= 2)
Version:	1.0.0
Built:	2025-02-16 03:00:28 UTC
Source:	https://github.com/marvels2031/multigroupsequential

Group-Sequential Procedures with Multiple Endpoints

Description

Provides various testing procedures for group-sequential trials with multiple endpoints. Two sets of procedures are provided.

Details

The DESCRIPTION file:

Package:	MultiGroupSequential
Type:	Package
Version:	1.0.0
Date:	2022-03-31
Title:	Group-Sequential Procedures with Multiple Endpoints
Description:	Provides various testing procedures for group-sequential trials with multiple endpoints. Two sets of procedures are provided.
Authors@R:	c( person(given="Xiaodong", family="Luo", email = "[email protected]", role =c("aut", "cre")), person(given="Hui", family="Quan", role = "ctb"), person("Sanofi", role = "cph"))
Depends:	R (>= 4.0.0)
Imports:	stats, rpact, gMCP, mvtnorm, OpenMx, hommel, minidown
License:	GPL (>= 2)
RoxygenNote:	7.1.2
LazyData:	true
Suggests:	knitr, rmarkdown
VignetteBuilder:	knitr
Config/pak/sysreqs:	make default-jdk libssl-dev libnode-dev
Repository:	https://marvels2031.r-universe.dev
RemoteUrl:	https://github.com/marvels2031/multigroupsequential
RemoteRef:	HEAD
RemoteSha:	0c9e830c268337fdaf57f76910ef96f4d0647a20
Author:	Xiaodong Luo [aut, cre], Hui Quan [ctb], Sanofi [cph]
Maintainer:	Xiaodong Luo <[email protected]>

Index of help topics:

MultiGroupSequential-package
                        Group-Sequential Procedures with Multiple
                        Endpoints
crosslist               Cross list all the scenarios
hxhochberg              Hochberg procedure with different alphas for
                        different endpoints
hxhommel                Hommel procedure with different alphas for
                        different endpoints
xccalgsp                Calculate group-sequential p-values
xccalgspcor             Calculate group-sequential p-values given the
                        correlation matrix of the test statistics
xccalgspsim             Calculate group-sequential p-values via
                        simulation
xccalgspsim1            Calculate group-sequential p-values via
                        simulation
xccrit                  Calculate critical values
xcmaurerbretz           Maurer-Bretz sequential graphical approach
xcseqgxgs               Sequential graphical procedure for multiple
                        endpoints based on group-sequential p-values
xcseqhh                 Sequential Hochberg/Hommel procedure for
                        multiple endpoints based on q-values
xcseqhhgs               Sequential Hochberg/Hommel procedure for
                        multiple endpoints based on group-sequential
                        p-values
xcspending              Calculate alpha spending

Author(s)

Xiaodong Luo [aut, cre], Hui Quan [ctb], Sanofi [cph]

Maintainer: Xiaodong Luo <[email protected]>

References

Luo (2022)

Cross list all the scenarios

Description

Cross list all the scenarios

Usage

crosslist(b=list(a1=c(2,3),a2=c(2,4),a3=c(0,1)))
crosslist(b=list(a1=c(2,3),a2=c(2,4),a3=c(0,1)))

Arguments

`b`	A list of lists

Value

`df`	dataframe consisting of all the scenarios row by row

Author(s)

Xiaodong Luo

Examples

crosslist(b=list(pbo.hazard=c(0.1,0.15,0.3), 
                 hazard.ratio=c(0.6,0.7,0.8), 
                 censoring.rate=c(0.05,0.06,0.07)
                 )
         )
crosslist(b=list(pbo.hazard=c(0.1,0.15,0.3), 
                 hazard.ratio=c(0.6,0.7,0.8), 
                 censoring.rate=c(0.05,0.06,0.07)
                 )
         )

Hochberg procedure with different alphas for different endpoints

Description

Hochberg procedure with different alphas for different endpoints

Usage

hxhochberg(pvalues,alpha,epsilon=1.0e-10,precision=10)
hxhochberg(pvalues,alpha,epsilon=1.0e-10,precision=10)

Arguments

`pvalues`	p-values from different endpoints
`alpha`	same length as `pvalues` with (different) alphas for different endpoints
`epsilon`	lower bound for the alpha
`precision`	precision of the values

Details

This procedure handles Hochberg procedure with different alphas for different endpoints

Value

decisions

an index of rejected hypoetheses

Author(s)

Xiaodong Luo

Examples

hxhochberg(pvalues=runif(5),alpha=seq(0.01,0.025,len=5),epsilon=1.0e-10,precision=10)
hxhochberg(pvalues=runif(5),alpha=seq(0.01,0.025,len=5),epsilon=1.0e-10,precision=10)

Hommel procedure with different alphas for different endpoints

Description

Hommel procedure with different alphas for different endpoints

Usage

hxhommel(pvalues,alpha,epsilon=1.0e-10,precision=10)
hxhommel(pvalues,alpha,epsilon=1.0e-10,precision=10)

Arguments

`pvalues`	p-values from different endpoints
`alpha`	same length as `pvalues` with (different) alphas for different endpoints
`epsilon`	lower bound for the alpha
`precision`	precision of the values, obsolete for backward compatibility

Details

It turns out [hommel](https://cran.r-project.org/web/packages/hommel/) can handle Hommel procedure with different alpha's for different endpoints, the function 'hxhommel' is just a wrapper function.

Value

decisions

an index of rejected hypotheses

Author(s)

Xiaodong Luo

Examples

hxhommel(pvalues=runif(5),alpha=seq(0.01,0.025,len=5),epsilon=1.0e-10,precision=10)
hxhommel(pvalues=runif(5),alpha=seq(0.01,0.025,len=5),epsilon=1.0e-10,precision=10)

Calculate group-sequential p-values

Description

This will calculate group-sequential p-values

Usage

xccalgsp(xm=qnorm(matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2)),
                alpham=matrix(rep(c(0.02,0.03,0.05),each=2),ncol=3,nrow=2),
                informationm=matrix(rep(c(0.4,0.8,1),each=2),ncol=3,nrow=2),direction=-1)
                
xccalgsp(xm=qnorm(matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2)),
                alpham=matrix(rep(c(0.02,0.03,0.05),each=2),ncol=3,nrow=2),
                informationm=matrix(rep(c(0.4,0.8,1),each=2),ncol=3,nrow=2),direction=-1)

Arguments

`xm`	a matrix of test statistics for each endpoint (in row) and each interim (in column)
`alpham`	a matrix of alpha spending for the statistics `xm`
`informationm`	a matrix of information fractions for the statistics `xm`
`direction`	-1: (one-sided)reject if test stat is smaller than or equal to the critical value; 1: (one-sided)reject if test stat is greater than or equal to the critical value; 0: (two-sided)reject if the absolute value of the test stat is greater than the critical value

Value

`pm`	group-sequential p-values
`critm`	critical values

Author(s)

Xiaodong Luo

Examples

xm=qnorm(matrix(rep(c(0.03,0.04,0.01),times=4),ncol=3,nrow=4))
im=matrix(rep(c(0.4,0.8,1),each=4),ncol=3,nrow=4)
alpham=matrix(0,nrow=4,ncol=3)
for (i in 1:4){
   alpham[i,]=xcspending(alpha=0.025,fractions=im[i,],family="OBF",rho=(i+1)/2)$aseq
}
xccalgsp(xm=xm,alpham=alpham,informationm=im,direction=-1)
xm=qnorm(matrix(rep(c(0.03,0.04,0.01),times=4),ncol=3,nrow=4))
im=matrix(rep(c(0.4,0.8,1),each=4),ncol=3,nrow=4)
alpham=matrix(0,nrow=4,ncol=3)
for (i in 1:4){
   alpham[i,]=xcspending(alpha=0.025,fractions=im[i,],family="OBF",rho=(i+1)/2)$aseq
}
xccalgsp(xm=xm,alpham=alpham,informationm=im,direction=-1)

Calculate group-sequential p-values given the correlation matrix of the test statistics

Description

This will calculate group-sequential p-values given the correlation matrix of the test statistics

Usage

xccalgspcor(xm=qnorm(c(0.03,0.04,0.01)),
                   alpham=c(0.02,0.03,0.05),
                   corrm=diag(length(xm)),direction=-1,tol=1e-10)
                
xccalgspcor(xm=qnorm(c(0.03,0.04,0.01)),
                   alpham=c(0.02,0.03,0.05),
                   corrm=diag(length(xm)),direction=-1,tol=1e-10)

Arguments

`xm`	a vector of test statistics at each analysis
`alpham`	a vector of alpha spending for the statistics `xm`
`corrm`	correlation matrix of the statistics `xm`
`direction`	-1: (one-sided)reject if test stat is smaller than or equal to the critical value; 1: (one-sided)reject if test stat is greater than or equal to the critical value; 0: (two-sided)reject if the absolute value of the test stat is greater than the critical value
`tol`	accuracy tolerance when calculating the quantiles

Value

`pm`	group-sequential p-values
`critm`	critical values

Author(s)

Xiaodong Luo

Examples

xm=qnorm(matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2))
ir=c(0.4,0.8,1)
corrm=diag(length(ir))
for (i in 1:length(ir))for(j in 1:length(ir))corrm[i,j]=sqrt(ir[pmin(i,j)]/ir[pmax(i,j)])
xccalgsp(xm=xm)$critm[1,]
xccalgspsim(xm=xm)$critm[1,]
xccalgspcor(xm=xm[1,],corrm=corrm)$critm
xm=qnorm(matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2))
ir=c(0.4,0.8,1)
corrm=diag(length(ir))
for (i in 1:length(ir))for(j in 1:length(ir))corrm[i,j]=sqrt(ir[pmin(i,j)]/ir[pmax(i,j)])
xccalgsp(xm=xm)$critm[1,]
xccalgspsim(xm=xm)$critm[1,]
xccalgspcor(xm=xm[1,],corrm=corrm)$critm

Calculate group-sequential p-values via simulation

Description

This will calculate group-sequential p-values via simulation

Usage

xccalgspsim(xm=qnorm(matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2)),
                   alpham=matrix(rep(c(0.02,0.03,0.05),each=2),ncol=3,nrow=2),
                   informationm=matrix(rep(c(0.4,0.8,1),each=2),ncol=3,nrow=2),
                   r.seed=rep(17,2),nsample=1e+6,direction=-1)
xccalgspsim(xm=qnorm(matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2)),
                   alpham=matrix(rep(c(0.02,0.03,0.05),each=2),ncol=3,nrow=2),
                   informationm=matrix(rep(c(0.4,0.8,1),each=2),ncol=3,nrow=2),
                   r.seed=rep(17,2),nsample=1e+6,direction=-1)

Arguments

`xm`	a matrix of test statistics for each endpoint (in row) and each interim (in column)
`alpham`	a matrix of alpha spending for the statistics `xm`
`informationm`	a matrix of information fractions for the statistics `xm`
`r.seed`	random seeds for each endpoints
`nsample`	number of random samples
`direction`	-1: (one-sided)reject if test stat is smaller than or equal to the critical value; 1: (one-sided)reject if test stat is greater than or equal to the critical value; 0: (two-sided)reject if the absolute value of the test stat is greater than the critical value

Value

`pm`	group-sequential p-values
`critm`	critical values

Note

This provides the calculation for the group-sequential p-values in case there is an issue in using rpact package.

Author(s)

Xiaodong Luo

Examples

xm=qnorm(matrix(rep(c(0.03,0.04,0.01),times=4),ncol=3,nrow=4))
im=matrix(rep(c(0.4,0.8,1),each=4),ncol=3,nrow=4)
alpham=matrix(0,nrow=4,ncol=3)
for (i in 1:4){
   alpham[i,]=xcspending(alpha=0.025,fractions=im[i,],family="OBF",rho=(i+1)/2)$aseq
}
xccalgspsim(xm=xm,alpham=alpham,informationm=im,r.seed=rep(17,4),direction=-1)
xm=qnorm(matrix(rep(c(0.03,0.04,0.01),times=4),ncol=3,nrow=4))
im=matrix(rep(c(0.4,0.8,1),each=4),ncol=3,nrow=4)
alpham=matrix(0,nrow=4,ncol=3)
for (i in 1:4){
   alpham[i,]=xcspending(alpha=0.025,fractions=im[i,],family="OBF",rho=(i+1)/2)$aseq
}
xccalgspsim(xm=xm,alpham=alpham,informationm=im,r.seed=rep(17,4),direction=-1)

Calculate group-sequential p-values via simulation

Description

This utility function will be called by function "xccalgspsim" to calculate group-sequential p-values via simulation for single endpoint

Usage

xccalgspsim1(xm=qnorm(c(0.03,0.04,0.01)),alpham=c(0.02,0.03,0.05),
                      informationm=c(0.4,0.8,1),
                      r.seed=17,nsample=1e+6,direction=0)
xccalgspsim1(xm=qnorm(c(0.03,0.04,0.01)),alpham=c(0.02,0.03,0.05),
                      informationm=c(0.4,0.8,1),
                      r.seed=17,nsample=1e+6,direction=0)

Arguments

`xm`	test statistics
`alpham`	alpha spending
`informationm`	information fractions
`r.seed`	random seed
`nsample`	number of random samples
`direction`	-1: (one-sided)reject if test stat is smaller than or equal to the critical value; 1: (one-sided)reject if test stat is greater than or equal to the critical value; 0: (two-sided)reject if the absolute value of the test stat is greater than the critical value

Value

`crit.value`	critical values
`p.value.gs`	group-sequential p-values
`xm`	test statistics
`alpham`	alpha spending
`informationm`	information fractions

Note

This provides the calculation for the group-sequential p-values in case there is an issue in using rpact package.

Author(s)

Xiaodong Luo

Examples

xm=qnorm(c(0.03,0.04,0.01))
im=c(0.4,0.8,1)
alpham=xcspending(alpha=0.025,fractions=im,family="OBF",rho=2)$aseq
xccalgspsim1(xm=xm,alpham=alpham,informationm=im,direction=-1)
xm=qnorm(c(0.03,0.04,0.01))
im=c(0.4,0.8,1)
alpham=xcspending(alpha=0.025,fractions=im,family="OBF",rho=2)$aseq
xccalgspsim1(xm=xm,alpham=alpham,informationm=im,direction=-1)

Calculate critical values

Description

This utility function calculates the critical values

Usage

xccrit(direction=-1,alpha=0.025,informationRates=c(0.4,0.7,1),
                 userAlphaSpending=c(0.01,0.015,0.025),alpha.low=1e-10)
  
xccrit(direction=-1,alpha=0.025,informationRates=c(0.4,0.7,1),
                 userAlphaSpending=c(0.01,0.015,0.025),alpha.low=1e-10)

Arguments

`direction`	-1: (one-sided)reject if test stat is smaller than or equal to the critical value; 1: (one-sided)reject if test stat is greater than or equal to the critical value; 0: (two-sided)reject if the absolute value of the test stat is greater than the critical value
`alpha`	overall familywise error rate
`informationRates`	information fractions
`userAlphaSpending`	alpha spent at each interim
`alpha.low`	default is 1e-10, if allocated alpha is smaller than this number, the corresponding critical value will be set to infinity

Value

crit

critical values

Author(s)

Xiaodong Luo

Examples

xccrit(direction=-1,alpha=0.025,informationRates=c(0.4,0.7,1),
                 userAlphaSpending=c(0.01,0.015,0.025),alpha.low=1e-10)
xccrit(direction=-1,alpha=0.025,informationRates=c(0.4,0.7,1),
                 userAlphaSpending=c(0.01,0.015,0.025),alpha.low=1e-10)

Maurer-Bretz sequential graphical approach

Description

This will conduct group-sequential testing for multiple endpoints based on Maurer-Bretz approach

Usage

xcmaurerbretz(xm=qnorm(matrix(rep(c(0.03,0.04,0.01),times=4),ncol=3,nrow=4)),
                         informationm=matrix(rep(c(0.4,0.8,1),each=4),ncol=3,nrow=4),
                         spending=rep("OBF",4),param.spending=rep(1,4),
                         alpha=0.025,direction=-1,graphin=BonferroniHolm(nrow(xm)),
                         alpha.low=1e-10,retrospective=0)
xcmaurerbretz(xm=qnorm(matrix(rep(c(0.03,0.04,0.01),times=4),ncol=3,nrow=4)),
                         informationm=matrix(rep(c(0.4,0.8,1),each=4),ncol=3,nrow=4),
                         spending=rep("OBF",4),param.spending=rep(1,4),
                         alpha=0.025,direction=-1,graphin=BonferroniHolm(nrow(xm)),
                         alpha.low=1e-10,retrospective=0)

Arguments

`xm`	a matrix of test statistics for each endpoint (in row) and each interim (in column)
`informationm`	a matrix of information fractions for the statistics `xm`
`spending`	spending functions for each endpoint
`param.spending`	parameters in the spending functions
`alpha`	overall familywise error rate
`direction`	-1: (one-sided)reject if test stat is smaller than or equal to the critical value; 1: (one-sided)reject if test stat is greater than or equal to the critical value; 0: (two-sided)reject if the absolute value of the test stat is greater than the critical value
`graphin`	a graph object generated from gMCP
`alpha.low`	default is 1e-10, if allocated alpha is smaller than this number, the corresponding critical value will be set to infinity
`retrospective`	retrospective: 0 (default) only compares the current test statistic with the updated critical value, 1 compares all the test statistics up to the current one with the updated critical values. Even though retrospective looking at the values is statistically valid in terms of control of the type-1 error rate, no retrospective looking at the past comparisons avoids the dilemma of retrospectively increasing the alpha level for the un-rejected hypothesis in the past

Value

`Hrej`	rejected hypotheses
`rejected`	the index set of rejected hypotheses
`decisionsm`	rejection decision for each endpoint (row) at each timepoint (column)
`cumdecisionsm`	cumulative rejection decision for each endpoint (row) at each timepoint (column)

Author(s)

Xiaodong Luo

Examples

Sys.setenv(JAVA_HOME="C:/Program Files/Java/jdk-17.0.2/")
library(gMCP)
xm=qnorm(matrix(rep(c(0.03,0.04,0.01),times=4),ncol=3,nrow=4))
im=matrix(rep(c(0.4,0.8,1),each=4),ncol=3,nrow=4)
spending=rep("OBF",4)
param.spending=rep(1,4)
graphin=gMCP::BonferroniHolm(nrow(xm))
xcmaurerbretz(xm=xm,
                informationm=im,
                spending=spending,
                param.spending=param.spending,
                graphin=graphin)
Sys.setenv(JAVA_HOME="C:/Program Files/Java/jdk-17.0.2/")
library(gMCP)
xm=qnorm(matrix(rep(c(0.03,0.04,0.01),times=4),ncol=3,nrow=4))
im=matrix(rep(c(0.4,0.8,1),each=4),ncol=3,nrow=4)
spending=rep("OBF",4)
param.spending=rep(1,4)
graphin=gMCP::BonferroniHolm(nrow(xm))
xcmaurerbretz(xm=xm,
                informationm=im,
                spending=spending,
                param.spending=param.spending,
                graphin=graphin)

Sequential graphical procedure for multiple endpoints based on group-sequential p-values

Description

Sequential graphical procedure for multiple endpoints based on group-sequential p-values

Usage

xcseqgxgs(pm=matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2),
          alpha=0.025,graphin=BonferroniHolm(2))
xcseqgxgs(pm=matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2),
          alpha=0.025,graphin=BonferroniHolm(2))

Arguments

`pm`	a matrix of group-sequential p-values for different endpoints (in row) at different times (in column)
`alpha`	overall familywise error rate
`graphin`	graph to be used, this is graph object defined by the gMCP package

Value

`rejected`	the index set of rejected hypotheses
`decisionsm`	rejection decision for each endpoint (row) at each timepoint (column)
`cumdecisionsm`	cumulative rejection decision for each endpoint (row) at each timepoint (column)

Note

This provides the calculation for the variance.

Author(s)

Xiaodong Luo

Examples

Sys.setenv(JAVA_HOME="C:/Program Files/Java/jdk-17.0.2/")
library(gMCP)
pm=matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2)
graphin=gMCP::BonferroniHolm(2)
xcseqgxgs(pm=pm,alpha=0.025,graphin=graphin)
Sys.setenv(JAVA_HOME="C:/Program Files/Java/jdk-17.0.2/")
library(gMCP)
pm=matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2)
graphin=gMCP::BonferroniHolm(2)
xcseqgxgs(pm=pm,alpha=0.025,graphin=graphin)

Sequential Hochberg/Hommel procedure for multiple endpoints based on q-values

Description

Sequential Hochberg/Hommel procedure for multiple endpoints based on q-values

Usage

xcseqhh(pm=matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2),
        alpham=matrix(rep(c(0.02,0.03,0.05),each=2),ncol=3,nrow=2),
        epsilon=1.0e-10,precision=10,method='Hochberg')          
          
xcseqhh(pm=matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2),
        alpham=matrix(rep(c(0.02,0.03,0.05),each=2),ncol=3,nrow=2),
        epsilon=1.0e-10,precision=10,method='Hochberg')

Arguments

`pm`	a matrix of group-sequential p-values for different endpoints (in row) at different times (in column)
`alpham`	a matrix of alpha spending corresponding to the p-values `pm`
`epsilon`	lower bound for the alpha
`precision`	precision of the values
`method`	"Hochberg" or "Hommel"

Value

`rejected`	the index set of rejected hypotheses
`decisionsm`	rejection decision for each endpoint (row) at each timepoint (column)
`cumdecisionsm`	cumulative rejection decision for each endpoint (row) at each timepoint (column)
`alphaused`	alpha levels actually used for each endpoint (row) at each timepoint (column)

Note

This provides the calculation for the variance.

Author(s)

Xiaodong Luo

Examples

pm=matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2)
alpham=matrix(rep(c(0.02,0.03,0.05),each=2),ncol=3,nrow=2)
xcseqhh(pm=pm,alpham=alpham,method="Hochberg")
xcseqhh(pm=pm,alpham=alpham,method="Hommel")
pm=matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2)
alpham=matrix(rep(c(0.02,0.03,0.05),each=2),ncol=3,nrow=2)
xcseqhh(pm=pm,alpham=alpham,method="Hochberg")
xcseqhh(pm=pm,alpham=alpham,method="Hommel")

Sequential Hochberg/Hommel procedure for multiple endpoints based on group-sequential p-values

Description

Sequential Hochberg/Hommel procedure for multiple endpoints based on group-sequential p-values

Usage

xcseqhhgs(pm=matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2),
                   alpha=0.025,epsilon=1.0e-10,precision=10,method='Hochberg')          
          
xcseqhhgs(pm=matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2),
                   alpha=0.025,epsilon=1.0e-10,precision=10,method='Hochberg')

Arguments

`pm`	a matrix of group-sequential p-values for different endpoints (in row) at different times (in column)
`alpha`	overall familywise error rate
`epsilon`	lower bound for the alpha
`precision`	precision of the values
`method`	"Hochberg" or "Hommel"

Value

`rejected`	the index set of rejected hypotheses
`decisionsm`	rejection decision for each endpoint (row) at each timepoint (column)
`cumdecisionsm`	cumulative rejection decision for each endpoint (row) at each timepoint (column)

Note

This provides the calculation for the variance.

Author(s)

Xiaodong Luo

Examples

pm=matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2)
xcseqhhgs(pm=pm,alpha=0.025,method="Hochberg")
xcseqhhgs(pm=pm,alpha=0.025,method="Hommel")
pm=matrix(rep(c(0.03,0.04,0.01),times=2),ncol=3,nrow=2)
xcseqhhgs(pm=pm,alpha=0.025,method="Hochberg")
xcseqhhgs(pm=pm,alpha=0.025,method="Hommel")

This utility function calculates alpha spending. Note that the OBF and Pocock spending functions are not the originally proposed ones, they are the modified ones that are closely resemble the original versions. That being said, you might still see some differences

Usage

xcspending(alpha,fractions=seq(0.2,1,by=0.2),family="OBF",rho=1)
xcspending(alpha,fractions=seq(0.2,1,by=0.2),family="OBF",rho=1)

Arguments

`alpha`	overall familywise error rate
`fractions`	information fractions
`family`	family of spending functions, one of "OBF", "pocock", "power"
`rho`	parameter of the spending function

Details

OBF: $2\{1-\Phi(\Phi^{-1}(1-\alpha/2)/t^{\rho/2})\}$ ; pocock: $\alpha \log\{1+(e-1)*t\}$ ; power: $\alpha*t^{\rho}$

Value

aseq

alpha spending

Author(s)

Xiaodong Luo

Examples

xcspending(alpha=0.025,fractions=seq(0.2,1,by=0.2),family="OBF",rho=1)
xcspending(alpha=0.025,fractions=seq(0.2,1,by=0.2),family="OBF",rho=1)

Package 'MultiGroupSequential'

Help Index

Group-Sequential Procedures with Multiple Endpoints

Description

Details

Author(s)

References

Cross list all the scenarios

Description

Usage

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Value

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Examples

Hochberg procedure with different alphas for different endpoints

Description

Usage

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Details

Value

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Examples

Hommel procedure with different alphas for different endpoints

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Calculate group-sequential p-values

Description

Usage

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Value

Author(s)

Examples

Calculate group-sequential p-values given the correlation matrix of the test statistics

Description

Usage

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Value

Author(s)

Examples

Calculate group-sequential p-values via simulation

Description

Usage

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Value

Note

Author(s)

Examples

Calculate group-sequential p-values via simulation

Description

Usage

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Value

Note

Author(s)

Examples

Calculate critical values

Description

Usage

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Value

Author(s)

Examples

Maurer-Bretz sequential graphical approach

Description

Usage

Arguments

Value

Author(s)

Examples

Sequential graphical procedure for multiple endpoints based on group-sequential p-values

Description

Usage

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Value

Note