Package 'permGS' reference manual

Title:	Permutational Group Sequential Test for Time-to-Event Data
Description:	Permutational group-sequential tests for time-to-event data based on the log-rank test statistic. Supports exact permutation test when the censoring distributions are equal in the treatment and the control group and approximate imputation-permutation methods when the censoring distributions are different.
Authors:	Matthias Brueckner [aut, cre], Martin Posch [aut], Franz Koenig [aut]
Maintainer:	Matthias Brueckner <[email protected]>
License:	GPL-3 \| file LICENSE
Version:	0.2.5
Built:	2025-03-05 03:47:02 UTC
Source:	https://github.com/mbrueckner/permgs

createPermGS

Description

Create permGS object representing a permutational group-sequential trial.

Usage

createPermGS(B = 1000, restricted = TRUE, method = "IPZ", pool = TRUE,
  type = c("logrank", "Gehan-Breslow", "Tarone-Ware", "Prentice",
  "Prentice-Marek", "Andersen-Borgan-Gill-Keiding", "Fleming-Harrington",
  "Self"), imputeData = NULL, permuteData = NULL)
createPermGS(B = 1000, restricted = TRUE, method = "IPZ", pool = TRUE,
  type = c("logrank", "Gehan-Breslow", "Tarone-Ware", "Prentice",
  "Prentice-Marek", "Andersen-Borgan-Gill-Keiding", "Fleming-Harrington",
  "Self"), imputeData = NULL, permuteData = NULL)

Arguments

`B`	number of random permutations
`restricted`	if TRUE only permute within strata
`method`	imputation/permuation method IPZ, IPT, Heinze or none (default: IPZ)
`pool`	if TRUE impute event times from Kaplan-Meier estimator calculated from pooled data
`type`	logrank weights to be used with coin::logrank_trafo
`imputeData`	user-supplied imputation function (ignored if method is given)
`permuteData`	user-supplied permutation function (ignore if method is given)

Value

object of class permGS

Examples

## standard permutation test (no imputation, free permutations)
x <- createPermGS(1000, FALSE, "none")
summary(x)
## imputation using IPT method, restricted permutations
y <- createPermGS(1000, TRUE, "IPT")
summary(y)
## standard permutation test (no imputation, free permutations)
x <- createPermGS(1000, FALSE, "none")
summary(x)
## imputation using IPT method, restricted permutations
y <- createPermGS(1000, TRUE, "IPT")
summary(y)

exactLR

Description

One-sided exact / approximate permutation and asymptotic log-rank test

Usage

exactLR(B, formula, data = parent.frame(), type = "exact")
exactLR(B, formula, data = parent.frame(), type = "exact")

Arguments

`B`	number of random permutations (only used if type="approximate")
`formula`	a formula object, as used by `coxph`, left hand side must be a 'Surv' object, right hand side may only consist of a single term (treatment indicator)
`data`	data.frame or list containing the variables in "formula", by default "formula" is evaluated in the parent frame
`type`	if type="exact" performs complete enumeration of all permutations, if type="approximate" draw random permutations, if type="asymptotic" perform asymptotic log-rank test

Details

This function performs a standard exact or approximate permutation test which is only valid under the extended null hypothesis of equal survival AND censoring distributions.

Value

A list containing the exact or approximate permutation p-value and the observed test statistic

Examples

T <- rexp(20)
C <- rexp(20)
data <- data.frame(time=pmin(T, C), status=(T<=C), trt=rbinom(20, 1, 0.5))

# Approximate permutation test using 1000 random permutations
x <- exactLR(1000, Surv(time, status) ~ trt, data, "approximate")

print(paste("Approximate permutation p-value:", x$p))

# Exact permutation test
y <- exactLR(0, Surv(time, status) ~ trt, data, "exact")
print(paste("Exact permutation p-value:", y$p))

T <- rexp(20)
C <- rexp(20)
data <- data.frame(time=pmin(T, C), status=(T<=C), trt=rbinom(20, 1, 0.5))

# Approximate permutation test using 1000 random permutations
x <- exactLR(1000, Surv(time, status) ~ trt, data, "approximate")

print(paste("Approximate permutation p-value:", x$p))

# Exact permutation test
y <- exactLR(0, Surv(time, status) ~ trt, data, "exact")
print(paste("Exact permutation p-value:", y$p))

imputeHeinze

Description

Impute data according to Heinze et al. method. Output is supposed to be passed to permute.heinze

Usage

imputeHeinze(data, pool = TRUE)
imputeHeinze(data, pool = TRUE)

Arguments

`data`	matrix as returned by as.matrix(generateData(param))
`pool`	if TRUE impute events times from pooled Kaplan-Meier estimator (default: TRUE)

Value

list containing Kaplan-Meier estimators of censoring and survival distributions and the original data

References

Heinze, G., Gnant, M. and Schemper, M. Exact Log-Rank Tests for Unequal Follow-Up. Biometrics, 59(4), December 2003.

imputeIPT

Description

Impute data according to IPT method. Output is supposed to be passed to permute.IPT

Usage

imputeIPT(data, pool = TRUE)
imputeIPT(data, pool = TRUE)

Arguments

`data`	matrix as returned by as.matrix(generateData(param))
`pool`	if TRUE impute events times from pooled Kaplan-Meier estimator (default: TRUE)

Value

matrix containing imputed survival and censoring times (columns 1 and 2), and original treatment indicator (column 3)

References

Wang, R., Lagakos, S.~W. and Gray, R.~J. Testing and interval estimation for two-sample survival comparisons with small sample sizes and unequal censoring. Biostatistics, 11(4), 676–692, January 2010.

imputeIPZ

Description

Impute data according to IPZ method. Output is supposed to be passed to permute.IPZ

Usage

imputeIPZ(data, pool = TRUE)
imputeIPZ(data, pool = TRUE)

Arguments

`data`	matrix as returned by as.matrix(generateData(param))
`pool`	if TRUE impute events times from pooled Kaplan-Meier estimator (default: TRUE)

Value

original data with 4 new columns (V1 and V2) containing the imputed observations

References

nextStage

Description

Imputation permutation group-sequential log-rank test. Random permutations of a block a reused in all later stages. This automatically results in blockwise permutations.

Usage

nextStage(pgs.obj, alpha, formula, data = parent.frame())
nextStage(pgs.obj, alpha, formula, data = parent.frame())

Arguments

`pgs.obj`	permGS object as returned by `createPermGS`
`alpha`	alpha at current stage
`formula`	a formula object, as used by `coxph`, left hand side must be a 'Surv' object, right hand side must only consist of a factor (treatment indicator) and optionally a special strata() term identifying the permutation strata
`data`	a data.frame or list containing the variables in "formula", by default "formula" is evaluated in the parent frame

Value

An updated permGS object.

Examples

## Two-stage design with one-sided O'Brien-Fleming boundaries using IPZ method
x <- createPermGS(1000, TRUE, "IPZ")

t1 <- 9  ## calendar time of interim analysis
t2 <- 18  ## calendar time of final analysis

T <- rexp(100) ## event times
R <- runif(100, 0, 12)  ## recruitment times
Z <- rbinom(100, 1, 0.5)  ## treatment assignment
C <- rexp(100) ## drop-out times

## Stage 1 data
data.t1 <- data.frame(time=pmin(T, C, max(0, (t1-R))), status=(T<=pmin(C, t1-R)), trt=Z)
data.t1 <- data.t1[R <= t1,]

## Stage 2 data
data.t2 <- data.frame(time=pmin(T, C, max(0, (t2-R))), status=(T<=pmin(C, t2-R)), trt=Z)
data.t2 <- data.t2[R <= t2,] 
x <- nextStage(x, 0.00153, Surv(time, status) ~ trt, data.t1)
summary(x)

if(!x$results$reject[1]) {
   data.t2$strata <- rep.int(c(1,2), c(nrow(data.t1), nrow(data.t2)-nrow(data.t1)))
   x <- nextStage(x, 0.025, Surv(time, status) ~ trt + strata(strata), data.t2)
   summary(x)
}
## Two-stage design with one-sided O'Brien-Fleming boundaries using IPZ method
x <- createPermGS(1000, TRUE, "IPZ")

t1 <- 9  ## calendar time of interim analysis
t2 <- 18  ## calendar time of final analysis

T <- rexp(100) ## event times
R <- runif(100, 0, 12)  ## recruitment times
Z <- rbinom(100, 1, 0.5)  ## treatment assignment
C <- rexp(100) ## drop-out times

## Stage 1 data
data.t1 <- data.frame(time=pmin(T, C, max(0, (t1-R))), status=(T<=pmin(C, t1-R)), trt=Z)
data.t1 <- data.t1[R <= t1,]

## Stage 2 data
data.t2 <- data.frame(time=pmin(T, C, max(0, (t2-R))), status=(T<=pmin(C, t2-R)), trt=Z)
data.t2 <- data.t2[R <= t2,] 
x <- nextStage(x, 0.00153, Surv(time, status) ~ trt, data.t1)
summary(x)

if(!x$results$reject[1]) {
   data.t2$strata <- rep.int(c(1,2), c(nrow(data.t1), nrow(data.t2)-nrow(data.t1)))
   x <- nextStage(x, 0.025, Surv(time, status) ~ trt + strata(strata), data.t2)
   summary(x)
}

Parse formula of survival model

Description

Parse formula of survival model

Usage

parseFormula(formula, data = parent.frame())
parseFormula(formula, data = parent.frame())

Arguments

`formula`	formula object
`data`	data.frame (optional)

Value

data.frame containing the parsed variables

permGS

Description

This package implements permutational group-sequential tests for time-to-event data based on (weighted) log-rank test statistics. It supports exact permutation test when the censoring distributions are equal in the treatment and the control group and the approximate imputation-permutation methods of Heinze et al. (2003) and Wang et al. (2010) and when the censoring distributions are different. Permutations can be stratified, i.e. only patients within the same stratum are treated as exchangeable. Rejection boundaries are monotone and finite even when only a random subset of all permutations is used. One- and Two-sided testing possible.

Author(s)

Matthias Brueckner [email protected], Franz Koenig [email protected], Martin Posch [email protected]

References

Brueckner, M., Koenig, F. and Posch, M. Group-sequential permutation tests for time-to-event data.

Heinze, G., Gnant, M. and Schemper, M. Exact Log-Rank Tests for Unequal Follow-Up. Biometrics, 59(4), December 2003.

Kelly, P., Zhou, Y., Whitehead, N. J., Stallard, N. and Bowman, C. Sequentially testing for a gene–drug interaction in a genomewide analysis. Statistics in Medicine, 27(11), 2022–2034, May 2008.

Examples

## IPZ method based on logrank test with 1000 restricted random permutations
x <- createPermGS(1000, TRUE, "IPZ", type="logrank")

T <- rexp(100) ## event times
R <- runif(100, 0, 12)  ## recruitment times
Z <- rbinom(100, 1, 0.5)  ## treatment assignment
C <- rexp(100) ## drop-out times

## two-stage design
t1 <- 9  ## calendar time of interim analysis
t2 <- 18  ## calendar time of final analysis

## Stage 1
data.t1 <- data.frame(time=pmin(T, C, max(0, (t1-R))), status=(T<=pmin(C, t1-R)), trt=Z)
data.t1 <- data.t1[R <= t1,] 
x <- nextStage(x, 0.00153, Surv(time, status) ~ trt, data.t1)
summary(x)

if(!x$results$reject[1]) { ## Stage 2
   data.t2 <- data.frame(time=pmin(T, C, max(0, (t2-R))), status=(T<=pmin(C, t2-R)), trt=Z)
   data.t2 <- data.t2[R <= t2,]
   data.t2$strata <- rep.int(c(1,2), c(nrow(data.t1), nrow(data.t2)-nrow(data.t1)))
   x <- nextStage(x, alpha=0.025, Surv(time, status) ~ trt + strata(strata), data.t2)           
   summary(x)
}

## IPZ method based on logrank test with 1000 restricted random permutations
x <- createPermGS(1000, TRUE, "IPZ", type="logrank")

T <- rexp(100) ## event times
R <- runif(100, 0, 12)  ## recruitment times
Z <- rbinom(100, 1, 0.5)  ## treatment assignment
C <- rexp(100) ## drop-out times

## two-stage design
t1 <- 9  ## calendar time of interim analysis
t2 <- 18  ## calendar time of final analysis

## Stage 1
data.t1 <- data.frame(time=pmin(T, C, max(0, (t1-R))), status=(T<=pmin(C, t1-R)), trt=Z)
data.t1 <- data.t1[R <= t1,] 
x <- nextStage(x, 0.00153, Surv(time, status) ~ trt, data.t1)
summary(x)

if(!x$results$reject[1]) { ## Stage 2
   data.t2 <- data.frame(time=pmin(T, C, max(0, (t2-R))), status=(T<=pmin(C, t2-R)), trt=Z)
   data.t2 <- data.t2[R <= t2,]
   data.t2$strata <- rep.int(c(1,2), c(nrow(data.t1), nrow(data.t2)-nrow(data.t1)))
   x <- nextStage(x, alpha=0.025, Surv(time, status) ~ trt + strata(strata), data.t2)           
   summary(x)
}

Convenience function which calls createPermGS and nextStage to perform fixed sample size permutation test with Heinze method

Description

Convenience function which calls createPermGS and nextStage to perform fixed sample size permutation test with Heinze method

Usage

permHeinze(formula, data, B = 1000, alpha = 0.05, pool = TRUE,
  type = c("logrank", "Gehan-Breslow", "Tarone-Ware", "Prentice",
  "Prentice-Marek", "Andersen-Borgan-Gill-Keiding", "Fleming-Harrington",
  "Self"))
permHeinze(formula, data, B = 1000, alpha = 0.05, pool = TRUE,
  type = c("logrank", "Gehan-Breslow", "Tarone-Ware", "Prentice",
  "Prentice-Marek", "Andersen-Borgan-Gill-Keiding", "Fleming-Harrington",
  "Self"))

Arguments

`formula`	a formula object, as used by `coxph`, left hand side must be a 'Surv' object, right hand side must only consist of a factor (treatment indicator) and optionally a special strata() term identifying the permutation strata
`data`	a data.frame or list containing the variables in "formula", by default "formula" is evaluated in the parent frame
`B`	number of random permutations (default: 1000)
`alpha`	significance level (default: 0.05)
`pool`	if TRUE impute event times from Kaplan-Meier estimator calculated from pooled data
`type`	logrank weights to be used with coin::logrank_trafo

Value

An object of class permGS

Examples

T <- rexp(30) ## event times
Z <- rbinom(30, 1, 0.5)  ## treatment assignment
C <- rexp(30) ## drop-out times
data <- data.frame(time=pmin(T,C), status=T<=C, Z=Z)
x <- permHeinze(Surv(time, status) ~ Z, data)
summary(x)
T <- rexp(30) ## event times
Z <- rbinom(30, 1, 0.5)  ## treatment assignment
C <- rexp(30) ## drop-out times
data <- data.frame(time=pmin(T,C), status=T<=C, Z=Z)
x <- permHeinze(Surv(time, status) ~ Z, data)
summary(x)

Convenience function which calls createPermGS and nextStage to perform fixed sample size permutation test with IPT method

Description

Convenience function which calls createPermGS and nextStage to perform fixed sample size permutation test with IPT method

Usage

permIPT(formula, data, B = 1000, alpha = 0.05, pool = TRUE,
  type = c("logrank", "Gehan-Breslow", "Tarone-Ware", "Prentice",
  "Prentice-Marek", "Andersen-Borgan-Gill-Keiding", "Fleming-Harrington",
  "Self"))
permIPT(formula, data, B = 1000, alpha = 0.05, pool = TRUE,
  type = c("logrank", "Gehan-Breslow", "Tarone-Ware", "Prentice",
  "Prentice-Marek", "Andersen-Borgan-Gill-Keiding", "Fleming-Harrington",
  "Self"))

Arguments

`formula`	a formula object, as used by `coxph`, left hand side must be a 'Surv' object, right hand side must only consist of a factor (treatment indicator) and optionally a special strata() term identifying the permutation strata
`data`	a data.frame or list containing the variables in "formula", by default "formula" is evaluated in the parent frame
`B`	number of random permutations (default: 1000)
`alpha`	significance level (default: 0.05)
`pool`	if TRUE impute event times from Kaplan-Meier estimator calculated from pooled data
`type`	logrank weights to be used with coin::logrank_trafo

Value

An object of class permGS

Examples

T <- rexp(30) ## event times
Z <- rbinom(30, 1, 0.5)  ## treatment assignment
C <- rexp(30) ## drop-out times
data <- data.frame(time=pmin(T,C), status=T<=C, Z=Z)
x <- permIPT(Surv(time, status) ~ Z, data)
summary(x)
T <- rexp(30) ## event times
Z <- rbinom(30, 1, 0.5)  ## treatment assignment
C <- rexp(30) ## drop-out times
data <- data.frame(time=pmin(T,C), status=T<=C, Z=Z)
x <- permIPT(Surv(time, status) ~ Z, data)
summary(x)

Convenience function which calls createPermGS and nextStage to perform fixed sample size permutation test with IPZ method

Description

Convenience function which calls createPermGS and nextStage to perform fixed sample size permutation test with IPZ method

Usage

permIPZ(formula, data, B = 1000, alpha = 0.05, pool = TRUE,
  type = c("logrank", "Gehan-Breslow", "Tarone-Ware", "Prentice",
  "Prentice-Marek", "Andersen-Borgan-Gill-Keiding", "Fleming-Harrington",
  "Self"))
permIPZ(formula, data, B = 1000, alpha = 0.05, pool = TRUE,
  type = c("logrank", "Gehan-Breslow", "Tarone-Ware", "Prentice",
  "Prentice-Marek", "Andersen-Borgan-Gill-Keiding", "Fleming-Harrington",
  "Self"))

Arguments

`formula`	a formula object, as used by `coxph`, left hand side must be a 'Surv' object, right hand side must only consist of a factor (treatment indicator) and optionally a special strata() term identifying the permutation strata
`data`	a data.frame or list containing the variables in "formula", by default "formula" is evaluated in the parent frame
`B`	number of random permutations (default: 1000)
`alpha`	significance level (default: 0.05)
`pool`	if TRUE impute event times from Kaplan-Meier estimator calculated from pooled data
`type`	logrank weights to be used with coin::logrank_trafo

Value

An object of class permGS

Examples

T <- rexp(30) ## event times
Z <- rbinom(30, 1, 0.5)  ## treatment assignment
C <- rexp(30) ## drop-out times
data <- data.frame(time=pmin(T,C), status=T<=C, Z=Z)
x <- permIPZ(Surv(time, status) ~ Z, data)
summary(x)
T <- rexp(30) ## event times
Z <- rbinom(30, 1, 0.5)  ## treatment assignment
C <- rexp(30) ## drop-out times
data <- data.frame(time=pmin(T,C), status=T<=C, Z=Z)
x <- permIPZ(Surv(time, status) ~ Z, data)
summary(x)

Convenience function which calls createPermGS and nextStage to perform fixed sample size permutation test without imputation

Description

Convenience function which calls createPermGS and nextStage to perform fixed sample size permutation test without imputation

Usage

permLR(formula, data, B = 1000, alpha = 0.05, pool = TRUE,
  type = c("logrank", "Gehan-Breslow", "Tarone-Ware", "Prentice",
  "Prentice-Marek", "Andersen-Borgan-Gill-Keiding", "Fleming-Harrington",
  "Self"))
permLR(formula, data, B = 1000, alpha = 0.05, pool = TRUE,
  type = c("logrank", "Gehan-Breslow", "Tarone-Ware", "Prentice",
  "Prentice-Marek", "Andersen-Borgan-Gill-Keiding", "Fleming-Harrington",
  "Self"))

Arguments

`formula`	a formula object, as used by `coxph`, left hand side must be a 'Surv' object, right hand side must only consist of a factor (treatment indicator) and optionally a special strata() term identifying the permutation strata
`data`	a data.frame or list containing the variables in "formula", by default "formula" is evaluated in the parent frame
`B`	number of random permutations (default: 1000)
`alpha`	significance level (default: 0.05)
`pool`	if TRUE impute event times from Kaplan-Meier estimator calculated from pooled data
`type`	logrank weights to be used with coin::logrank_trafo

Value

An object of class permGS

Examples

## Two-sided permutation test
T <- rexp(100) ## event times
Z <- rbinom(100, 1, 0.5)  ## treatment assignment
C <- rexp(100) ## drop-out times
data <- data.frame(time=pmin(T,C), status=T<=C, Z=Z)
x <- permLR(Surv(time, status) ~ Z, data, alpha=c(0.025, 0.025))
summary(x)
## Two-sided permutation test
T <- rexp(100) ## event times
Z <- rbinom(100, 1, 0.5)  ## treatment assignment
C <- rexp(100) ## drop-out times
data <- data.frame(time=pmin(T,C), status=T<=C, Z=Z)
x <- permLR(Surv(time, status) ~ Z, data, alpha=c(0.025, 0.025))
summary(x)

permuteHeinze

Description

Perform single imputation and permutation step

Usage

permuteHeinze(imp, pp, index = TRUE)
permuteHeinze(imp, pp, index = TRUE)

Arguments

`imp`	list as returned by impute.heinze
`pp`	vector of permuted indices
`index`	not used

Value

matrix with time, status, trt columns

References

Heinze, G., Gnant, M. and Schemper, M. Exact Log-Rank Tests for Unequal Follow-Up. Biometrics, 59(4), December 2003.

permuteIPT

Description

Permute survival times after imputation (IPT)

Usage

permuteIPT(data, pp, index = TRUE)
permuteIPT(data, pp, index = TRUE)

Arguments

`data`	matrix as returned by impute.IPT
`pp`	vector of permuted indices
`index`	not used

Value

matrix with time, status, trt columns

References

permuteIPZ

Description

Permute treatment assignment after imputation (IPZ)

Usage

permuteIPZ(data, pZ, index = FALSE)
permuteIPZ(data, pZ, index = FALSE)

Arguments

`data`	matrix as returned by impute.IPT
`pZ`	vector of permuted indices if index is TRUE, else binary vector of treatment assignments
`index`	indicates if pZ is a vector of indices or a binary vector of treatment assignments

Value

matrix with time, status, Z columns

References

sampleFromCondKM

Description

Sample from conditional distribution estimated by Kaplan-Meier estimator. Imputed values > tmax are right-censored.

Usage

sampleFromCondKM(U, fit, tmax = NULL, dv = 1, f = NULL)
sampleFromCondKM(U, fit, tmax = NULL, dv = 1, f = NULL)

Arguments

`U`	vector of observed times
`fit`	Kaplan-Meier fit as returned by survfit
`tmax`	largest observation of the pooled sample
`dv`	1 if imputing events, 0 if imputing censoring times
`f`	interpolated Kaplan-Meier estimate

Value

Random sample of survival times drawn from conditional distribution of T given T > U

sampleFromKM

Description

Sample from distribution estimated by Kaplan-Meier estimator. Imputed values > tmax are right-censored.

Usage

sampleFromKM(n, fit, start = 0, tmax = NULL, dv = 1)
sampleFromKM(n, fit, start = 0, tmax = NULL, dv = 1)

Arguments

`n`	sample size
`fit`	Kaplan-Meier fit as returned by survfit
`start`	if 0 sample from L(T), else sample from L(T, T > start)
`tmax`	largest observation in pooled sample
`dv`	1 if imputing events, 0 if imputing censoring times

Value

Random sample of survival times

shuffleBlock Permute block preserving group sizes, randomization blocks

Description

shuffleBlock Permute block preserving group sizes, randomization blocks

Usage

shuffleBlock(block, strata = 0)
shuffleBlock(block, strata = 0)

Arguments

`block`	vector of row indices to be permuted
`strata`	factor defining strata with block

Value

random permutation of each stratum within block

summary of permGS object

Description

summary of permGS object

Usage

## S3 method for class 'permGS'
summary(object, ...)
## S3 method for class 'permGS'
summary(object, ...)

Arguments

`object`	permGS object as returned by `createPermGS`
`...`	additional parameters (currently unused)

Value

nothing

Package 'permGS'

Help Index

createPermGS

Description

Usage

Arguments

Value

Examples

exactLR

Description

Usage

Arguments

Details

Value

Examples

imputeHeinze

Description

Usage

Arguments

Value

References

imputeIPT

Description

Usage

Arguments

Value

References

imputeIPZ

Description

Usage

Arguments

Value

References

nextStage

Description

Usage

Arguments

Value

Examples

Parse formula of survival model

Description

Usage

Arguments

Value

permGS

Description

Author(s)

References

Examples

Convenience function which calls createPermGS and nextStage to perform fixed sample size permutation test with Heinze method

Description

Usage

Arguments

Value

Examples

Convenience function which calls createPermGS and nextStage to perform fixed sample size permutation test with IPT method

Description

Usage

Arguments

Value

Examples

Convenience function which calls createPermGS and nextStage to perform fixed sample size permutation test with IPZ method

Description

Usage

Arguments

Value

Examples

Convenience function which calls createPermGS and nextStage to perform fixed sample size permutation test without imputation

Description

Usage

Arguments

Value

Examples

permuteHeinze

Description

Usage

Arguments

Value

References

permuteIPT