Lower and Upper Bounds Generator

Description

Generate lower and upper bounds for programs calculating the secondary endpoint's type I error when the correlation rho between the primary endpoint and the secondary endpoint equals 1.

Usage

cdBoundary(cvec, dvec, gammaVec, dlt, upper = TRUE)

Arguments

Details

This function generates upper and lower bounds for further computation. For more details, refer to Tamhane et al. (2018, Biometrics), section 4.2.

Value

lower and upper bounds for programs calculating the secondary endpoint's type I error when the correlation rho is 1.

Author(s)

Jiangtao Gou

References

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. 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.

Examples

cvec <- rep(1.992,3)
dvec <- c(1.535*sqrt(3),1.535*sqrt(3/2),1.535)
gammaVec <- c(sqrt(1/3),sqrt(2/3),1)
dlt <- 2
uBoundary <- cdBoundary(cvec, dvec, gammaVec, dlt, upper=TRUE)

Correlation Matrix Generator

Description

Generate correlation matrix between standardized sample mean test statistics for the two endpoint at different looks.

Usage

genCorrMat(gammaVec, type, rhoPS = 0)

Arguments

Details

This function generates correlation matrix between different mean statistics. For more details, refer to Tamhane et al. (2018, Biometrics), section 2.

Value

correlation matrix, K by K for primary endpoint, (K+1) by (K+1) for secondary endpoint, where K is the number of interims.

Author(s)

Jiangtao Gou

Fengqing (Zoe) Zhang

References

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

corrMat <- genCorrMat(gammaVec=c(sqrt(1/3), sqrt(2/3), 1), type=2, rhoPS = 0.3)

Find the Location of Maximum, Standard OBF and POC

Description

Calculate the location of maximal tyep I error of the standard O'Brien-Fleming and Pocock refined secondary boundaries.

Usage

initLocPeak(alpha, tVec, cvec, type = 2, initIntvl = c(1, 4))

Arguments

Details

This function search the location of the maximal point, in order to calculate the standard (origiinal) O'Brien-Fleming (OBF) and Pocock (POC) refined secondary boundaries.

Value

location of maximum, a number between 1 and the number of interims

Author(s)

Jiangtao Gou

References

O'Brien, P. C., and Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics 35, 549-556.

Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika 64, 191-199.

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, to appear.

See Also

SecondaryBoundary, ldInitLocBeak

Examples

require(mvtnorm)
K <- 8
gammaVec <- sqrt((1:K)/K)
tVec <- gammaVec^2
alpha <- 0.025
c <- 2.072274
cvec <- c/gammaVec
loc <- initLocPeak(alpha,tVec,cvec,type=2,initIntvl=c(1,3))

Find the Location of Maximum, Error Spending Approach

Description

Calculate the location of maximal type I error of secondary endpoint.

Usage

ldInitLocPeak(alpha, tVec, cvec, type = 2, initIntvl = c(0.8, 4))

Arguments

Details

This function searches the location of maximal type I error of secondary endpoint by using the error spending approach.

Value

location of maximum, a number between 1 and the number of interims.

Author(s)

Jiangtao Gou

References

Lan, K. K. G., and Demets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika 70, 659-663.

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, 40-48.

See Also

ldSecondaryBoundary, initLocBeak

Examples

## Not run: 
require(mvtnorm)
require(ldbounds)
K <- 6;
tVec <- c(140,328,453,578,659,1080)/1080;
alpha = 0.025;
cvec.obf <- ldbounds::ldBounds(tVec,iuse=c(1),alpha=c(alpha),sides=1);
cvec <- cvec.obf$upper.bounds;
loc <- ldInitLocPeak(alpha,tVec,cvec,type=2,initIntvl=c(0.9,4))

## End(Not run)

Calculate Nominal Significance, Error Spending Approach

Description

Nominal significance for the secondary endpoint are calculated by using the error spending approach.

Usage

ldNominalSig(alpha, tVec, cvec, locPeak, type = 2, initIntvl = c(1, 4))

Arguments

Details

This function calculates the nominal significance level of any Lan-DeMets error spending boundary. The original significance level is used to choose the initial searching range of the nominal significance.

Value

nominal significance of the secondary group sequential boundary.

Author(s)

Jiangtao Gou

References

Lan, K. K. G., and Demets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika 70, 659-663.

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, 40-48.

See Also

nominalSig, secondaryBoundaryVecLD

Examples

## Not run: 
require(mvtnorm)
require(ldbounds)
K <- 6;
tVec <- c(140,328,453,578,659,1080)/1080;
alpha <- 0.025;
cvec.obf <- ldbounds::ldBounds(t=tVec,iuse=c(1),alpha=c(alpha),sides = 1);
cvec <- cvec.obf$upper.bounds;
alphaprime <- ldNominalSig(alpha,tVec,cvec,locPeak=4,type=2,
      initIntvl=c(1,4))

## End(Not run)

Calculate Primary Boundaries, the Error Spending Approach

Description

Primary boundaries calculation of Lan-DeMets OBF and POC.

Usage

ldPrimaryBoundary(tVec, alpha, type = 1, initIntvl = c(0.8, 8))

Arguments

Value

a vector of primary boundaries.

Author(s)

Jiangtao Gou

References

Lan, K. K. G., and Demets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika 70, 659-663.

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.

Gou, J. (2023). Trigger strategy in repeated tests on multiple hypotheses. Statistics in Biopharmaceutical Research, 15(1), 133–140.

See Also

primaryBoundary

Difference between the Error Rate and Significance Level, the Error Spending Approach

Description

Calculate the difference between the error rate and significance level for the secondary endpoint, Lan-DeMets error spending approach.

Usage

ldSecControl(ap, alpha, cvec, tVec, ExtrmLoc, type = 2)

Arguments

Value

difference between alpha and the calculated error rate.

Author(s)

Jiangtao Gou

References

Lan, K. K. G., and Demets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika 70, 659-663.

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.

See Also

secControl

Calculate Refined Secondary Boundary, Error Spending Approach

Description

Refined secondary boundaries are calculated by using the error spending approach.

Usage

ldSecondaryBoundary(
  alpha,
  tVec,
  cvec,
  locPeak,
  type = 2,
  initIntvl = c(0.6, 4)
)

Arguments

Details

This function calculates the refined secondary boundaries of any Lan-DeMets error spending boundary based on the primary boundaries.

Value

refined secondary boundaries.

Author(s)

Jiangtao Gou

References

Lan, K. K. G., and Demets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika 70, 659-663.

Tamhane, A. C., Gou, J., Jennison, C., Mehta, C. R., and Curto, T. (2017+). A gatekeeping procedure to test a primary and a secondary endpoint in a group sequential design with multiple interim looks. Biometrics, 74, 40-48.

See Also

secondaryBoundary, secondaryBoundaryVecLD

Examples

## Not run: 
require(mvtnorm)
require(ldbounds)
K <- 6;
tVec <- c(140,328,453,578,659,1080)/1080;
alpha = 0.025;
cvec.obf <- ldbounds::ldBounds(t=tVec,iuse=c(1),alpha=c(alpha),sides = 1);
cvec <- cvec.obf$upper.bounds;
secbound <- ldSecondaryBoundary(alpha,tVec,cvec,locPeak=4,type=2,
    initIntvl=c(0.8,8))

## End(Not run)

Calculate Nominal Significance, Standard Approach

Description

Nominal significance for the secondary endpoint are calculated by using the standard (original) approach.

Usage

nominalSig(gammaVec, cvec)

Arguments

Details

This function calculates he nominal significance level of any given boundary.

Value

nominal significance

Author(s)

Jiangtao Gou

References

O'Brien, P. C., and Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics 35, 549-556.

Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika 64, 191-199.

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, 40-48.

See Also

ldNominalSig, secondaryBoundaryVecOrig

Examples

require(mvtnorm)
require(ldbounds)
nSig <- nominalSig(gammaVec=c(sqrt(1/3),1),cvec=c(2.2,1.8))

Calculate Primary Boundaries, Standard Approach

Description

Primary boundaries calculation of standard (original) OBF and POC.

Usage

primaryBoundary(gammaVec, alpha, type = 1, initIntvl = c(1, 4))

Arguments

Value

original OBF and POC boundaries (primary endpoints) (a number, c_(K)).

Author(s)

Jiangtao Gou

References

Tamhane, A. C., Gou, J., Jennison, C., Mehta, C. R., and Curto, T. (2017+). A gatekeeping procedure to test a primary and a secondary endpoint in a group sequential design with multiple interim looks. Biometrics, to appear.

See Also

ldPrimaryBoundary

Calculate the Primary Boundaries

Description

Primary boundaries are calculated, including the standard approach and the error spending approach.

Usage

primaryBoundaryVec(
  alpha,
  tVec,
  OBF = TRUE,
  LanDeMets = FALSE,
  digits = 2,
  printOut = TRUE,
  initIntvl = c(1, 8)
)

Arguments

Value

OBF and POC boundaries (primary endpoints) (vector).

Author(s)

Jiangtao Gou

References

Jennison, C. and Turnbull, B. W. (2000). Group Sequential Methods with Applications to Clinical Trials. Chapman and Hall/CRC, New York.

Lan, K. K. G., and Demets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika 70, 659-663.

O'Brien, P. C., and Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics 35, 549-556.

Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika 64, 191-199.

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.

Examples

require(mvtnorm)
K <- 4
alpha <- 0.025
tVec <- (1:K)/K
boundaryVector <- primaryBoundaryVec(alpha,tVec,initIntvl=c(1,4),
   OBF=TRUE,LanDeMets=FALSE,digits=3,printOut=TRUE)
boundaryVector <- primaryBoundaryVec(alpha,tVec,initIntvl=c(1,4),
   OBF=FALSE,LanDeMets=FALSE,digits=3,printOut=TRUE)
boundaryVector <- primaryBoundaryVec(alpha,tVec,initIntvl=c(1,8),
   OBF=TRUE,LanDeMets=TRUE,digits=3,printOut=TRUE)
boundaryVector <- primaryBoundaryVec(alpha,tVec,initIntvl=c(1,4),
   OBF=FALSE,LanDeMets=TRUE,digits=3,printOut=TRUE)

Summarize Primary and Refined Secondary Boundaries in a TeX table

Description

Primary boundaries and refined secondary boundaries are listed in a TeX table.

Usage

psbTeXtable(
  alpha,
  tVec,
  pOBF = TRUE,
  sOBF = FALSE,
  LanDeMets = FALSE,
  digits = 2
)

Arguments

Details

This function gives a TeX format table including both primary boundary and refined secondary boundary. The number of digits after decimal point can be specified through parameter digits.

Value

a TeX format table including both primary boundary and refined secondary boundary.

Author(s)

Jiangtao Gou

Fengqing (Zoe) Zhang

References

Glimm, E., Maurer, W., and Bretz, F. (2010). Hierarchical testing of multiple endpoints in group-sequential trials. Statistics in Medicine 29, 219-228.

Hung, H. M. J., Wang, S.-J., and O'Neill, R. (2007). Statistical considerations for testing multiple endpoints in group sequential or adaptive clinical trials. Journal of Biopharmaceutical Statistics 17, 1201-1210.

Jennison, C. and Turnbull, B. W. (2000). Group Sequential Methods with Applications to Clinical Trials. Chapman and Hall/CRC, New York.

Lan, K. K. G., and Demets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika 70, 659-663.

O'Brien, P. C., and Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics 35, 549-556.

Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika 64, 191-199.

Tamhane, A. C., Mehta, C. R., and Liu, L. (2010). Testing a primary and a secondary endpoint in a group sequential design. Biometrics 66, 1174-1184.

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, 40-48.

Examples

require(mvtnorm)
require(ldbounds)
require(xtable)
psbTeXtable(alpha=0.025,tVec=c(1/2,3/4,1),pOBF=TRUE,sOBF=FALSE,LanDeMets=FALSE)

Summarize Primary and Refined Secondary Boundaries, Nominal Significance

Description

Primary boundaries, refined secondary boundaries, and nominal significance for the secondary endpoint are listed.

Usage

refinedBoundary(
  alpha,
  tVec,
  pOBF = TRUE,
  sOBF = FALSE,
  LanDeMets = FALSE,
  digits = 2
)

Arguments

Details

This function gives a list including primary boundary, refined secondary boundary, and the nominal significance for the secondary endpoint. The number of digits for the nominal significance depends on parameter alpha.

Value

a result list including primary boundary, refined secondary boundary, and the nominal significance for the secondary endpoint.

Author(s)

Jiangtao Gou

References

Glimm, E., Maurer, W., and Bretz, F. (2010). Hierarchical testing of multiple endpoints in group-sequential trials. Statistics in Medicine 29, 219-228.

Hung, H. M. J., Wang, S.-J., and O'Neill, R. (2007). Statistical considerations for testing multiple endpoints in group sequential or adaptive clinical trials. Journal of Biopharmaceutical Statistics 17, 1201-1210.

Jennison, C. and Turnbull, B. W. (2000). Group Sequential Methods with Applications to Clinical Trials. Chapman and Hall/CRC, New York.

Lan, K. K. G., and Demets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika 70, 659-663.

O'Brien, P. C., and Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics 35, 549-556.

Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika 64, 191-199.

Tamhane, A. C., Mehta, C. R., and Liu, L. (2010). Testing a primary and a secondary endpoint in a group sequential design. Biometrics 66, 1174-1184.

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, 40-48

Examples

require(mvtnorm)
require(ldbounds)
result <- refinedBoundary(alpha=0.05,tVec=c(0.2,0.6,1))
result$primaryBoundary
result$secondaryBoundary
result$nomialSignificance

Difference between the Error Rate and Significance Level, Standard Approach

Description

Calculate the difference between the error rate and significance level for the secondary endpoint, standard (original) approach.

Usage

secControl(d, alpha, cvec, gammaVec, ExtrmLoc, type = 2)

Arguments

Value

difference between alpha and the calculated error rate.

Author(s)

Jiangtao Gou

References

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.

See Also

ldSecControl

Calculate the Refined Secondary Boundaries, Standard OBF and POC

Description

Calculate the standard O'Brien-Fleming and Pocock refined secondary boundaries

Usage

secondaryBoundary(alpha, tVec, cvec, locPeak, type = 2, initIntvl = c(1, 4))

Arguments

Details

This function calculates the standard (origiinal) O'Brien-Fleming (OBF) and Pocock (POC) refined secondary boundaries.

Value

standard O'Brien-Fleming and Pocock refined secondary boundaries.

Author(s)

Jiangtao Gou

References

O'Brien, P. C., and Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics 35, 549-556.

Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika 64, 191-199.

Tamhane, A. C., Gou, J., Jennison, C., Mehta, C. R., and Curto, T. (2017+). A gatekeeping procedure to test a primary and a secondary endpoint in a group sequential design with multiple interim looks. Biometrics, 74, 40-48.

See Also

ldSecondaryBoundary, initLocBeak

Examples

## Not run: 
require(mvtnorm)
K <- 8
gammaVec <- sqrt((1:K)/K)
tVec <- gammaVec^2
alpha = 0.025
c <- 2.072274
cvec <- c/gammaVec
loc <- initLocPeak(alpha,tVec,cvec,type=2,initIntvl=c(1,4))
sbvec <- secondaryBoundary(alpha,tVec,cvec,loc,type=2,
       initIntvl=c(1,8))

## End(Not run)

Calculate Refined Secondary Boundaries and Nominal Significance

Description

Refined secondary boundaries, and nominal significance for the secondary endpoint are calculated.

Usage

secondaryBoundaryVec(
  alpha,
  tVec,
  pOBF = TRUE,
  sOBF = FALSE,
  LanDeMets = FALSE,
  initIntvl = c(0.8, 8)
)

Arguments

Details

This function gives a list including refined secondary boundary and the nominal significance for the secondary endpoint. There are a computing parameter initIntvl. Parameter initIntvl contains the end-points of the interval to be searched for the root. For Lan-DeMets error spending approach, the lower end point should choose a number slightly less than 1, and the upper end point should choose a number between 4 and 10.

Value

a result list including refined secondary boundary and the nominal significance for the secondary endpoint.

Author(s)

Jiangtao Gou

References

Glimm, E., Maurer, W., and Bretz, F. (2010). Hierarchical testing of multiple endpoints in group-sequential trials. Statistics in Medicine 29, 219-228.

Hung, H. M. J., Wang, S.-J., and O'Neill, R. (2007). Statistical considerations for testing multiple endpoints in group sequential or adaptive clinical trials. Journal of Biopharmaceutical Statistics 17, 1201-1210.

Jennison, C. and Turnbull, B. W. (2000). Group Sequential Methods with Applications to Clinical Trials. Chapman and Hall/CRC, New York.

Lan, K. K. G., and Demets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika 70, 659-663.

O'Brien, P. C., and Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics 35, 549-556.

Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika 64, 191-199.

Tamhane, A. C., Mehta, C. R., and Liu, L. (2010). Testing a primary and a secondary endpoint in a group sequential design. Biometrics 66, 1174-1184.

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, 40-48.

See Also

secondaryBoundaryVecLD, secondaryBoundaryVecOrig

Examples

require(mvtnorm)
require(ldbounds)
result <- secondaryBoundaryVec(alpha=0.025,tVec=c(1/2,1),pOBF=TRUE,sOBF=FALSE,
       LanDeMets=FALSE,initIntvl=c(0.8,5))
result$secondaryBoundary
result$nomialSignificance

Calculate Refined Secondary Boundaries and Nominal Significance, the Error Spending Approach

Description

Lan-DeMets refined secondary boundaries, and nominal significance for the secondary endpoint are calculated by using the error spending approach.

Usage

secondaryBoundaryVecLD(
  alpha,
  tVec,
  primaryOBF = TRUE,
  secondaryOBF = FALSE,
  initIntvl = c(0.8, 8)
)

Arguments

Details

This function uses the Lan-DeMets error spending approach, and gives a list including refined secondary boundary and the nominal significance for the secondary endpoint. There is a computing parameter initIntvl. Parameter initIntvl contains the end-points of the interval to be searched for the root. For Lan-DeMets error spending approach, the lower end point should choose a number slightly less than 1, and the upper end point should choose a number between 4 and 10.

Value

a result list including Lan-DeMets refined secondary boundary and the nominal significance for the secondary endpoint.

Author(s)

Jiangtao Gou

References

Glimm, E., Maurer, W., and Bretz, F. (2010). Hierarchical testing of multiple endpoints in group-sequential trials. Statistics in Medicine 29, 219-228.

Hung, H. M. J., Wang, S.-J., and O'Neill, R. (2007). Statistical considerations for testing multiple endpoints in group sequential or adaptive clinical trials. Journal of Biopharmaceutical Statistics 17, 1201-1210.

Jennison, C. and Turnbull, B. W. (2000). Group Sequential Methods with Applications to Clinical Trials. Chapman and Hall/CRC, New York.

Lan, K. K. G., and Demets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika 70, 659-663.

O'Brien, P. C., and Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics 35, 549-556.

Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika 64, 191-199.

Tamhane, A. C., Mehta, C. R., and Liu, L. (2010). Testing a primary and a secondary endpoint in a group sequential design. Biometrics 66, 1174-1184.

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, 40-48.

See Also

secondaryBoundaryVec, secondaryBoundaryVecOrig

Examples

require(mvtnorm)
require(ldbounds)
result <- secondaryBoundaryVecLD(alpha=0.025,tVec=c(1/2,1),primaryOBF=TRUE,
        secondaryOBF=FALSE,initIntvl=c(0.8,6))
result$secondaryBoundary
result$nomialSignificance

Calculate Refined Secondary Boundaries and Nominal Significance, Standard Approach

Description

Standard refined secondary boundaries, and nominal significance for the secondary endpoint are calculated by using the standard (original) approach.

Usage

secondaryBoundaryVecOrig(
  alpha,
  tVec,
  primaryOBF = TRUE,
  secondaryOBF = FALSE,
  initIntvl = c(1, 8)
)

Arguments

Details

This function uses the standard approach (O'Brien and Fleming 1979, Pocock 1977), and gives a list including refined secondary boundary and the nominal significance for the secondary endpoint. There is a computing parameter initIntvl. Parameter initIntvl contains the end-points of the interval to be searched for the root. The lower end point should choose a number around 1, and the upper end point should choose a number between 4 and 10.

Value

a result list including standard refined secondary boundary and the nominal significance for the secondary endpoint.

Author(s)

Jiangtao Gou

References

Glimm, E., Maurer, W., and Bretz, F. (2010). Hierarchical testing of multiple endpoints in group-sequential trials. Statistics in Medicine 29, 219-228.

Hung, H. M. J., Wang, S.-J., and O'Neill, R. (2007). Statistical considerations for testing multiple endpoints in group sequential or adaptive clinical trials. Journal of Biopharmaceutical Statistics 17, 1201-1210.

Jennison, C. and Turnbull, B. W. (2000). Group Sequential Methods with Applications to Clinical Trials. Chapman and Hall/CRC, New York.

O'Brien, P. C., and Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics 35, 549-556.

Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika 64, 191-199.

Tamhane, A. C., Mehta, C. R., and Liu, L. (2010). Testing a primary and a secondary endpoint in a group sequential design. Biometrics 66, 1174-1184.

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, 40-48.

See Also

secondaryBoundaryVec, secondaryBoundaryVecLD

Examples

require(mvtnorm)
require(ldbounds)
result <- secondaryBoundaryVecOrig(alpha=0.025,tVec=c(1/2,1),primaryOBF=TRUE,
       secondaryOBF=FALSE, initIntvl=c(1,4))
result$secondaryBoundary
result$nomialSignificance