# secondaryBoundaryVecLD: Calculate Refined Secondary Boundaries and Nominal... In gsrsb: Group Sequential Refined Secondary Boundary

## Description

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

## Usage

 ```1 2``` ```secondaryBoundaryVecLD(alpha, tVec, primaryOBF = TRUE, secondaryOBF = FALSE, nRepVec = c(10, 10, 10, 10), initIntvl = c(0.8, 8)) ```

## Arguments

 `alpha` type I error probability. `tVec` vector of relative information levels. The last element in the vector is 1. `primaryOBF` type of primary boundary, `TURE` is the O'Brien-Fleming boundary, `FALSE` is the Pocock boundary. `secondaryOBF` type of secondary boundary, `TURE` is the O'Brien-Fleming boundary, `FALSE` is the Pocock boundary. `nRepVec` computing paramter, number of replica, a vector of four numbers. `initIntvl` computing paramter, a pair of numbers containing the end-points of the interval to be searched for the root.

## 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 are two computing parameters `nRepVec` and `initIntvl`. Parameter `nRepVec` includes four numbers: `nRepVec[1]` is the number of replica for calculating primary boundaries, `nRepVec[2]` is the number of replica for searching the location of peak, `nRepVec[3]` is the number of replica for calculating secondary boundaries, `nRepVec[4]` is the number of replica for calculating the nominal significance. 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.

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. (2017+). A gatekeeping procedure to test a primary and a secondary endpoint in a group sequential design with multiple interim looks. Biometrics, to appear.

`secondaryBoundaryVec`, `secondaryBoundaryVecOrig`
 ```1 2 3 4 5 6``` ```#require(mvtnorm) #require(ldbounds) #result <- secondaryBoundaryVecLD(alpha=0.025,tVec=c(1/2,1),primaryOBF=TRUE, # secondaryOBF=FALSE, nRepVec=c(1,1,1,1),initIntvl=c(0.8,6)) #result\$secondaryBoundary #result\$nomialSignificance ```