gMCP (version 0.6-5)

generateBounds: generateBounds

Description

compute rejection bounds for z-scores of each elementary hypotheses within each intersection hypotheses

Usage

generateBounds(g, w, cr, al = 0.05, hint = generateWeights(g, w))

Arguments

g

graph defined as a matrix, each element defines how much of the local alpha reserved for the hypothesis corresponding to its row index is passed on to the hypothesis corresponding to its column index

w

vector of weights, defines how much of the overall alpha is initially reserved for each elementary hypothesis

cr

correlation matrix defining pairwise correlations between the elementary hypotheses. Unknown values can be set to NA. (See details for more information)

al

overall alpha level at which the family error is controlled

hint

if intersection hypotheses weights have already been computed (output of generateWeights) can be passed here otherwise will be computed during execution

Value

• Returns a matrix of rejection bounds. Each row corresponds to an intersection hypothesis. The intersection corresponding to each line is given by conversion of the line number into binary (eg. 13 is binary 1101 and corresponds to (H1,H2,H4))

Details

The correlation has to be passed as a numeric matrix with elements of the form: cr[i,i] = 1, cr[i,j] = cor(i,j) if known or cr[i,j] = NA if unknown. For example cr[1,2]=0 would indicate that the first and second test statistics are uncorrelated, whereas cr[2,3] = NA would mean that statistics two and three might have correlation between -1 and 1. The correlation has to be specified for complete blocks (ie.: if cor(i,j), and cor(i,j') for i!=j!=j' are known than cor(j,j') has to be known as well) otherwise multcomp will throw an exception as NA correlations are fed to the multivariate normal distribution

References

Bretz F, Maurer W, Brannath W, Posch M; (2008) - A graphical approach to sequentially rejective multiple testing procedures. - Stat Med - 28/4, 586-604 Bretz F, Posch M, Glimm E, Klinglmueller F, Maurer W, Rohmeyer K; (2011) - Graphical approaches for multiple endpoint problems using weighted Bonferroni, Simes or parametric tests - to appear

Examples

## Define some graph as matrix
 g <- matrix(c(0,0,1,0,
               0,0,0,1,
               0,1,0,0,
               1,0,0,0), nrow = 4,byrow=TRUE)
 ## Choose weights
 w <- c(.5,.5,0,0)
 ## Some correlation (upper and lower first diagonal 1/2)
 c <- diag(4)
 c[1:2,3:4] <- NA
 c[3:4,1:2] <- NA
 c[1,2] <- 1/2
 c[2,1] <- 1/2
 c[3,4] <- 1/2
 c[4,3] <- 1/2

 ## Boundaries for correlated test statistics at alpha level .05:
 generateBounds(g,w,c,.05)