gMCP (version 0.8-5)

graphTest: Multiple testing using graphs

Description

Implements the graphical test procedure described in Bretz et al. (2009). Note that the gMCP function in the gMCP package performs the same task.

Usage

graphTest(pvalues, weights = NULL, alpha = 0.05, G = NULL, cr = NULL,
            graph = NULL, verbose = FALSE, test)

Arguments

pvalues

Either a vector or a matrix containing the local p-values for the hypotheses in the rows.

weights

Initial weight levels for the test procedure, in case of multiple graphs this needs to be a matrix.

alpha

Overall alpha level of the procedure.

G

Matrix determining the graph underlying the test procedure. Note that the diagonal need to contain only 0s, while the rows need to sum to 1. When multiple graphs should be used this needs to be a list containing the different graphs as element

graph

As an alternative to the specification via alphas and G one can also hand over a graphMCP object to the code. graphMCP objects can be created for example with the graphGUI functi

cr

Correlation matrix that should be used for the parametric test. If cr==NULL the Bonferroni based test procedure is used.

verbose

If verbose is TRUE, additional information about the graphical rejection procedure is displayed.

test

In the parametric case there is more than one way to handle subgraphs with less than the full alpha. If the parameter test is missing, the tests are performed as described by Bretz et al. (2011), i.e. tests of intersection null

Value

• A vector or a matrix containing the test results for the hypotheses under consideration. Significant tests are denoted by a 1, non-significant results by a 0.

References

Bretz, F., Maurer, W., Brannath, W. and Posch, M. (2009) A graphical approach to sequentially rejective multiple test procedures. Statistics in Medicine, 28, 586--604

Bretz, F., Maurer, W. and Hommel, G. (2010) Test and power considerations for multiple endpoint analyses using sequentially rejective graphical procedures, to appear in Statistics in Medicine

Examples

#### example from Bretz et al. (2010)
weights <- c(1/3, 1/3, 1/3, 0, 0, 0)
graph <- rbind(c(0,       0.5, 0,     0.5, 0,      0),
               c(1/3,     0,   1/3,	  0,   1/3,    0),
               c(0,       0.5, 0,     0,   0,      0.5),
               c(0,       1,   0,     0,   0,      0),
               c(0.5,     0,   0.5,   0,   0,      0),
               c(0,       1,   0,     0,   0,      0))
pvals <- c(0.1, 0.008, 0.005, 0.15, 0.04, 0.006)
graphTest(pvals, weights, alpha=0.025, graph)

## observe graphical procedure in detail
graphTest(pvals, weights, alpha=0.025, graph, verbose = TRUE)

## now use many p-values (useful for power simulations)
pvals <- matrix(rbeta(6e4, 1, 30), ncol = 6)
out <- graphTest(pvals, weights, alpha=0.025, graph)
head(out)

## example using multiple graphs (instead of 1)
G1 <- rbind(c(0,0.5,0.5,0,0), c(0,0,1,0,0),
            c(0, 0, 0, 1-0.01, 0.01), c(0, 1, 0, 0, 0),
            c(0, 0, 0, 0, 0))
G2 <- rbind(c(0,0,1,0,0), c(0.5,0,0.5,0,0),
            c(0, 0, 0, 0.01, 1-0.01), c(0, 0, 0, 0, 0),
            c(1, 0, 0, 0, 0))
weights <- rbind(c(1, 0, 0, 0, 0), c(0, 1, 0, 0, 0))
pvals <- c(0.012, 0.025, 0.005, 0.0015, 0.0045)
out <- graphTest(pvals, weights, alpha=c(0.0125, 0.0125), G=list(G1, G2), verbose = TRUE)

## now again with many p-values
pvals <- matrix(rbeta(5e4, 1, 30), ncol = 5)
out <- graphTest(pvals, weights, alpha=c(0.0125, 0.0125), G=list(G1, G2))
head(out)