graphTest: Multiple testing using graphs
In gMCP: Graph Based Multiple Comparison Procedures

Description Usage Arguments Value References Examples

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

1 2	graphTest(pvalues, weights = NULL, alpha = 0.05, G = NULL, cr = NULL, graph = NULL, verbose = FALSE, test, upscale = FALSE)

`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. For entangled graphs `alpha` should be a numeric vector of length equal to the number of graphs, each element specifying the partial alpha for the respective graph. The overall alpha level equals `sum(alpha)`.
`G`	For simple graphs `G` should be a numeric 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. For entangled graphs it needs to be a list containing the different graph matrices as elements.
`graph`	As an alternative to the specification via `weights` and `G` one can also hand over a `graphMCP` object to the code. `graphMCP` objects can be created for example with the `graphGUI` function.
`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 hypotheses always exhaust the full alpha level even if the sum of weights is strictly smaller than one. If `test="simple-parametric"` the tests are performed as defined in Equation (3) of Bretz et al. (2011).
`upscale`	Logical. If `upscale=FALSE` then for each intersection of hypotheses (i.e. each subgraph) a weighted test is performed at the possibly reduced level alpha of sum(w)*alpha, where sum(w) is the sum of all node weights in this subset. If `upscale=TRUE` all weights are upscaled, so that sum(w)=1.

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.

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

#### 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)