Graph based Multiple Comparison Procedures
Description
Performs a graph based multiple test procedure for a given graph and unadjusted pvalues.
Usage
1 2 3 4 
Arguments
graph 
A graph of class 
pvalues 
A numeric vector specifying the pvalues for the graph based MCP. Note the assumptions in the details section for the parametric tests, when a correlation is specified. 
test 
Should be either 
correlation 
Optional correlation matrix. If the weighted Simes test
is performed, it is checked whether type I error rate can be ensured and a
warning is given if this is not the case. For parametric tests the pvalues
must arise from onesided tests with multivariate normal distributed test
statistics for which the correlation is (partially) known. In that case a
weighted parametric closed test is performed (also see

alpha 
A numeric specifying the maximal allowed type one error rate. 
approxEps 
A boolean specifying whether epsilon values should be
substituted with the value given in the parameter 
eps 
A numeric scalar specifying a value for epsilon edges. 
... 
Test specific arguments can be given here. 
upscale 
Logical. If For backward comptibility the default value is TRUE if a the parameter 
useC 
Logical scalar. If 
verbose 
Logical scalar. If 
keepWeights 
Logical scalar. If 
adjPValues 
Logical scalar. If 
Details
For the Bonferroni procedure the pvalues can arise from any statistical test, but if you improve the test by specifying a correlation matrix, the following assumptions apply:
It is assumed that under the global null hypothesis
(Φ^{1}(1p_1),...,Φ^{1}(1p_m)) follow a multivariate normal
distribution with correlation matrix correlation
where
Φ^{1} denotes the inverse of the standard normal distribution
function.
For example, this is the case if p_1,..., p_m are the raw pvalues
from onesided ztests for each of the elementary hypotheses where the
correlation between ztest statistics is generated by an overlap in the
observations (e.g. comparison with a common control, groupsequential
analyses etc.). An application of the transformation Φ^{1}(1p_i)
to raw pvalues from a twosided test will not in general lead to a
multivariate normal distribution. Partial knowledge of the correlation
matrix is supported. The correlation matrix has to be passed as a numeric
matrix with elements of the form: correlation[i,i] = 1 for diagonal
elements, correlation[i,j] = ρ_{ij}, where ρ_{ij} is the
known value of the correlation between Φ^{1}(1p_i) and
Φ^{1}(1p_j) or NA
if the corresponding correlation is
unknown. For example correlation[1,2]=0 indicates that the first and second
test statistic are uncorrelated, whereas correlation[2,3] = NA means that
the true correlation between statistics two and three is unknown and may
take values 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 specified
then cor(j,j') has to be specified as well) otherwise the corresponding
intersection null hypotheses tests are not uniquely defined and an error is
returned.
For further details see the given references.
Value
An object of class gMCPResult
, more specifically a list with
elements
graphs
list of graphs
pvalues
pvalues
rejected
logical whether hyptheses could be rejected
adjPValues
adjusted pvalues
Author(s)
Kornelius Rohmeyer rohmeyer@smallprojects.de
References
Frank Bretz, Willi Maurer, Werner Brannath, Martin Posch: A graphical approach to sequentially rejective multiple test procedures. Statistics in Medicine 2009 vol. 28 issue 4 page 586604. http://www.meduniwien.ac.at/fwf_adaptive/papers/bretz_2009_22.pdf
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. Biometrical Journal 53 (6), pages 894913, Wiley. http://onlinelibrary.wiley.com/doi/10.1002/bimj.201000239/full
Strassburger K., Bretz F.: Compatible simultaneous lower confidence bounds for the Holm procedure and other Bonferroni based closed tests. Statistics in Medicine 2008; 27:49144927.
Hommel G., Bretz F., Maurer W.: Powerful shortcuts for multiple testing procedures with special reference to gatekeeping strategies. Statistics in Medicine 2007; 26:40634073.
Guilbaud O.: Simultaneous confidence regions corresponding to Holm's stepdown procedure and other closedtesting procedures. Biometrical Journal 2008; 50:678692.
See Also
graphMCP
graphNEL
Examples
1 2 3 4 5 6 7 8 9 10 11  g < BonferroniHolm(5)
gMCP(g, pvalues=c(0.01, 0.02, 0.04, 0.04, 0.7))
# Simple Bonferroni with empty graph:
g2 < matrix2graph(matrix(0, nrow=5, ncol=5))
gMCP(g2, pvalues=c(0.01, 0.02, 0.04, 0.04, 0.7))
# With 'upscale=TRUE' equal to BonferroniHolm:
gMCP(g2, pvalues=c(0.01, 0.02, 0.04, 0.04, 0.7), upscale=TRUE)
# Entangled graphs:
g3 < Entangled2Maurer2012()
gMCP(g3, pvalues=c(0.01, 0.02, 0.04, 0.04, 0.7), correlation=diag(5))

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