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Graph based Multiple Comparison Procedures

Source: R/gMCP.extended.R
gMCP.extended.Rd

Performs a graph based multiple test procedure for a given graph and unadjusted p-values.

Usage

gMCP.extended(
  graph,
  pvalues,
  test,
  alpha = 0.05,
  eps = 10^(-3),
  upscale = FALSE,
  verbose = FALSE,
  adjPValues = TRUE,
  ...
)

Arguments

graph

A graph of class graphMCP.

pvalues

A numeric vector specifying the p-values for the graph based MCP. Note the assumptions in the description of the selected test (if there are any - for example test=bonferroni.test has no further assumptions, but test=parametric.test assumes p-values from a multivariate normal distribution).

test

A weighted test function.

The package gMCP provides the following weighted test functions:

bonferroni.test

Bonferroni test - see ?bonferroni.test for details.

parametric.test

Parametric test - see ?parametric.test for details.

simes.test

Simes test - see ?simes.test for details.

bonferroni.trimmed.simes.test

Trimmed Simes test for intersections of two hypotheses and otherwise Bonferroni - see ?bonferroni.trimmed.simes.test for details.

simes.on.subsets.test

Simes test for intersections of hypotheses from certain sets and otherwise Bonferroni - see ?simes.on.subsets.test for details.

To provide your own test function see ?weighted.test.function.

alpha

A numeric specifying the maximal allowed type one error rate.

eps

A numeric scalar specifying a value for epsilon edges.

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.

verbose

Logical scalar. If TRUE verbose output is generated during sequentially rejection steps.

adjPValues

Logical scalar. If FALSE no adjusted p-values will be calculated. Especially for the weighted Simes test this will result in significantly less calculations in most cases.

...

Test specific arguments can be given here.

Value

An object of class gMCPResult, more specifically a list with elements

graphs

list of graphs

pvalues

p-values

rejected

logical whether hypotheses could be rejected

adjPValues

adjusted p-values

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 586-604. https://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 894-913, Wiley. doi:10.1002/bimj.201000239

Strassburger K., Bretz F.: Compatible simultaneous lower confidence bounds for the Holm procedure and other Bonferroni based closed tests. Statistics in Medicine 2008; 27:4914-4927.

Hommel G., Bretz F., Maurer W.: Powerful short-cuts for multiple testing procedures with special reference to gatekeeping strategies. Statistics in Medicine 2007; 26:4063-4073.

Guilbaud O.: Simultaneous confidence regions corresponding to Holm's stepdown procedure and other closed-testing procedures. Biometrical Journal 2008; 50:678-692.

See also

graphMCP multcomp::contrMat()

Author

Kornelius Rohmeyer rohmeyer@small-projects.de

Examples

g <- BonferroniHolm(5)
gMCP(g, pvalues=c(0.01, 0.02, 0.04, 0.04, 0.7))
#> gMCP-Result
#> 
#> Initial graph:
#> A graphMCP graph
#> H1 (weight=0.2)
#> H2 (weight=0.2)
#> H3 (weight=0.2)
#> H4 (weight=0.2)
#> H5 (weight=0.2)
#> Edges:
#> H1  -( 0.25 )->  H2 
#> H1  -( 0.25 )->  H3 
#> H1  -( 0.25 )->  H4 
#> H1  -( 0.25 )->  H5 
#> H2  -( 0.25 )->  H1 
#> H2  -( 0.25 )->  H3 
#> H2  -( 0.25 )->  H4 
#> H2  -( 0.25 )->  H5 
#> H3  -( 0.25 )->  H1 
#> H3  -( 0.25 )->  H2 
#> H3  -( 0.25 )->  H4 
#> H3  -( 0.25 )->  H5 
#> H4  -( 0.25 )->  H1 
#> H4  -( 0.25 )->  H2 
#> H4  -( 0.25 )->  H3 
#> H4  -( 0.25 )->  H5 
#> H5  -( 0.25 )->  H1 
#> H5  -( 0.25 )->  H2 
#> H5  -( 0.25 )->  H3 
#> H5  -( 0.25 )->  H4 
#> 
#> 
#> P-values:
#>   H1   H2   H3   H4   H5 
#> 0.01 0.02 0.04 0.04 0.70 
#> 
#> Adjusted p-values:
#>   H1   H2   H3   H4   H5 
#> 0.05 0.08 0.12 0.12 0.70 
#> 
#> Alpha: 0.05 
#> 
#> Hypothesis rejected:
#>    H1    H2    H3    H4    H5 
#>  TRUE FALSE FALSE FALSE FALSE 
#> 
#> Final graph after1steps:
#> A graphMCP graph
#> H1 (rejected, weight=0)
#> H2 (weight=0.25)
#> H3 (weight=0.25)
#> H4 (weight=0.25)
#> H5 (weight=0.25)
#> Edges:
#> H2  -( 0.333333333333333 )->  H3 
#> H2  -( 0.333333333333333 )->  H4 
#> H2  -( 0.333333333333333 )->  H5 
#> H3  -( 0.333333333333333 )->  H2 
#> H3  -( 0.333333333333333 )->  H4 
#> H3  -( 0.333333333333333 )->  H5 
#> H4  -( 0.333333333333333 )->  H2 
#> H4  -( 0.333333333333333 )->  H3 
#> H4  -( 0.333333333333333 )->  H5 
#> H5  -( 0.333333333333333 )->  H2 
#> H5  -( 0.333333333333333 )->  H3 
#> H5  -( 0.333333333333333 )->  H4 
#> 
# 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))
#> gMCP-Result
#> 
#> Initial graph:
#> A graphMCP graph
#> H1 (weight=0.2)
#> H2 (weight=0.2)
#> H3 (weight=0.2)
#> H4 (weight=0.2)
#> H5 (weight=0.2)
#> No edges.
#> 
#> 
#> P-values:
#>   H1   H2   H3   H4   H5 
#> 0.01 0.02 0.04 0.04 0.70 
#> 
#> Adjusted p-values:
#>   H1   H2   H3   H4   H5 
#> 0.05 0.10 0.20 0.20 1.00 
#> 
#> Alpha: 0.05 
#> 
#> Hypothesis rejected:
#>    H1    H2    H3    H4    H5 
#>  TRUE FALSE FALSE FALSE FALSE 
#> 
#> Final graph after1steps:
#> A graphMCP graph
#> Sum of weight: 0.8
#> H1 (rejected, weight=0)
#> H2 (weight=0.2)
#> H3 (weight=0.2)
#> H4 (weight=0.2)
#> H5 (weight=0.2)
#> No edges.
#> 
# With 'upscale=TRUE' equal to BonferroniHolm:
gMCP(g2, pvalues=c(0.01, 0.02, 0.04, 0.04, 0.7), upscale=TRUE)
#> gMCP-Result
#> 
#> Initial graph:
#> A graphMCP graph
#> H1 (weight=0.2)
#> H2 (weight=0.2)
#> H3 (weight=0.2)
#> H4 (weight=0.2)
#> H5 (weight=0.2)
#> No edges.
#> 
#> 
#> P-values:
#>   H1   H2   H3   H4   H5 
#> 0.01 0.02 0.04 0.04 0.70 
#> 
#> Adjusted p-values:
#>   H1   H2   H3   H4   H5 
#> 0.05 0.08 0.12 0.12 0.70 
#> 
#> Alpha: 0.05 
#> 
#> Hypothesis rejected:
#>    H1    H2    H3    H4    H5 
#>  TRUE FALSE FALSE FALSE FALSE 
#> 
#> Final graph after1steps:
#> A graphMCP graph
#> H1 (rejected, weight=0)
#> H2 (weight=0.25)
#> H3 (weight=0.25)
#> H4 (weight=0.25)
#> H5 (weight=0.25)
#> No edges.
#> 

# Entangled graphs:
g3 <- Entangled2Maurer2012()
gMCP(g3, pvalues=c(0.01, 0.02, 0.04, 0.04, 0.7), correlation=diag(5))
#> gMCP-Result
#> 
#> Initial graph:
#> An object of class "entangledMCP"
#> Slot "subgraphs":
#> [[1]]
#> A graphMCP graph
#> H1 (weight=1)
#> H2 (weight=0)
#> H3 (weight=0)
#> H4 (weight=0)
#> H5 (weight=0)
#> Edges:
#> H1  -( 1 )->  H3 
#> H2  -( 1 )->  H5 
#> H3  -( 1 )->  H4 
#> H4  -( 1 )->  H2 
#> 
#> 
#> [[2]]
#> A graphMCP graph
#> H1 (weight=0)
#> H2 (weight=1)
#> H3 (weight=0)
#> H4 (weight=0)
#> H5 (weight=0)
#> Edges:
#> H1  -( 1 )->  H4 
#> H2  -( 1 )->  H3 
#> H3  -( 1 )->  H5 
#> H5  -( 1 )->  H1 
#> 
#> 
#> 
#> Slot "weights":
#> [1] 0.5 0.5
#> 
#> Slot "graphAttr":
#> list()
#> 
#> 
#> P-values:
#>   H1   H2   H3   H4   H5 
#> 0.01 0.02 0.04 0.04 0.70 
#> 
#> Adjusted p-values:
#>     H1     H2     H3     H4     H5 
#> 0.0199 0.0396 0.0400 0.0784 0.7000 
#> 
#> Alpha: 0.05 
#> 
#> Hypothesis rejected:
#>    H1    H2    H3    H4    H5 
#>  TRUE  TRUE  TRUE FALSE FALSE