exampleGraphs: Functions that create different example graphs
In gMCP: Graph Based Multiple Comparison Procedures

Description Usage Arguments Details Value Author(s) References Examples

Functions that creates example graphs, e.g. graphs that represents a Bonferroni-Holm adjustment, parallel gatekeeping or special procedures from selected papers.

BonferroniHolm(n)

BretzEtAl2011()

BauerEtAl2001()

BretzEtAl2009a()

BretzEtAl2009b()

BretzEtAl2009c()

HommelEtAl2007()

HommelEtAl2007Simple()

parallelGatekeeping()

improvedParallelGatekeeping()

fallback(weights)

fixedSequence(n)

simpleSuccessiveI()

simpleSuccessiveII()

truncatedHolm(gamma)

generalSuccessive(weights = c(1/2, 1/2), gamma, delta)

HuqueAloshEtBhore2011()

HungEtWang2010(nu, tau, omega)

MaurerEtAl1995()

cycleGraph(nodes, weights)

improvedFallbackI(weights = rep(1/3, 3))

improvedFallbackII(weights = rep(1/3, 3))

FerberTimeDose2011(times, doses, w = "\\nu")

Ferber2011(w)

Entangled1Maurer2012()

Entangled2Maurer2012()

WangTing2014(nu, tau)

`n`	Number of hypotheses.
`nodes`	Character vector of node names.
`weights`	Numeric vector of node weights.
`times`	Number of time points.
`doses`	Number of dose levels.
`w`	Further variable weight(s) in graph.
`gamma`	An optional number in [0,1] specifying the value for variable gamma.
`delta`	An optional number in [0,1] specifying the value for variable delta.
`nu`	An optional number in [0,1] specifying the value for variable nu.
`tau`	An optional number in [0,1] specifying the value for variable tau.
`omega`	An optional number in [0,1] specifying the value for variable omega.

We are providing functions and not the resulting graphs directly because this way you have additional examples: You can look at the function body with body and see how the graph is built.

list("BonferroniHolm"): Returns a graph that represents a Bonferroni-Holm adjustment. The result is a complete graph, where all nodes have the same weights and each edge weight is 1/(n-1).
list("BretzEtAl2011"): Graph in figure 2 from Bretz et al. See references (Bretz et al. 2011).
list("HommelEtAl2007"): Graph from Hommel et al. See references (Hommel et al. 2007).
list("parallelGatekeeping"): Graph for parallel gatekeeping. See references (Dmitrienko et al. 2003).
list("improvedParallelGatekeeping"): Graph for improved parallel gatekeeping. See references (Hommel et al. 2007).
list("HungEtWang2010"): Graph from Hung et Wang. See references (Hung et Wang 2010).
list("MaurerEtAl1995"): Graph from Maurer et al. See references (Maurer et al. 1995).
list("cycleGraph"): Cycle graph. The weight weights[i] specifies the edge weight from node i to node i+1 for i=1,...,n-1 and weight[n] from node n to node 1.
list("improvedFallbackI"): Graph for the improved Fallback Procedure by Wiens & Dmitrienko. See references (Wiens et Dmitrienko 2005).
list("improvedFallbackII"): Graph for the improved Fallback Procedure by Hommel & Bretz. See references (Hommel et Bretz 2008).
list("Ferber2011"): Graph from Ferber et al. See references (Ferber et al. 2011).
list("FerberTimeDose2011"): Graph from Ferber et al. See references (Ferber et al. 2011).
list("Entangled1Maurer2012"): Entangled graph from Maurer et al. TODO: Add references as soon as they are available.

A graph of class graphMCP that represents a sequentially rejective multiple test procedure.

Kornelius Rohmeyer rohmeyer@small-projects.de

Holm, S. (1979). A simple sequentally rejective multiple test procedure. Scandinavian Journal of Statistics 6, 65-70.

Dmitrienko, A., Offen, W., Westfall, P.H. (2003). Gatekeeping strategies for clinical trials that do not require all primary effects to be significant. Statistics in Medicine. 22, 2387-2400.

Bretz, F., Maurer, W., Brannath, W., Posch, M.: A graphical approach to sequentially rejective multiple test procedures. Statistics in Medicine 2009 vol. 28 issue 4 page 586-604. http://www.meduniwien.ac.at/fwf_adaptive/papers/bretz_2009_22.pdf

Bretz, F., Maurer, W. and Hommel, G. (2011), Test and power considerations for multiple endpoint analyses using sequentially rejective graphical procedures. Statistics in Medicine, 30: 1489–1501.

Hommel, G., Bretz, F. und Maurer, W. (2007). Powerful short-cuts for multiple testing procedures with special reference to gatekeeping strategies. Statistics in Medicine, 26(22), 4063-4073.

Hommel, G., Bretz, F. (2008): Aesthetics and power considerations in multiple testing - a contradiction? Biometrical Journal 50:657-666.

Hung H.M.J., Wang S.-J. (2010). Challenges to multiple testing in clinical trials. Biometrical Journal 52, 747-756.

W. Maurer, L. Hothorn, W. Lehmacher: Multiple comparisons in drug clinical trials and preclinical assays: a-priori ordered hypotheses. In Biometrie in der chemisch-pharmazeutischen Industrie, Vollmar J (ed.). Fischer Verlag: Stuttgart, 1995; 3-18.

Maurer, W., & Bretz, F. (2013). Memory and other properties of multiple test procedures generated by entangled graphs. Statistics in medicine, 32 (10), 1739-1753.

Wiens, B.L., Dmitrienko, A. (2005): The fallback procedure for evaluating a single family of hypotheses. Journal of Biopharmaceutical Statistics 15:929-942.

Wang, B., Ting, N. (2014). An Application of Graphical Approach to Construct Multiple Testing Procedures in a Hypothetical Phase III Design. Frontiers in public health, 1 (75).

Ferber, G. Staner, L. and Boeijinga, P. (2011): Structured multiplicity and confirmatory statistical analyses in pharmacodynamic studies using the quantitative electroencephalogram, Journal of neuroscience methods, Volume 201, Issue 1, Pages 204-212.

g <- BonferroniHolm(5)

gMCP(g, pvalues=c(0.1, 0.2, 0.4, 0.4, 0.7))

HungEtWang2010()
HungEtWang2010(nu=1)

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 
0.1 0.2 0.4 0.4 0.7 

Adjusted p-values:
 H1  H2  H3  H4  H5 
0.5 0.8 1.0 1.0 1.0 

Alpha: 0.05 

No hypotheses could be rejected.
A graphMCP graph
H_{1,NI} (weight=1)
H_{1,S} (weight=0)
H_{2,NI} (weight=0)
H_{2,S} (weight=0)
Edges:
H_{1,NI}  -( \nu )->  H_{1,S} 
H_{1,NI}  -( 1-\nu )->  H_{2,NI} 
H_{1,S}  -( \tau )->  H_{2,NI} 
H_{1,S}  -( 1-\tau )->  H_{2,S} 
H_{2,NI}  -( \omega )->  H_{1,S} 
H_{2,NI}  -( 1-\omega )->  H_{2,S} 

A graphMCP graph
H_{1,NI} (weight=1)
H_{1,S} (weight=0)
H_{2,NI} (weight=0)
H_{2,S} (weight=0)
Edges:
H_{1,NI}  -( 1 )->  H_{1,S} 
H_{1,NI}  -( 1-1 )->  H_{2,NI} 
H_{1,S}  -( \tau )->  H_{2,NI} 
H_{1,S}  -( 1-\tau )->  H_{2,S} 
H_{2,NI}  -( \omega )->  H_{1,S} 
H_{2,NI}  -( 1-\omega )->  H_{2,S}