exampleGraphs {gMCP}

Functions that create different example graphs

Description

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

Usage

BonferroniHolm(n, weights = rep(1/n, 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)

Arguments

n

Number of hypotheses.

weights

Numeric vector of node weights.

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.

nodes

Character vector of node names.

times

Number of time points.

doses

Number of dose levels.

w

Further variable weight(s) in graph.

Details

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 \frac{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,\ldots,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.

Value

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

Author(s)

Kornelius Rohmeyer [e-mail]

References

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. https://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.

Examples

g <- BonferroniHolm(5)

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

HungEtWang2010()
HungEtWang2010(nu=1)