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 \(i=1,\ldots,n-1\) andweight[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.
References
Holm, S. (1979). A simple sequentially 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.
Author
Kornelius Rohmeyer rohmeyer@small-projects.de
Examples
g <- BonferroniHolm(5)
gMCP(g, pvalues=c(0.1, 0.2, 0.4, 0.4, 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
#> 0.1 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.
HungEtWang2010()
#> 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}
#>
HungEtWang2010(nu=1)
#> 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}
#>