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Example graphs of commonly used multiple comparison procedures

Source: R/example_graphs.R
example_graphs.Rd

Built-in functions to quickly generate select graphical multiple comparison procedures.

Usage

bonferroni(hypotheses, hyp_names = NULL)

bonferroni_holm(hypotheses, hyp_names = NULL)

huque_etal(hyp_names = NULL)

fallback(hypotheses, hyp_names = NULL)

fallback_improved_1(hypotheses, hyp_names = NULL)

fallback_improved_2(hypotheses, epsilon = 1e-04, hyp_names = NULL)

fixed_sequence(num_hyps, hyp_names = NULL)

simple_successive_1(hyp_names = NULL)

simple_successive_2(hyp_names = NULL)

random_graph(num_hyps, hyp_names = NULL)

two_doses_two_primary_two_secondary(hyp_names = NULL)

three_doses_two_primary_two_secondary(hyp_names = NULL)

Arguments

hypotheses

(Optional) A numeric vector of hypothesis weights in a graphical multiple comparison procedure. Must be a vector of values between 0 & 1 (inclusive). The length should match num_hyps and the length of hyp_names. The sum of hypothesis weights should not exceed 1.

hyp_names

(Optional) A character vector of hypothesis names. The length should match num_hyps and the length of hypotheses. If hyp_names are not specified, hypotheses will be named sequentially as H1, H2, .......

epsilon

(Optional) A numeric scalar indicating the value of the \(\epsilon\) edge. This should be a much smaller value than hypothesis and transition weights. The default is 1e-4.

num_hyps

(Optional) Number of hypotheses in a graphical multiple comparison procedure.

Value

An S3 object as returned by graph_create().

References

Bretz, F., Maurer, W., Brannath, W., and Posch, M. (2009). A graphical approach to sequentially rejective multiple test procedures. Statistics in Medicine, 28(4), 586-604.

Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., and Rohmeyer, K. (2011). Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests. Biometrical Journal, 53(6), 894-913.

Huque, M. F., Alosh, M., and Bhore, R. (2011). Addressing multiplicity issues of a composite endpoint and its components in clinical trials. Journal of Biopharmaceutical Statistics, 21(4), 610-634.

Maurer, W., Hothorn, L., and Lehmacher, W. (1995). Multiple comparisons in drug clinical trials and preclinical assays: a-priori ordered hypotheses. Biometrie in der chemisch-pharmazeutischen Industrie, 6, 3-18.

Westfall, P. H., and Krishen, A. (2001). Optimally weighted, fixed sequence and gatekeeper multiple testing procedures. Journal of Statistical Planning and Inference, 99(1), 25-40.

Wiens, B. L. (2003). A fixed sequence Bonferroni procedure for testing multiple endpoints. Pharmaceutical Statistics, 2(3), 211-215.

Wiens, B. L., and Dmitrienko, A. (2005). The fallback procedure for evaluating a single family of hypotheses. Journal of Biopharmaceutical Statistics, 15(6), 929-942.

Xi, D., and Bretz, F. (2019). Symmetric graphs for equally weighted tests, with application to the Hochberg procedure. Statistics in Medicine, 38(27), 5268-5282.

See also

graph_create() for a general way to create the initial graph.

Examples

# Bretz et al. (2009)
bonferroni(hypotheses = rep(1 / 3, 3))
#> Initial graph
#> 
#> --- Hypothesis weights ---
#> H1: 0.3333
#> H2: 0.3333
#> H3: 0.3333
#> 
#> --- Transition weights ---
#>     H1 H2 H3
#>  H1  0  0  0
#>  H2  0  0  0
#>  H3  0  0  0
# Bretz et al. (2009)
bonferroni_holm(hypotheses = rep(1 / 3, 3))
#> Initial graph
#> 
#> --- Hypothesis weights ---
#> H1: 0.3333
#> H2: 0.3333
#> H3: 0.3333
#> 
#> --- Transition weights ---
#>      H1  H2  H3
#>  H1 0.0 0.5 0.5
#>  H2 0.5 0.0 0.5
#>  H3 0.5 0.5 0.0
# Huque et al. (2011)
huque_etal()
#> Initial graph
#> 
#> --- Hypothesis weights ---
#> H1: 1
#> H2: 0
#> H3: 0
#> H4: 0
#> 
#> --- Transition weights ---
#>      H1  H2  H3  H4
#>  H1 0.0 0.5 0.5 0.0
#>  H2 0.0 0.0 0.0 1.0
#>  H3 0.0 0.5 0.0 0.5
#>  H4 0.0 1.0 0.0 0.0
# Wiens (2003)
fallback(hypotheses = rep(1 / 3, 3))
#> Initial graph
#> 
#> --- Hypothesis weights ---
#> H1: 0.3333
#> H2: 0.3333
#> H3: 0.3333
#> 
#> --- Transition weights ---
#>     H1 H2 H3
#>  H1  0  1  0
#>  H2  0  0  1
#>  H3  0  0  0
# Wiens and Dmitrienko (2005)
fallback_improved_1(hypotheses = rep(1 / 3, 3))
#> Initial graph
#> 
#> --- Hypothesis weights ---
#> H1: 0.3333
#> H2: 0.3333
#> H3: 0.3333
#> 
#> --- Transition weights ---
#>      H1  H2  H3
#>  H1 0.0 1.0 0.0
#>  H2 0.0 0.0 1.0
#>  H3 0.5 0.5 0.0
# Bretz et al. (2009)
fallback_improved_2(hypotheses = rep(1 / 3, 3))
#> Initial graph
#> 
#> --- Hypothesis weights ---
#> H1: 0.3333
#> H2: 0.3333
#> H3: 0.3333
#> 
#> --- Transition weights ---
#>         H1     H2     H3
#>  H1 0.0000 1.0000 0.0000
#>  H2 0.9999 0.0000 0.0001
#>  H3 1.0000 0.0000 0.0000
# Maurer et al. (1995); Westfall and Krishen (2001)
fixed_sequence(num_hyps = 3)
#> Initial graph
#> 
#> --- Hypothesis weights ---
#> H1: 1
#> H2: 0
#> H3: 0
#> 
#> --- Transition weights ---
#>     H1 H2 H3
#>  H1  0  1  0
#>  H2  0  0  1
#>  H3  0  0  0
# Figure 1 in Bretz et al. (2011)
simple_successive_1()
#> Initial graph
#> 
#> --- Hypothesis weights ---
#> H1: 0.5
#> H2: 0.5
#> H3: 0.0
#> H4: 0.0
#> 
#> --- Transition weights ---
#>     H1 H2 H3 H4
#>  H1  0  0  1  0
#>  H2  0  0  0  1
#>  H3  0  1  0  0
#>  H4  1  0  0  0
# Figure 4 in Bretz et al. (2011)
simple_successive_2()
#> Initial graph
#> 
#> --- Hypothesis weights ---
#> H1: 0.5
#> H2: 0.5
#> H3: 0.0
#> H4: 0.0
#> 
#> --- Transition weights ---
#>      H1  H2  H3  H4
#>  H1 0.0 0.5 0.5 0.0
#>  H2 0.5 0.0 0.0 0.5
#>  H3 0.0 1.0 0.0 0.0
#>  H4 1.0 0.0 0.0 0.0
# Create a random graph with three hypotheses
random_graph(num_hyps = 3)
#> Initial graph
#> 
#> --- Hypothesis weights ---
#> H1: 0.3333
#> H2: 0.3333
#> H3: 0.3333
#> 
#> --- Transition weights ---
#>         H1     H2     H3
#>  H1 0.0000 0.6000 0.4000
#>  H2 0.6667 0.0000 0.3333
#>  H3 0.7500 0.2500 0.0000
# Figure 6 in Xi and Bretz et al. (2019)
two_doses_two_primary_two_secondary()
#> Initial graph
#> 
#> --- Hypothesis weights ---
#> H1: 0.5
#> H2: 0.0
#> H3: 0.0
#> H4: 0.5
#> H5: 0.0
#> H6: 0.0
#> 
#> --- Transition weights ---
#>         H1     H2     H3     H4     H5     H6
#>  H1 0.0000 0.5000 0.5000 0.0000 0.0000 0.0000
#>  H2 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000
#>  H3 0.0000 0.9999 0.0000 0.0001 0.0000 0.0000
#>  H4 0.0000 0.0000 0.0000 0.0000 0.5000 0.5000
#>  H5 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
#>  H6 0.0001 0.0000 0.0000 0.0000 0.9999 0.0000
# Add another dose to Figure 6 in Xi and Bretz et al. (2019)
three_doses_two_primary_two_secondary()
#> Initial graph
#> 
#> --- Hypothesis weights ---
#> H1: 0.3333
#> H2: 0.0000
#> H3: 0.0000
#> H4: 0.3333
#> H5: 0.0000
#> H6: 0.0000
#> H7: 0.3333
#> H8: 0.0000
#> H9: 0.0000
#> 
#> --- Transition weights ---
#>          H1      H2      H3      H4      H5      H6      H7      H8      H9
#>  H1 0.00000 0.50000 0.50000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#>  H2 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#>  H3 0.00000 0.99990 0.00000 0.00005 0.00000 0.00000 0.00005 0.00000 0.00000
#>  H4 0.00000 0.00000 0.00000 0.00000 0.50000 0.50000 0.00000 0.00000 0.00000
#>  H5 0.00000 0.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000
#>  H6 0.00005 0.00000 0.00000 0.00000 0.99990 0.00000 0.00005 0.00000 0.00000
#>  H7 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.50000 0.50000
#>  H8 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1.00000
#>  H9 0.00005 0.00000 0.00000 0.00005 0.00000 0.00000 0.00000 0.99990 0.00000