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 ofhyp_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 ofhypotheses
. Ifhyp_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