graphicalMCP (version 0.2.8)

bonferroni: Example graphs of commonly used multiple comparison procedures

Description

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

Usage

bonferroni(num_hyps, hyp_names = NULL)
bonferroni_weighted(hypotheses, hyp_names = NULL)
bonferroni_holm(num_hyps, hyp_names = NULL)
bonferroni_holm_weighted(hypotheses, hyp_names = NULL)
dunnett_single_step(num_hyps, hyp_names = NULL)
dunnett_single_step_weighted(hypotheses, hyp_names = NULL)
dunnett_closure_weighted(hypotheses, hyp_names = NULL)
hochberg(num_hyps, hyp_names = NULL)
hommel(num_hyps, 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)
sidak(num_hyps, hyp_names = NULL)
simple_successive_1(hyp_names = NULL)
simple_successive_2(hyp_names = NULL)
two_doses_two_primary_two_secondary(hyp_names = NULL)
three_doses_two_primary_two_secondary(hyp_names = NULL)
random_graph(num_hyps, hyp_names = NULL)

Value

An S3 object as returned by graph_create().

Arguments

num_hyps

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

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, .......

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.

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.

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.

Hochberg, Y. (1988). A sharper Bonferroni procedure for multiple tests of significance. Biometrika, 75(4), 800-802.

Hommel, G. (1988). A stagewise rejective multiple test procedure based on a modified Bonferroni test. Biometrika, 75(2), 383-386.

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.

Šidák, Z. (1967). Rectangular confidence regions for the means of multivariate normal distributions. Journal of the American Statistical Association, 62(318), 626-633.

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(num_hyps = 3)
# Bretz et al. (2009)
hypotheses <- c(0.5, 0.3, 0.2)
bonferroni_weighted(hypotheses)
# Bretz et al. (2009)
bonferroni_holm(num_hyps = 3)
# Bretz et al. (2009)
hypotheses <- c(0.5, 0.3, 0.2)
bonferroni_holm_weighted(hypotheses)
# Xi et al. (2017)
dunnett_single_step(num_hyps = 3)
# Xi et al. (2017)
hypotheses <- c(0.5, 0.3, 0.2)
dunnett_single_step_weighted(hypotheses)
# Xi et al. (2009)
hypotheses <- c(0.5, 0.3, 0.2)
dunnett_closure_weighted(hypotheses)
# Hochberg (1988)
hochberg(num_hyps = 3)
# Hommel (1988)
hommel(num_hyps = 3)
# Huque et al. (2011)
huque_etal()
# Wiens (2003)
hypotheses <- c(0.5, 0.3, 0.2)
fallback(hypotheses)
# Wiens and Dmitrienko (2005)
hypotheses <- c(0.5, 0.3, 0.2)
fallback_improved_1(hypotheses)
# Bretz et al. (2009)
hypotheses <- c(0.5, 0.3, 0.2)
fallback_improved_2(hypotheses)
# Maurer et al. (1995); Westfall and Krishen (2001)
fixed_sequence(num_hyps = 3)
# sidak (1967)
sidak(num_hyps = 3)
# Figure 1 in Bretz et al. (2011)
simple_successive_1()
# Figure 4 in Bretz et al. (2011)
simple_successive_2()
# Figure 6 in Xi and Bretz et al. (2019)
two_doses_two_primary_two_secondary()
# Add another dose to Figure 6 in Xi and Bretz et al. (2019)
three_doses_two_primary_two_secondary()
# Create a random graph with three hypotheses
random_graph(num_hyps = 3)