Perform shortcut (sequentially rejective) graphical multiple comparison procedures

Shortcut graphical multiple comparison procedures are sequentially rejective procedure based on Bretz et al. (2009). With $m$ hypotheses, there are at most $m$ steps to obtain all rejection decisions. These procedure are equivalent to closed graphical multiple comparison procedures using Bonferroni tests for intersection hypotheses, but shortcut procedures are faster to perform. See vignette("shortcut-testing") for more illustration of shortcut procedures and interpretation of their outputs.

Usage

graph_test_shortcut(
  graph,
  p,
  alpha = 0.025,
  verbose = FALSE,
  test_values = FALSE
)

Arguments

graph

An initial graph as returned by graph_create().

p

A numeric vector of p-values (unadjusted, raw), whose values should be between 0 & 1. The length should match the number of hypotheses in graph.

alpha

A numeric scalar of the overall significance level, which should be between 0 & 1. The default is 0.025 for one-sided hypothesis testing problems; another common choice is 0.05 for two-sided hypothesis testing problems.

verbose

A logical scalar specifying whether the details of intermediate update graphs should be included in results. When verbose = TRUE, intermediate update graphs are provided after deleting each hypothesis, which has been rejected. The default is verbose = FALSE.

test_values

A logical scalar specifying whether adjusted significance levels should be provided for each hypothesis. When test_values = TRUE, it provides an equivalent way of performing graphical multiple comparison procedures by comparing each p-value with its significance level. If the p-value of a hypothesis is less than or equal to its significance level, the hypothesis is rejected. The order of rejection is based on the order of adjusted p-values from the smallest to the largest. The default is test_values = FALSE.

Value

An S3 object of class graph_report with a list of 4 elements:

• inputs - Input parameters, which is a list of:

  • graph - Initial graph, *p - (Unadjusted or raw) p-values,

  • alpha - Overall significance level,

  • test_groups - Groups of hypotheses for different types of tests, which are the list of all hypotheses for graph_test_shortcut(),

  • test_types - Different types of tests, which are "bonferroni" for graph_test_shortcut().

• Output parameters outputs, which is a list of:

  • adjusted_p - Adjusted p-values,

  • rejected - Rejected hypotheses,

  • graph - Updated graph after deleting all rejected hypotheses.

• details - Verbose outputs with intermediate updated graphs, if verbose = TRUE.

• test_values - Adjusted significance levels, if test_values = TRUE.

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.

See also

• graph_test_closure() for graphical multiple comparison procedures using the closed test,

• graph_rejection_orderings() for all possible rejection orderings.

Examples

# A graphical multiple comparison procedure with two primary hypotheses (H1
# and H2) and two secondary hypotheses (H3 and H4)
# See Figure 1 in Bretz et al. (2011).
hypotheses <- c(0.5, 0.5, 0, 0)
transitions <- rbind(
  c(0, 0, 1, 0),
  c(0, 0, 0, 1),
  c(0, 1, 0, 0),
  c(1, 0, 0, 0)
)
g <- graph_create(hypotheses, transitions)

p <- c(0.018, 0.01, 0.105, 0.006)
alpha <- 0.025
graph_test_shortcut(g, p, alpha)
#> 
#> Test parameters ($inputs) ------------------------------------------------------
#>   Initial graph
#> 
#>   --- Hypothesis weights ---
#>   H1: 0.5
#>   H2: 0.5
#>   H3: 0.0
#>   H4: 0.0
#> 
#>   --- Transition weights ---
#>      H1 H2 H3 H4
#>   H1  0  0  1  0
#>   H2  0  0  0  1
#>   H3  0  1  0  0
#>   H4  1  0  0  0
#> 
#>   Alpha = 0.025
#> 
#>                           H1    H2    H3    H4
#>   Unadjusted p-values: 0.018 0.010 0.105 0.006
#> 
#>   Test types
#>   bonferroni: (H1, H2, H3, H4)
#> 
#> Test summary ($outputs) --------------------------------------------------------
#>   Hypothesis Adj. P-value Reject
#>           H1        0.020   TRUE
#>           H2        0.020   TRUE
#>           H3        0.105  FALSE
#>           H4        0.020   TRUE
#> 
#>   Final updated graph after removing rejected hypotheses
#> 
#>   --- Hypothesis weights ---
#>   H1: NA
#>   H2: NA
#>   H3:  1
#>   H4: NA
#> 
#>   --- Transition weights ---
#>      H1 H2 H3 H4
#>   H1 NA NA NA NA
#>   H2 NA NA NA NA
#>   H3 NA NA  0 NA
#>   H4 NA NA NA NA
#>