Obtain an updated graph by updating an initial graphical after deleting hypotheses

After a hypothesis is deleted, an initial graph will be updated. The deleted hypothesis will have the hypothesis weight of 0 and the transition weight of 0. Remaining hypotheses will have updated hypothesis weights and transition weights according to Algorithm 1 of Bretz et al. (2009).

Usage

graph_update(graph, delete)

Arguments

graph: An initial graph as returned by graph_create().
delete: A logical or integer vector, denoting which hypotheses to delete. A logical vector results in the "unordered mode", which means that hypotheses corresponding to TRUE in delete will be deleted. The sequence of deletion will follow the sequence of TRUE's in delete. In this case, the length of the logical vector must match the number of hypotheses in graph. An integer vector results in the "ordered mode", which means that delete specifies the sequence in which hypotheses should be deleted by indicating the location of deleted hypotheses, e.g., 1st, 2nd, etc. In this case, the integer vector can have any length, but must only contain valid hypothesis numbers (greater than 0, and less than or equal to he number of hypotheses in graph).

Value

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

initial_graph: The initial graph object.
updated_graph: The updated graph object with specified hypotheses deleted.
deleted: A numeric vector indicating which hypotheses were deleted.
intermediate_graphs: When using the ordered mode, a list of intermediate updated graphs after each hypothesis is deleted according to the sequence specified by delete.

Sequence of deletion

When there are multiple hypotheses to be deleted from a graph, there are many sequences of deletion in which an initial graph is updated to an updated graph. If the interest is in the updated graph after all hypotheses specified by delete are deleted, this updated graph is the same no matter which sequence of deletion is used. This property has been proved by Bretz et al. (2009). If the interest is in the intermediate updated graph after each hypothesis is deleted according to the sequence specified by delete, an integer vector of delete should be specified and these detailed outputs will be provided.

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.

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)

# Delete the second and third hypotheses in the "unordered mode"
graph_update(g, delete = c(FALSE, TRUE, TRUE, FALSE))
#> Initial and final graphs -------------------------------------------------------
#> 
#> 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
#> 
#> Updated graph after deleting hypotheses 2, 3
#> 
#> --- Hypothesis weights ---
#> H1: 0.5
#> H2:  NA
#> H3:  NA
#> H4: 0.5
#> 
#> --- Transition weights ---
#>     H1 H2 H3 H4
#>  H1  0 NA NA  1
#>  H2 NA NA NA NA
#>  H3 NA NA NA NA
#>  H4  1 NA NA  0

# Equivalent way in the "ordered mode" to obtain the updated graph after
# deleting the second and third hypotheses
# Additional intermediate updated graphs are also provided
graph_update(g, delete = 2:3)
#> Initial and final graphs -------------------------------------------------------
#> 
#> 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
#> 
#> Updated graph after deleting hypotheses 2, 3
#> 
#> --- Hypothesis weights ---
#> H1: 0.5
#> H2:  NA
#> H3:  NA
#> H4: 0.5
#> 
#> --- Transition weights ---
#>     H1 H2 H3 H4
#>  H1  0 NA NA  1
#>  H2 NA NA NA NA
#>  H3 NA NA NA NA
#>  H4  1 NA NA  0
#> 
#> Deletion sequence ($intermediate_graphs) ---------------------------------------
#> 
#>   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
#> 
#>     Step 1: Updated graph after removing hypothesis 2
#> 
#>     --- Hypothesis weights ---
#>     H1: 0.5
#>     H2:  NA
#>     H3: 0.0
#>     H4: 0.5
#> 
#>     --- Transition weights ---
#>        H1 H2 H3 H4
#>     H1  0 NA  1  0
#>     H2 NA NA NA NA
#>     H3  0 NA  0  1
#>     H4  1 NA  0  0
#> 
#>       Step 2: Updated graph after removing hypotheses 2, 3
#> 
#>       --- Hypothesis weights ---
#>       H1: 0.5
#>       H2:  NA
#>       H3:  NA
#>       H4: 0.5
#> 
#>       --- Transition weights ---
#>          H1 H2 H3 H4
#>       H1  0 NA NA  1
#>       H2 NA NA NA NA
#>       H3 NA NA NA NA
#>       H4  1 NA NA  0
#> 
#>   Final updated graph after removing deleted hypotheses
#> 
#>   --- Hypothesis weights ---
#>   H1: 0.5
#>   H2:  NA
#>   H3:  NA
#>   H4: 0.5
#> 
#>   --- Transition weights ---
#>      H1 H2 H3 H4
#>   H1  0 NA NA  1
#>   H2 NA NA NA NA
#>   H3 NA NA NA NA
#>   H4  1 NA NA  0
#>