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TrialSimulator (version 1.7.0)

GraphicalTesting: Class of GraphicalTesting

Description

Perform graphical testing under group sequential design for one or multiple endpoints. See Maurer & Bretz (2013).

Arguments

Methods

Method new()

Initialize an object for graphical testing procedure. Group sequential design is also supported.

Usage

GraphicalTesting$new(
  alpha,
  transition,
  alpha_spending,
  planned_max_info,
  hypotheses = NULL,
  silent = FALSE
)

Arguments

alpha

initial alpha allocated to each of the hypotheses.

transition

matrix of transition weights. Its diagonals should be all 0s. The row sums should be 1s (for better power) or 0s (if no outbound edge from a node).

alpha_spending

character vector of same length of alpha. Currently it supports 'asP', 'asOF', and 'asUser'.

planned_max_info

vector of integers. Maximum numbers of events (tte endpoints) or patients (non-tte endpoints) at the final analysis of each hypothesis when planning a trial. The actual numbers could be different, which can be specified elsewhere.

hypotheses

vector of characters. Names of hypotheses.

silent

TRUE if muting all messages and not generating plots.

Method reset()

reset an object of class GraphicalTesting to original status so that it can be reused.

Usage

GraphicalTesting$reset()

Method is_valid_hid()

determine if index of a hypothesis is valid

Usage

GraphicalTesting$is_valid_hid(hid)

Arguments

hid

an integer

Method get_hypothesis_name()

get name of a hypothesis given its index.

Usage

GraphicalTesting$get_hypothesis_name(hid)

Arguments

hid

an integer

Method get_weight()

return weight between two nodes

Usage

GraphicalTesting$get_weight(hid1, hid2)

Arguments

hid1

an integer

hid2

an integer

Method set_weight()

update weight between two nodes

Usage

GraphicalTesting$set_weight(hid1, hid2, value)

Arguments

hid1

an integer

hid2

an integer

value

numeric value to be set as a weight two nodes

Method get_alpha()

return alpha allocated to a hypothesis when calling this function. Note that a function can be called several time with the graph is updated dynamically. Thus, returned alpha can be different even for the same hid.

Usage

GraphicalTesting$get_alpha(hid)

Arguments

hid

an integer

Method set_alpha()

update alpha of a hypothesis

Usage

GraphicalTesting$set_alpha(hid, value)

Arguments

hid

integer. Index of a hypothesis

value

numeric value to be allocated

Method get_hypotheses_ids()

return all valid hid

Usage

GraphicalTesting$get_hypotheses_ids()

Method get_number_hypotheses()

return number of hypotheses, including those been rejected.

Usage

GraphicalTesting$get_number_hypotheses()

Method get_hids_not_in_graph()

return index of hypotheses that are rejected.

Usage

GraphicalTesting$get_hids_not_in_graph()

Method get_testable_hypotheses()

return index of hypotheses with non-zero alphas, thus can be tested at the current stage.

Usage

GraphicalTesting$get_testable_hypotheses()

Method has_testable_hypotheses()

determine whether at least one hypothesis is testable. If return FALSE, the testing procedure is completed.

Usage

GraphicalTesting$has_testable_hypotheses()

Method is_in_graph()

determine whether a hypothesis is not yet rejected (in graph).

Usage

GraphicalTesting$is_in_graph(hid)

Arguments

hid

integer. Index of a hypothesis

Method is_testable()

determine whether a hypothesis has a non-zero alpha allocated.

Usage

GraphicalTesting$is_testable(hid)

Arguments

hid

integer. Index of a hypothesis

Method get_hid()

convert hypothesis's name into (unique) index.

Usage

GraphicalTesting$get_hid(hypothesis)

Arguments

hypothesis

character. Name of a hypothesis. It is different from hid, which is an index.

Method reject_a_hypothesis()

remove a node from graph when a hypothesis is rejected

Usage

GraphicalTesting$reject_a_hypothesis(hypothesis)

Arguments

hypothesis

name of a hypothesis. It is different from hid, which is an index.

Method set_trajectory()

save new testing results at current stage

Usage

GraphicalTesting$set_trajectory(result)

Arguments

result

a data frame of specific columns.

Method get_trajectory()

return testing results by the time this function is called. Note that graphical test is carried out in a sequential manner. Users may want to review the results anytime. Value returned by this function can possibly vary over time.

Usage

GraphicalTesting$get_trajectory()

Method test_hypotheses()

test hypotheses using p-values (and other information in stats) base on the current graph. All rows should have the same order number.

Usage

GraphicalTesting$test_hypotheses(stats)

Arguments

stats

a data frame. It must contain the following columns:

order

integer. P-values (among others) of hypotheses that can be tested at the same time (e.g., an interim, or final analysis) should be labeled with the same order number. If a hypothesis is not tested at a stage, simply don't put it in stats with that order number.

hypotheses

character. Name of hypotheses to be tested. They should be identical to those when calling GraphicalTesting$new.

p

nominal p-values.

info

observed number of events or samples at test. These will be used to compute information fractions in group sequential design.

max_info

integers. Maximum information at test. At interim, max_info should be equal to planned_max_info when calling GraphicalTesting$new. At the final stage of a hypothesis, one can update it with observed numbers.

Method test()

test hypotheses using p-values (and other information in stats) base on the current graph. Users can call this function multiple times. P-values of the same order should be passed through stats together. P-values of multiple orders can be passed together as well. For example, if users only have p-values at current stage, they can call this function and update the graph accordingly. In this case, column order in stats is a constant. They can call this function again when p-values of next stage is available, where order is another integer. In simulation, if p-values of all stages are on hand, users can call this function to test them all in a single pass. In this case, column order in stats can have different values.

Usage

GraphicalTesting$test(stats)

Arguments

stats

a data frame. It must contain the following columns:

order

integer. P-values (among others) of hypotheses that can be tested at the same time (e.g., an interim, or final analysis) should be labeled with the same order number. If a hypothesis is not tested at a stage, simply don't put it in stats with that order number. If all p-values in stats are tested at the same stage, order can be absent.

hypotheses

character. Name of hypotheses to be tested. They should be identical to those when calling GraphicalTesting$new.

p

nominal p-values.

info

observed number of events or samples at test. These will be used to compute information fractions in group sequential design.

max_info

integers. Maximum information at test. At interim, max_info should be equal to planned_max_info when calling GraphicalTesting$new. At the final stage of a hypothesis, one can update it with observed numbers.

alpha_spent

accumulative proportion of allocated alpha to be spent if alpha_spending = "asUser". Set it to NA_real_ otherwise. If no hypothesis uses "asUser" in stats, this column could be ignored.

Returns

a data frame returned by get_current_testing_results. It contains details of each of the testing steps.

Method get_current_testing_results()

return testing results with details by the time this function is called. This function can be called by users by multiple times, thus the returned value varies over time. This function is called by GraphicalTesting::test, and returns a data frame consisting of columns

hypothesis

name of hypotheses.

obs_p_value

observed p-values.

max_allocated_alpha

maximum allocated alpha for the hypothesis.

decision

'reject' or 'accept' the hypotheses.

stages

stage of a hypothesis.

order

order number that this hypothesis is tested for the last time. It is different from stages.

typeOfDesign

name of alpha spending functions.

Usage

GraphicalTesting$get_current_testing_results()

Method get_current_decision()

get current decisions for all hypotheses. Returned value could changes over time because it depends on the stages being tested already.

Usage

GraphicalTesting$get_current_decision()

Returns

a named vector of values "accept" or "reject". Note that if a hypothesis is not yet tested when calling this function, the decision for that hypothesis would be "accept".

Method print()

generic function for print

Usage

GraphicalTesting$print(graph = TRUE, trajectory = TRUE, ...)

Arguments

graph

logic. TRUE if visualizing the current graph, which can vary over time.

trajectory

logic. TRUE if print the current data frame of trajectory, which can vary over time.

...

other arguments supported in gMCPLite::hGraph, e.g., trhw and trhh to control the size of transition box, and trdigits to control the digits displayed for transition weights.

Method clone()

The objects of this class are cloneable with this method.

Usage

GraphicalTesting$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

Run this code

## Example 1
## dry-run to study the behavior of a graph
## without group sequential design
if(interactive()){
eps <- .01
alpha <- c(.01, .04, 0, 0, 0)
transition <- matrix(c(
  0, 0, 0, 0, 1,
  0, 0, .75, 0, .25,
  0, 1/2-eps/2, 0, eps, 1/2-eps/2,
  0, 0, 0, 0, 0,
  0, 1/2, 1/2, 0, 0
), nrow = 5, byrow = TRUE)

## dummy can be anything, we don't actually use it
asf <- rep('asOF', 5)
## dummy can be anything, we don't actually use it
max_info <- c(300, 1100, 1100, 1100, 500)

hs <- c('H1: UPCR IgA', 'H2: eGFR GN', 'H3: eGFR GN 10wk', 'H5: 2nd Endpoints', 'H4: eGFR IgA')

## initialize an object
gt <- GraphicalTesting$new(alpha, transition, asf, max_info, hs)
print(gt)

## reject hypotheses based on customized order
## to understand the behavior of a testing strategy
## Any other rejection order is possible
gt$reject_a_hypothesis('H1: UPCR IgA')
print(gt)

gt$reject_a_hypothesis('H2: eGFR GN')
print(gt)

gt$reject_a_hypothesis('H4: eGFR IgA')
print(gt)

gt$reject_a_hypothesis('H3: eGFR GN 10wk')
print(gt)

gt$reset()
}

## Example 2
## Example modified from vignettes in gMCPLite:
## Graphical testing for group sequential design
if(interactive()){
## initial alpha split to each of the hypotheses
alpha <- c(.01, .01, .004, .0, .0005, .0005)

## transition matrix of the initial graph
transition <- matrix(c(
  0, 1, 0, 0, 0, 0,
  0, 0, .5, .5, 0, 0,
  0, 0, 0, 1, 0, 0,
  0, 0, 0, 0, .5, .5,
  0, 0, 0, 0, 0, 1,
  .5, .5, 0, 0, 0, 0
), nrow = 6, byrow = TRUE)

## alpha spending functions per hypothesis
asf <- c('asUser', 'asOF', 'asUser', 'asOF', 'asOF', 'asOF')

## planned maximum number of events per hypothesis
max_info <- c(295, 800, 310, 750, 500, 1100)

## name of hypotheses
hs <- c('H1: OS sub',
        'H2: OS all',
        'H3: PFS sub',
        'H4: PFS all',
        'H5: ORR sub',
        'H6: ORR all')

gt <- GraphicalTesting$new(alpha, transition, asf, max_info, hs)

## print initial graph
gt

## nominal p-values at each stage
## Note: p-values with same order are calculated with the same locked data
## Note: alpha_spent is only specified for hypotheses using custom alpha
##       spending function "asUser"
stats <-
  data.frame(
    order = c(1:3, 1:3, 1:2, 1:2, 1, 1),
    hypotheses = c(rep('H1: OS sub', 3), rep('H2: OS all', 3),
                   rep('H3: PFS sub', 2), rep('H4: PFS all', 2),
                   'H5: ORR sub', 'H6: ORR all'),
    p = c(.03, .0001, .000001, .2, .15, .1, .2, .001, .3, .2, .00001, .1),
    info = c(185, 245, 295, 529, 700, 800, 265, 310, 675, 750, 490, 990),
    is_final = c(F, F, T, F, F, T, F, T, F, T, T, T),
    max_info = c(rep(295, 3), rep(800, 3), rep(310, 2), rep(750, 2), 490, 990),
    alpha_spent = c(c(.1, .4, 1), rep(NA, 3), c(.3, 1), rep(NA, 2), NA, NA)
  )

## test the p-values from the first analysis, plot the updated graph
gt$test(stats %>% dplyr::filter(order==1))

## test the p-values from the second analysis, plot the updated graph
gt$test(stats %>% dplyr::filter(order==2))

## test the p-values from the third analysis, plot the updated graph
## because no futher test would be done, displayed results are final
gt$test(stats %>% dplyr::filter(order==3))


## plot the final status of the graph
print(gt, trajectory = FALSE)

## you can get final testing results as follow
gt$get_current_testing_results()

## if you want to see step-by-step details
print(gt$get_trajectory())

## equivalently, you can call gt$test(stats) for only once to get same results.
gt$reset()
gt$test(stats)

## if you only want to get the final testing results
gt$get_current_decision()
}

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