This vignette provides examples of various trial specifications using different combinations of settings, including various randomisation strategies including fixed randomisation, response-adaptive randomisation (RAR), and combinations.
The general-purpose function for specifying a trial is
setu_trial(), but because trials with binary, binomially
distributed and continuous, normally distributed outcomes are so common,
the package comes with two convenience functions for specifying such
trial designs: setup_trial_binom() and
setup_trial_norm().
To keep things simple, this vignette uses only the
setup_trial_binom() function and focuses on settings that
apply to trial designs regardless of outcome type. The code is heavily
annotated, but comments focus on settings not touched on earlier in the
vignette (e.g. we do not keep annotating the arm and
true_ys arguments).
For a general overview of how to use the adaptr package,
please see vignette("Overview", "adaptr").
An advanced example on how to specify a trial design
with setup_trial(), including the use of custom functions
for generating outcomes and yielding posterior draws, is provided in
vignette("Advanced-example", "adaptr").
First, the package is loaded:
library(adaptr)In this section, several examples for trials without a common control arm are provided. General settings applicable for all trial designs (including both trial specifications with and without a common control arm) are covered in this section.
setup_trial_binom(
# Four arms
arms = c("A", "B", "C", "D"),
# Set true outcomes (in this example event probabilities) for all arms
true_ys = c(0.3, 0.35, 0.31, 0.27), # 30%, 34%, 31% and 27%, respectively
# Set starting allocation probabilities
# Defaults to equal allocation if not specified
start_probs = c(0.3, 0.3, 0.2, 0.2),
# Set fixed allocation probability for first arm
# NA corresponds to no limits for specific arms
# Default (NULL) corresponds to no limits for all arms
fixed_probs = c(0.3, NA, NA, NA),
# Set minimum and maximum probability limits for some arms
# NA corresponds to no limits for specific arms
# Default (NULL) corresponds to no limits for all arms
# Must be NA for arms with fixed_probs (first arm in this example)
# sum(fixed_probs) + sum(min_probs) must not exceed 1
# sum(fixed_probs) + sum(max_probs) may be greater than 1, and must be at least
# 1 if specified for all arms
min_probs = c(NA, 0.2, NA, NA),
max_probs = c(NA, 0.7, NA, NA),
# Set looks - alternatively, specify both max_n AND look_after_every
data_looks = seq(from = 300, to = 1000, by = 100),
# No common control arm (as default, but explicitly specified in this example)
control = NULL,
# Set inferiority/superiority thresholds (different values than the defaults)
inferiority = 0.025,
superiority = 0.975,
# Define that the outcome is desirable (as opposed to the default setting)
highest_is_best = TRUE,
# No softening (the default setting, but made explicit here)
soften_power = 1,
# Use different simulation/summary settings than default
cri_width = 0.89, # 89% credible intervals
n_draws = 1000, # Only 1000 posterior draws in each arm
robust = TRUE, # Summarise posteriors using medians/MAD-SDs (as default)
# Trial description (used by print methods)
description = "example trial specification 1"
)
#> Trial specification: example trial specification 1
#> * Desirable outcome
#> * No common control arm
#> * Best arm: B
#>
#> Arms, true outcomes, starting allocation probabilities
#> and allocation probability limits:
#> arms true_ys start_probs fixed_probs min_probs max_probs
#> A 0.30 0.3 0.3 NA NA
#> B 0.35 0.3 NA 0.2 0.7
#> C 0.31 0.2 NA NA NA
#> D 0.27 0.2 NA NA NA
#>
#> Maximum sample size: 1000
#> Maximum number of data looks: 8
#> Planned data looks after: 300, 400, 500, 600, 700, 800, 900, 1000 patients
#>
#> Superiority threshold: 0.975
#> Inferiority threshold: 0.025
#> No equivalence threshold
#> No futility threshold (not relevant - no common control)
#> Soften power for all analyses: 1 (no softening)setup_trial_binom(
# Specify arms and true outcome probabilities (undesirable outcome as default)
arms = c("A", "B", "C", "D"),
true_ys = c(0.2, 0.22, 0.24, 0.18),
# Specify adaptive analysis looks using max_n and look_after_every
# max_n does not need to be a multiple of look_after_every - a final look
# will be conducted at max_n regardless
max_n = 1250, # Maximum 1250 patients
look_after_every = 100, # Look after every 100 patients
# Assess equivalence between all arms: stop if >90 % probability that the
# absolute difference between the best and worst arms is < 5 %-points
# Note: equivalence_only_first must be NULL (default) in designs without a
# common control arm (such as this trial)
equivalence_prob = 0.9,
equivalence_diff = 0.05,
# Different softening powers at each look (13 possible looks in total)
# Starts at 0 (softens all allocation probabilities to be equal) and ends at
# 1 (no softening) for the final possible look in the trial
soften_power = seq(from = 0, to = 1, length.out = 13)
)
#> Trial specification: generic binomially distributed outcome trial
#> * Undesirable outcome
#> * No common control arm
#> * Best arm: D
#>
#> Arms, true outcomes, starting allocation probabilities
#> and allocation probability limits:
#> arms true_ys start_probs fixed_probs min_probs max_probs
#> A 0.20 0.25 NA NA NA
#> B 0.22 0.25 NA NA NA
#> C 0.24 0.25 NA NA NA
#> D 0.18 0.25 NA NA NA
#>
#> Maximum sample size: 1250
#> Maximum number of data looks: 13
#> Planned looks after every 100 patients until maximum sample size
#> Superiority threshold: 0.99
#> Inferiority threshold: 0.01
#> Equivalence threshold: 0.9 (no common control)
#> Absolute equivalence difference: 0.05
#> No futility threshold (not relevant - no common control)
#> Soften power for each consequtive analysis: 0, 0.083, 0.167, 0.25, 0.333, 0.417, 0.5, 0.583, 0.667, 0.75, 0.833, 0.917, 1In this section, several examples for trials with a common control arm are provided and focus mostly on options specific to trial designs with a common control arm.
setup_trial())setup_trial_binom(
arms = c("A", "B", "C", "D"),
# Specify control arm
control = "A",
true_ys = c(0.2, 0.22, 0.24, 0.18),
data_looks = seq(from = 100, to = 1000, by = 100),
# Fixed, square-root-transformation-based allocation throughout
control_prob_fixed = "sqrt-based fixed",
# Assess equivalence: drop non-control arms if > 90% probability that they
# are equivalent to the common control, defined as an absolute difference of
# < 3 %-points
equivalence_prob = 0.9,
equivalence_diff = 0.03,
# Only assess against the initial control (i.e., not assessed if an arm is
# declared superior to the initial control and becomes the new control)
equivalence_only_first = TRUE,
# Assess futility: drop non-control arms if > 80% probability that they are
# < 10 %-points better (in this case lower because outcome is undesirable in
# this example) compared to the common control
futility_prob = 0.8,
futility_diff = 0.1,
# Only assessed for the initial control, as described above
futility_only_first = TRUE
)
#> Trial specification: generic binomially distributed outcome trial
#> * Undesirable outcome
#> * Common control arm: A
#> * Control arm probability fixed at 0.366 (for 4 arms), 0.414 (for 3 arms), 0.5 (for 2 arms)
#> * Best arm: D
#>
#> Arms, true outcomes, starting allocation probabilities
#> and allocation probability limits:
#> arms true_ys start_probs fixed_probs min_probs max_probs
#> A 0.20 0.366 0.366 NA NA
#> B 0.22 0.211 0.211 NA NA
#> C 0.24 0.211 0.211 NA NA
#> D 0.18 0.211 0.211 NA NA
#>
#> Maximum sample size: 1000
#> Maximum number of data looks: 10
#> Planned data looks after: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000 patients
#>
#> Superiority threshold: 0.99
#> Inferiority threshold: 0.01
#> Equivalence threshold: 0.9 (only checked for first control)
#> Absolute equivalence difference: 0.03
#> Futility threshold: 0.8 (only checked for first control)
#> Absolute futility difference (in beneficial direction): 0.1
#> Soften power for all analyses: 1 (no softening - all arms fixed)setup_trial_binom(
arms = c("A", "B", "C", "D"),
control = "A",
true_ys = c(0.2, 0.22, 0.24, 0.18),
data_looks = seq(from = 100, to = 1000, by = 100),
# Square-root-transformation-based control arm allocation including for
# subsequent controls and initial equal allocation to the non-control arms,
# followed by response-adaptive randomisation
control_prob_fixed = "sqrt-based",
# Restricted response-adaptive randomisation
# Minimum probabilities of 20% for non-control arms, must be NA for the
# control arm with fixed allocation probability
# Limits are ignored for arms that become subsequent controls
min_probs = c(NA, 0.2, 0.2, 0.2),
# Constant softening of 0.5 (= square-root transformation)
soften_power = 0.5
)
#> Trial specification: generic binomially distributed outcome trial
#> * Undesirable outcome
#> * Common control arm: A
#> * Control arm probability fixed at 0.366 (for 4 arms), 0.414 (for 3 arms), 0.5 (for 2 arms)
#> * Best arm: D
#>
#> Arms, true outcomes, starting allocation probabilities
#> and allocation probability limits:
#> arms true_ys start_probs fixed_probs min_probs max_probs
#> A 0.20 0.366 0.366 NA NA
#> B 0.22 0.211 NA 0.2 NA
#> C 0.24 0.211 NA 0.2 NA
#> D 0.18 0.211 NA 0.2 NA
#>
#> Maximum sample size: 1000
#> Maximum number of data looks: 10
#> Planned data looks after: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000 patients
#>
#> Superiority threshold: 0.99
#> Inferiority threshold: 0.01
#> No equivalence threshold
#> No futility threshold
#> Soften power for all analyses: 0.5This example is similar to that above (with different restriction settings), but only use square-root-transformation-based allocation probabilities to the initial control arm. Hence, this will not apply if another arm is declared superior and becomes the new control.
setup_trial_binom(
arms = c("A", "B", "C", "D"),
control = "A",
true_ys = c(0.2, 0.22, 0.24, 0.18),
data_looks = seq(from = 100, to = 1000, by = 100),
# Square-root-transformation-based control arm allocation for the initial
# control only and initial equal allocation to the non-control arms, followed
# by response-adaptive randomisation
control_prob_fixed = "sqrt-based start",
# Restrict response-adaptive randomisation
# Minimum probabilities of 20% for all non-control arms
# - must be NA for the initial control arm with fixed allocation probability
min_probs = c(NA, 0.2, 0.2, 0.2),
# Maximum probabilities of 65% for all non-control arms
# - must be NA for the initial control arm with fixed allocation probability
max_probs = c(NA, 0.65, 0.65, 0.65),
soften_power = 0.75
)
#> Trial specification: generic binomially distributed outcome trial
#> * Undesirable outcome
#> * Common control arm: A
#> * Control arm probability fixed at 0.366
#> * Best arm: D
#>
#> Arms, true outcomes, starting allocation probabilities
#> and allocation probability limits:
#> arms true_ys start_probs fixed_probs min_probs max_probs
#> A 0.20 0.366 0.366 NA NA
#> B 0.22 0.211 NA 0.2 0.65
#> C 0.24 0.211 NA 0.2 0.65
#> D 0.18 0.211 NA 0.2 0.65
#>
#> Maximum sample size: 1000
#> Maximum number of data looks: 10
#> Planned data looks after: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000 patients
#>
#> Superiority threshold: 0.99
#> Inferiority threshold: 0.01
#> No equivalence threshold
#> No futility threshold
#> Soften power for all analyses: 0.75setup_trial_binom(
arms = c("A", "B", "C", "D"),
control = "A",
true_ys = c(0.2, 0.22, 0.24, 0.18),
data_looks = seq(from = 100, to = 1000, by = 100),
# Specify starting probabilities
# When "match" is specified below in control_prob_fixed, the initial control
# arm's initial allocation probability must match the highest initial
# non-control arm allocation probability
start_probs = c(0.3, 0.3, 0.2, 0.2),
control_prob_fixed = "match",
# Restrict response-adaptive randomisation
# - these are applied AFTER "matching" when calculating new allocation
# probabilities
# - min_probs must be NA for the initial control arm when using matching
min_probs = c(NA, 0.2, 0.2, 0.2),
soften_power = 0.7
)
#> Trial specification: generic binomially distributed outcome trial
#> * Undesirable outcome
#> * Common control arm: A
#> * Control arm probability matched to best non-control arm
#> * Best arm: D
#>
#> Arms, true outcomes, starting allocation probabilities
#> and allocation probability limits:
#> arms true_ys start_probs fixed_probs min_probs max_probs
#> A 0.20 0.3 NA NA NA
#> B 0.22 0.3 NA 0.2 NA
#> C 0.24 0.2 NA 0.2 NA
#> D 0.18 0.2 NA 0.2 NA
#>
#> Maximum sample size: 1000
#> Maximum number of data looks: 10
#> Planned data looks after: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000 patients
#>
#> Superiority threshold: 0.99
#> Inferiority threshold: 0.01
#> No equivalence threshold
#> No futility threshold
#> Soften power for all analyses: 0.7