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gs_power_rd.R
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gs_power_rd.R
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# Copyright (c) 2024 Merck & Co., Inc., Rahway, NJ, USA and its affiliates.
# All rights reserved.
#
# This file is part of the gsDesign2 program.
#
# gsDesign2 is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#' Group sequential design power of binary outcome measuring in risk difference
#'
#' @param p_c Rate at the control group.
#' @param p_e Rate at the experimental group.
#' @param n Sample size.
#' @param rd0 Treatment effect under super-superiority designs, the default is 0.
#' @param ratio Experimental:control randomization ratio.
#' @param upper Function to compute upper bound.
#' @param upar Parameters passed to `upper`.
#' @param lower Function to compare lower bound.
#' @param lpar Parameters passed to `lower`.
#' @param info_scale Information scale for calculation. Options are:
#' - `"h0_h1_info"` (default): variance under both null and alternative hypotheses is used.
#' - `"h0_info"`: variance under null hypothesis is used.
#' - `"h1_info"`: variance under alternative hypothesis is used.
#' @param weight Weighting method, can be `"unstratified"`, `"ss"`,
#' or `"invar"`.
#' @param binding Indicator of whether futility bound is binding;
#' default of `FALSE` is recommended.
#' @param test_upper Indicator of which analyses should include an upper
#' (efficacy) bound; single value of `TRUE` (default) indicates all analyses;
#' otherwise, a logical vector of the same length as `info` should indicate
#' which analyses will have an efficacy bound.
#' @param test_lower Indicator of which analyses should include a lower bound;
#' single value of `TRUE` (default) indicates all analyses;
#' single value `FALSE` indicated no lower bound; otherwise,
#' a logical vector of the same length as `info` should indicate which
#' analyses will have a lower bound.
#' @param r Integer value controlling grid for numerical integration as in
#' Jennison and Turnbull (2000); default is 18, range is 1 to 80.
#' Larger values provide larger number of grid points and greater accuracy.
#' Normally, `r` will not be changed by the user.
#' @param tol Tolerance parameter for boundary convergence (on Z-scale).
#'
#' @return A list with input parameter, analysis, and bound.
#'
#' @export
#'
#' @examples
#' # Example 1 ----
#' library(gsDesign)
#'
#' # unstratified case with H0: rd0 = 0
#' gs_power_rd(
#' p_c = tibble::tibble(
#' stratum = "All",
#' rate = .2
#' ),
#' p_e = tibble::tibble(
#' stratum = "All",
#' rate = .15
#' ),
#' n = tibble::tibble(
#' stratum = "All",
#' n = c(20, 40, 60),
#' analysis = 1:3
#' ),
#' rd0 = 0,
#' ratio = 1,
#' upper = gs_b,
#' lower = gs_b,
#' upar = gsDesign(k = 3, test.type = 1, sfu = sfLDOF, sfupar = NULL)$upper$bound,
#' lpar = c(qnorm(.1), rep(-Inf, 2))
#' )
#'
#' # Example 2 ----
#' # unstratified case with H0: rd0 != 0
#' gs_power_rd(
#' p_c = tibble::tibble(
#' stratum = "All",
#' rate = .2
#' ),
#' p_e = tibble::tibble(
#' stratum = "All",
#' rate = .15
#' ),
#' n = tibble::tibble(
#' stratum = "All",
#' n = c(20, 40, 60),
#' analysis = 1:3
#' ),
#' rd0 = 0.005,
#' ratio = 1,
#' upper = gs_b,
#' lower = gs_b,
#' upar = gsDesign(k = 3, test.type = 1, sfu = sfLDOF, sfupar = NULL)$upper$bound,
#' lpar = c(qnorm(.1), rep(-Inf, 2))
#' )
#'
#' # use spending function
#' gs_power_rd(
#' p_c = tibble::tibble(
#' stratum = "All",
#' rate = .2
#' ),
#' p_e = tibble::tibble(
#' stratum = "All",
#' rate = .15
#' ),
#' n = tibble::tibble(
#' stratum = "All",
#' n = c(20, 40, 60),
#' analysis = 1:3
#' ),
#' rd0 = 0.005,
#' ratio = 1,
#' upper = gs_spending_bound,
#' lower = gs_b,
#' upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
#' lpar = c(qnorm(.1), rep(-Inf, 2))
#' )
#'
#' # Example 3 ----
#' # stratified case under sample size weighting and H0: rd0 = 0
#' gs_power_rd(
#' p_c = tibble::tibble(
#' stratum = c("S1", "S2", "S3"),
#' rate = c(.15, .2, .25)
#' ),
#' p_e = tibble::tibble(
#' stratum = c("S1", "S2", "S3"),
#' rate = c(.1, .16, .19)
#' ),
#' n = tibble::tibble(
#' stratum = rep(c("S1", "S2", "S3"), each = 3),
#' analysis = rep(1:3, 3),
#' n = c(10, 20, 24, 18, 26, 30, 10, 20, 24)
#' ),
#' rd0 = 0,
#' ratio = 1,
#' weight = "ss",
#' upper = gs_b,
#' lower = gs_b,
#' upar = gsDesign(k = 3, test.type = 1, sfu = sfLDOF, sfupar = NULL)$upper$bound,
#' lpar = c(qnorm(.1), rep(-Inf, 2))
#' )
#'
#' # Example 4 ----
#' # stratified case under inverse variance weighting and H0: rd0 = 0
#' gs_power_rd(
#' p_c = tibble::tibble(
#' stratum = c("S1", "S2", "S3"),
#' rate = c(.15, .2, .25)
#' ),
#' p_e = tibble::tibble(
#' stratum = c("S1", "S2", "S3"),
#' rate = c(.1, .16, .19)
#' ),
#' n = tibble::tibble(
#' stratum = rep(c("S1", "S2", "S3"), each = 3),
#' analysis = rep(1:3, 3),
#' n = c(10, 20, 24, 18, 26, 30, 10, 20, 24)
#' ),
#' rd0 = 0,
#' ratio = 1,
#' weight = "invar",
#' upper = gs_b,
#' lower = gs_b,
#' upar = gsDesign(k = 3, test.type = 1, sfu = sfLDOF, sfupar = NULL)$upper$bound,
#' lpar = c(qnorm(.1), rep(-Inf, 2))
#' )
#'
#' # Example 5 ----
#' # stratified case under sample size weighting and H0: rd0 != 0
#' gs_power_rd(
#' p_c = tibble::tibble(
#' stratum = c("S1", "S2", "S3"),
#' rate = c(.15, .2, .25)
#' ),
#' p_e = tibble::tibble(
#' stratum = c("S1", "S2", "S3"),
#' rate = c(.1, .16, .19)
#' ),
#' n = tibble::tibble(
#' stratum = rep(c("S1", "S2", "S3"), each = 3),
#' analysis = rep(1:3, 3),
#' n = c(10, 20, 24, 18, 26, 30, 10, 20, 24)
#' ),
#' rd0 = 0.02,
#' ratio = 1,
#' weight = "ss",
#' upper = gs_b,
#' lower = gs_b,
#' upar = gsDesign(k = 3, test.type = 1, sfu = sfLDOF, sfupar = NULL)$upper$bound,
#' lpar = c(qnorm(.1), rep(-Inf, 2))
#' )
#'
#' # Example 6 ----
#' # stratified case under inverse variance weighting and H0: rd0 != 0
#' gs_power_rd(
#' p_c = tibble::tibble(
#' stratum = c("S1", "S2", "S3"),
#' rate = c(.15, .2, .25)
#' ),
#' p_e = tibble::tibble(
#' stratum = c("S1", "S2", "S3"),
#' rate = c(.1, .16, .19)
#' ),
#' n = tibble::tibble(
#' stratum = rep(c("S1", "S2", "S3"), each = 3),
#' analysis = rep(1:3, 3),
#' n = c(10, 20, 24, 18, 26, 30, 10, 20, 24)
#' ),
#' rd0 = 0.03,
#' ratio = 1,
#' weight = "invar",
#' upper = gs_b,
#' lower = gs_b,
#' upar = gsDesign(k = 3, test.type = 1, sfu = sfLDOF, sfupar = NULL)$upper$bound,
#' lpar = c(qnorm(.1), rep(-Inf, 2))
#' )
gs_power_rd <- function(
p_c = tibble::tibble(
stratum = "All",
rate = .2
),
p_e = tibble::tibble(
stratum = "All",
rate = .15
),
n = tibble::tibble(
stratum = "All",
n = c(40, 50, 60),
analysis = 1:3
),
rd0 = 0,
ratio = 1,
weight = c("unstratified", "ss", "invar"),
upper = gs_b,
lower = gs_b,
upar = gsDesign(k = 3, test.type = 1, sfu = sfLDOF, sfupar = NULL)$upper$bound,
lpar = c(qnorm(.1), rep(-Inf, 2)),
info_scale = c("h0_h1_info", "h0_info", "h1_info"),
binding = FALSE,
test_upper = TRUE,
test_lower = TRUE,
r = 18,
tol = 1e-6) {
# get the number of analysis
n_analysis <- max(n$analysis)
# get the info_scale
info_scale <- match.arg(info_scale)
# get the weighting scheme
weight <- if (methods::missingArg(weight)) {
"unstratified"
} else {
match.arg(weight)
}
# Calculate the asymptotic variance and statistical information ----
x <- gs_info_rd(
p_c = p_c,
p_e = p_e,
n = n,
rd0 = rd0,
ratio = ratio,
weight = weight
)
# Given the above statistical information calculate the power ----
y_h1 <- gs_power_npe(
theta = x$rd,
info = x$info1,
info0 = x$info0,
info1 = x$info1,
info_scale = info_scale,
binding = binding,
upper = upper,
lower = lower,
upar = upar,
lpar = lpar,
test_upper = test_upper,
test_lower = test_lower,
r = r,
tol = tol
)
y_h0 <- gs_power_npe(
theta = x$rd0,
info = x$info0,
info0 = x$info0,
info1 = x$info1,
info_scale = info_scale,
binding = binding,
upper = upper,
upar = upar,
test_upper = test_upper,
lower = lower,
lpar = lpar,
test_lower = test_lower,
r = r,
tol = tol
)
# Organize the outputs ----
# summarize the bounds
suppressMessages(
bound <- y_h1 %>%
mutate(
`~risk difference at bound` = z / sqrt(info) / theta * (x$rd[1] - x$rd0[1]) + x$rd0[1],
`nominal p` = pnorm(-z)
) %>%
left_join(
y_h0 %>%
select(analysis, bound, probability) %>%
dplyr::rename(probability0 = probability)
) %>%
select(analysis, bound, probability, probability0, z, `~risk difference at bound`, `nominal p`)
)
# summarize the analysis
suppressMessages(
analysis <- x %>%
select(analysis, n, rd, rd0, theta1, theta0) %>%
left_join(
y_h1 %>%
select(analysis, info, info_frac) %>%
unique()
) %>%
left_join(
y_h0 %>%
select(analysis, info, info_frac) %>%
dplyr::rename(info0 = info, info_frac0 = info_frac) %>%
unique()
) %>%
select(analysis, n, rd, rd0, theta1, theta0, info, info0, info_frac, info_frac0)
)
ans <- list(
bound = bound %>% filter(!is.infinite(z)),
analysis = analysis
)
class(ans) <- c("rd", "gs_design", class(ans))
if (!binding) {
class(ans) <- c("non_binding", class(ans))
}
return(ans)
}