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des_gs_norm.R
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des_gs_norm.R
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#' Design a multi-stage group-sequential multi-arm clinical trial for a normally
#' distributed primary outcome
#'
#' \code{des_gs_norm()} determines multi-stage group-sequential multi-arm
#' clinical trial designs assuming the primary outcome variable is normally
#' distributed. It computes required design components and returns information
#' on key operating characteristics.
#'
#' @param K A \code{\link{numeric}} indicating the chosen value for
#' \ifelse{html}{\out{<i>K</i>}}{\eqn{K}}, the (initial) number of experimental
#' treatment arms. Defaults to \code{2}.
#' @param J A \code{\link{numeric}} indicating the chosen value for
#' \ifelse{html}{\out{<i>J</i>}}{\eqn{J}}, the (maximum) number of allowed
#' stages. Defaults to \code{2}.
#' @param alpha A \code{\link{numeric}} indicating the chosen value for
#' \ifelse{html}{\out{<i>α</i>}}{\eqn{\alpha}}, the significance level
#' (family-wise error-rate). Defaults to \code{0.025}.
#' @param beta A \code{\link{numeric}} indicating the chosen value for
#' \ifelse{html}{\out{<i>β</i>}}{\eqn{\beta}}, used in the definition of
#' the desired power. Defaults to \code{0.1}.
#' @param delta1 A \code{\link{numeric}} indicating the chosen value for
#' \ifelse{html}{\out{<i>δ</i><sub>1</sub>}}{\eqn{\delta_1}}, the
#' 'interesting' treatment effect. Defaults to \code{0.5}.
#' @param delta0 A \code{\link{numeric}} indicating the chosen value for
#' \ifelse{html}{\out{<i>δ</i><sub>0</sub>}}{\eqn{\delta_0}}, the
#' 'uninteresting' treatment effect. Defaults to \code{0}.
#' @param sigma A \code{\link{numeric}} \code{\link{vector}} indicating the
#' chosen values for
#' \ifelse{html}{\out{<i>σ</i><sub>0</sub>}}{\eqn{\sigma_0}} and
#' \ifelse{html}{\out{<i>σ</i><sub>1</sub>}}{\eqn{\sigma_1}}, the standard
#' deviations of the responses in the control and experimental arms. Must be of
#' \code{\link{length}} 1 or 2. If of \code{\link{length}} 1, it is assumed that
#' \ifelse{html}{\out{<i>σ</i><sub>0</sub>
#' =<i>σ</i><sub>1</sub>}}{\eqn{\sigma_0=\sigma_1}}.
#' Defaults to \code{1}.
#' @param ratio A \code{\link{numeric}} indicating the chosen value for
#' \ifelse{html}{\out{<i>r</i>}}{\eqn{r}}, the stage-wise allocation ratio to
#' present experimental arms. Defaults to \code{1}.
#' @param power A \code{\link{character}} string indicating the chosen type of
#' power to design the trial for. Can be \code{"disjunctive"} or
#' \code{"marginal"}. Defaults to \code{"marginal"}.
#' @param stopping A \code{\link{character}} string indicating the chosen type
#' of stopping rule. Can be \code{"separate"} or \code{"simultaneous"}. Defaults
#' to \code{"simultaneous"}.
#' @param type A \code{\link{character}} string indicating the choice for the
#' stage-wise sample size. Can be \code{"variable"} or \code{"fixed"}. Defaults
#' to \code{"variable"}.
#' @param fshape A \code{\link{character}} string indicating the choice for the
#' futility (lower) stopping boundaries. Can be any of \code{"fixed"},
#' \code{"obf"}, \code{"pocock"}, and \code{"triangular"}. Defaults to
#' \code{"pocock"}.
#' @param eshape A \code{\link{character}} string indicating the choice for the
#' efficacy (upper) stopping boundaries. Can be any of \code{"fixed"},
#' \code{"obf"}, \code{"pocock"}, and \code{"triangular"}. Defaults to
#' \code{"pocock"}.
#' @param ffix A \code{\link{numeric}} indicating the chosen value for the fixed
#' interim futility bounds. Only used when \code{fshape = "fixed"}. Defaults to
#' \code{"-3"}.
#' @param efix A \code{\link{numeric}} indicating the chosen value for the fixed
#' interim efficacy bounds. Only used when \code{eshape = "fixed"}. Defaults to
#' \code{"3"}.
#' @param spacing A \code{\link{numeric}} \code{\link{vector}} indicating the
#' chosen spacing of the interim analyses in terms of the proportion of the
#' maximal possible sample size. It must contain strictly increasing values,
#' with final element equal to \code{1}. Defaults to
#' \code{(1:J)/J} (i.e., to equally spaced analyses).
#' @param integer A \code{\link{logical}} variable indicating whether the
#' computed possible sample sizes required in each arm in each stage should be
#' forced to be whole numbers. Defaults to \code{FALSE}. WARNING: If you set
#' \code{integer = TRUE} and \code{ratio != 1}, obscure results can occur due to
#' difficulties in identifying a suitable whole number sample size that meets
#' the allocation ratio requirement.
#' @param summary A \code{\link{logical}} variable indicating whether a summary
#' of the function's progress should be printed to the console. Defaults to
#' \code{FALSE}.
#' @return A \code{\link{list}}, with additional class
#' \code{"multiarm_des_gs_norm"}, containing the following elements:
#' \itemize{
#' \item A \code{\link{tibble}} in the slot \code{$opchar} summarising the
#' operating characteristics of the identified design.
#' \item A \code{\link{tibble}} in the slot \code{$pmf_N} summarising the
#' probability mass function of the random required sample size under key
#' scenarios.
#' \item A \code{\link{numeric}} \code{\link{vector}} in the slot \code{$e}
#' specifying \ifelse{html}{\out{<b><i>e</i></b>}}{\eqn{\bold{e}}}, the trial's
#' efficacy (upper) stopping boundaries.
#' \item A \code{\link{numeric}} \code{\link{vector}} in the slot \code{$f}
#' specifying \ifelse{html}{\out{<b><i>f</i></b>}}{\eqn{\bold{f}}}, the trial's
#' futility (lower) stopping boundaries.
#' \item A \code{\link{numeric}} in the slot \code{$maxN} specifying
#' \ifelse{html}{\out{max <i>N</i>}}{max \eqn{N}}, the trial's maximum required
#' sample size.
#' \item A \code{\link{numeric}} in the slot \code{$n_factor}, for internal use
#' in other functions.
#' \item A \code{\link{numeric}} in the slot \code{$n1} specifying
#' \ifelse{html}{\out{<i>n</i><sub>1</sub>}}{\eqn{n_1}}, the total sample size
#' required in stage one of the trial.
#' \item A \code{\link{numeric}} in the slot \code{$n10} specifying
#' \ifelse{html}{\out{<i>n</i><sub>10</sub>}}{\eqn{n_{10}}}, the sample size
#' required in the control arm in stage one of the trial.
#' \item Each of the input variables.
#' }
#' @examples
#' # The design for the default parameters
#' des <- des_gs_norm()
#' @seealso \code{\link{build_gs_norm}}, \code{\link{gui}},
#' \code{\link{opchar_gs_norm}}, \code{\link{plot.multiarm_des_gs_norm}},
#' \code{\link{sim_gs_norm}}.
#' @export
des_gs_norm <- function(K = 2, J = 2, alpha = 0.025, beta = 0.1, delta1 = 0.5,
delta0 = 0, sigma = 1, ratio = 1, power = "marginal",
stopping = "simultaneous", type = "variable",
fshape = "pocock", eshape = "pocock", ffix = -3,
efix = 3, spacing = (1:J)/J, integer = FALSE,
summary = FALSE) {
##### Check input variables ##################################################
K <- check_integer_range(K, "K", c(1, Inf), 1)
J <- check_integer_range(J, "J", c(1, Inf), 1)
check_real_range_strict(alpha, "alpha", c(0, 1), 1)
check_real_range_strict(beta, "beta", c(0, 1), 1)
check_delta0_delta1(delta0, delta1, "delta0", "delta1")
sigma <- check_sigma(sigma, name_sigma = "sigma", des = "mams")
check_real_range_strict(ratio, "ratio", c(0, Inf), 1)
check_belong(power, "power", c("conjunctive", "disjunctive", "marginal"), 1)
check_belong(stopping, "stopping", c("simultaneous", "separate"), 1)
check_belong(type, "type", c("fixed", "variable"), 1)
check_boundaries(fshape, eshape, ffix, efix, "fshape", "eshape", "ffix",
"efix")
#check_spacing(spacing, "spacing", J)
check_logical(integer, "integer")
check_logical(summary, "summary")
##### Print summary ##########################################################
comp <- components_gs_init(alpha, beta, delta0, delta1, efix, eshape, ffix,
fshape, integer, J, K, power, ratio, spacing,
stopping, summary, type, sigma)
if (summary) {
#summary_des_gs_norm(comp)
message("")
}
##### Perform main computations ##############################################
if (summary) {
message(" Building required design components..")
}
comp <- components_gs_hg_lfc(comp)
if (summary) {
message("..built required design components.")
message(" Identifying the stopping boundaries..")
}
C <- stats::uniroot(f = root_bounds_gs,
interval = c(1e-16, 1e2),
comp = comp)$root
comp <- bounds_gs(C, comp)
if (summary) {
message("..identified the stopping boundaries.")
message(" Identifying the required sample size..")
}
comp$n_factor <- stats::uniroot(f = root_ss_gs,
interval = c(1e-16, 1e4),
comp = comp)$root
if (summary) {
message("..identified the required sample size.")
message(" Preparing for outputting..")
}
comp <- integer_gs(comp)
if (type == "variable") {
n10 <- comp$n_factor
n1 <- comp$n_factor*(1 + ratio*K)
} else if (type == "fixed") {
n10 <- comp$n_factor/(1 + ratio*K)
n1 <- comp$n_factor
}
comp <-
components_gs_update(comp, rbind(rep(0, K), rep(delta1, K),
matrix(delta0, K, K) +
(delta1 - delta0)*diag(K)))
comp <- opchar_gs_internal(comp)
##### Outputting #############################################################
if (summary) {
message("..outputting.")
}
output <- list(alpha = alpha,
beta = beta,
delta0 = delta0,
delta1 = delta1,
e = comp$e,
efix = efix,
eshape = eshape,
f = comp$f,
ffix = ffix,
fshape = fshape,
integer = integer,
J = J,
K = K,
maxN = comp$opchar$maxN[1],
n_factor = comp$n_factor,
n10 = n10,
n1 = n1,
opchar = comp$opchar,
pmf_N = comp$pmf_N,
power = power,
ratio = ratio,
sigma = sigma,
spacing = spacing,
stopping = stopping,
summary = summary,
type = type)
class(output) <- c("multiarm_des_gs_norm", class(output))
output
}