#' Design a single-stage multi-arm clinical trial for a Bernoulli distributed
#' primary outcome
#'
#' \code{des_ss_bern()} determines single-stage multi-arm clinical trial designs
#' assuming the primary outcome variable is Bernoulli distributed. It supports a
#' variety of multiple comparison corrections, along with the determination of
#' \emph{A}-, \emph{D}-, and \emph{E}-optimal allocation ratios. In all
#' instances, \code{des_ss_bern()} computes the required sample size in each
#' arm, 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 number of experimental treatment
#' arms. 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.
#' Defaults to \code{0.052}.
#' @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 pi0 A \code{\link{numeric}} indicating the chosen value for
#' \ifelse{html}{\out{<i>π</i><sub>0</sub>}}{\eqn{\pi_0}}, the
#' response rate in the control arm. Defaults to \code{0.3}.
#' @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{0.2}.
#' @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 ratio Either a \code{\link{numeric}} vector or a
#' \code{\link{character}} string indicating the chosen value for
#' \ifelse{html}{\out{<b><i>r</i></b>}}{\eqn{\bold{r}}}, the vector of
#' allocation ratios to the experimental arms. Can be specified explicitly
#' as a \code{\link{numeric}} vector, or can be specified as \code{"A"},
#' \code{"D"}, or \code{"E"} to instruct \code{des_ss_bern()} to compute the
#' \emph{A}-, \emph{D}-, or \emph{E}-optimal value for
#' \ifelse{html}{\out{<b><i>r</i></b>}}{\eqn{\bold{r}}}. Defaults to
#' \code{rep(1, K)}.
#' @param correction A \code{\link{character}} string indicating the chosen
#' multiple comparison correction. Can be any of \code{"benjamini_hochberg"},
#' \code{"benjamini_yekutieli"}, \code{"bonferroni"}, \code{"dunnett"},
#' \code{"hochberg"}, \code{"holm_bonferroni"}, \code{"holm_sidak"},
#' \code{"none"}, \code{"sidak"}, and \code{"step_down_dunnett"}. Defaults to
#' \code{"dunnett"}.
#' @param power A \code{\link{character}} string indicating the chosen type of
#' power to design the trial for. Can be one of \code{"conjunctive"},
#' \code{"disjunctive"}, and \code{"marginal"}. Defaults to \code{"marginal"}.
#' @param integer A \code{\link{logical}} variable indicating whether the
#' computed values in \ifelse{html}{\out{<b><i>n</i></b>}}{\eqn{\bold{n}}}, the
#' vector of sample sizes required in each arm, should be forced to be whole
#' numbers. Defaults to \code{FALSE}.
#' @param ratio_scenario Only used if \code{ratio} is a \code{\link{character}}
#' string. A \code{\link{character}} string indicating the chosen response rate
#' scenario for which to optimise the allocation ratios. Can be one of
#' \code{"HG"} and \code{"HA"}. Defaults to \code{"HG"}.
#' @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}} of class \code{"multiarm_des_ss_bern"}
#' containing the following elements
#' \itemize{
#' \item A \code{\link{tibble}} in the slot \code{$opchar} summarising the
#' operating characteristics of the identified design.
#' \item A \code{\link{numeric}} in the slot \code{$N} specifying
#' \ifelse{html}{\out{<i>N</i>}}{\eqn{N}}, the trial's total required sample
#' size.
#' \item A \code{\link{numeric}} vector in the slot \code{$n} specifying
#' \ifelse{html}{\out{<b><i>n</i></b>}}{\eqn{\bold{n}}}, the vector of sample
#' sizes required in each arm.
#' \item A \code{\link{numeric}} in the slot \code{$gamma} specifying the
#' critical threshold for \emph{p}-values,
#' \ifelse{html}{\out{<i>γ</i>}}{\eqn{\gamma}}, below which null
#' hypotheses would be rejected. Will be \code{\link{NA}} if \code{correction}
#' is not a single-step testing procedure.
#' \item A \code{\link{numeric}} vector in the slot \code{$gammaO} specifying
#' the critical thresholds for ordered \emph{p}-values,
#' \ifelse{html}{\out{<b><i>γ</i></b>}}{\eqn{\bold{\gamma}}}, to use with
#' the chosen step-wise testing procedure. Will be \code{\link{NA}} if
#' \code{correction} is not a step-wise testing procedure.
#' \item Each of the input variables.
#' }
#' @examples
#' # The design for the default parameters
#' des <- des_ss_bern()
#' # An A-optimal design
#' des_A <- des_ss_bern(ratio = "A")
#' # Using the root-K allocation rule, modifying the desired type of power, and
#' # choosing an alternative multiple comparison correction
#' des_root_K <- des_ss_bern(ratio = rep(1/sqrt(2), 2),
#' correction = "holm_bonferroni",
#' power = "disjunctive")
#' @seealso \code{\link{build_ss_bern}}, \code{\link{gui}},
#' \code{\link{opchar_ss_bern}}, \code{\link{plot.multiarm_des_ss_bern}},
#' \code{\link{sim_ss_bern}}.
#' @export
des_ss_bern <- function(K = 2, alpha = 0.025, beta = 0.1, pi0 = 0.3,
delta1 = 0.2, delta0 = 0, ratio = rep(1, K),
correction = "dunnett", power = "marginal",
integer = FALSE, ratio_scenario = "HG",
summary = FALSE) {
##### Check input variables ##################################################
K <- check_integer_range(K, "K", 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_real_range_strict(pi0, "pi0", c(0, 1), 1)
check_delta0_delta1(delta0, delta1, "delta0", "delta1", pi0, "pi0")
check_ratio(ratio, K, name_ratio = "ratio", name_K = "K")
check_belong(correction, "correction",
c("benjamini_hochberg", "benjamini_yekutieli", "bonferroni",
"dunnett", "hochberg", "holm_bonferroni", "holm_sidak", "none",
"sidak", "step_down_dunnett"), 1)
check_belong(power, "power", c("conjunctive", "disjunctive", "marginal"), 1)
check_belong(ratio_scenario, "ratio_scenario", c("HG", "HA"), 1)
check_logical(integer, "integer")
check_logical(summary, "summary")
##### Preliminaries ##########################################################
if (is.character(ratio)) {
ratio_n <- rep(1, K)
} else {
ratio_n <- ratio
}
comp <- components_ss_bern(alpha, beta, correction, delta0, delta1, integer,
K, pi0, power, ratio, ratio_scenario,
c(1, ratio_n)/(1 + sum(ratio_n)))
if (summary) {
summary_des_ss_bern(comp)
message("")
}
##### Main computations ######################################################
if (ratio_scenario == "HG") {
sigma <- rep(sqrt(pi0*(1 - pi0)), K + 1)
} else if (ratio_scenario == "HA") {
sigma <-
c(sqrt(pi0*(1 - pi0)), rep(sqrt((pi0 + delta1)*(1 - pi0 - delta1)), K))
}
if (is.character(ratio)) {
ratio_init <- ratio
if (summary) {
message(" Identifying the ", ratio, "-optimal allocation ratio..")
}
if (ratio == "A") {
rho0 <- sigma[1]*sqrt(K)
comp$n <- c(rho0, sigma[-1])/(rho0 + sum(sigma[-1]))
} else {
Kp1 <- K + 1L
if (ratio == "D") {
obj_func <- determinant_ss
} else {
obj_func <- max_eigenvalue_ss
}
comp$n <-
Rsolnp::solnp(pars = rep(1/Kp1, Kp1),
fun = obj_func,
eqfun = function(rho, K, sigma) { sum(rho) - 1 },
eqB = 0L,
LB = integer(Kp1),
UB = rep(1L, Kp1),
control = list(trace = 0L),
K = K,
sigma = sigma)$pars
}
comp$ratio <- comp$n[-1]/comp$n[1]
if (summary) {
message("..identified the ", ratio_init, "-optimal allocation ratio.")
}
}
if (summary) {
message(" Building required design components..")
}
comp <- components_ss_power_setup(comp)
comp <- components_ss_update(comp)
if (summary) {
message("..built required design components.")
message(" Identifying the required sample size..")
}
comp <- sample_size_ss(comp)
if (summary) {
message("..identified the required sample size.")
message(" Preparing for outputting..")
}
comp <- integer_ss(comp)
tau <- rbind(numeric(K), rep(delta1, K),
matrix(delta0, K, K) + (delta1 - delta0)*diag(K))
comp <- components_ss_update(comp, tau, cbind(pi0, tau + pi0))
comp <- opchar_ss_internal(comp)
##### Outputting #############################################################
if (summary) {
message("..outputting.")
}
output <- list(alpha = alpha,
beta = beta,
correction = correction,
delta0 = delta0,
delta1 = delta1,
gamma = comp$gamma,
gammaO = comp$gammaO,
integer = integer,
K = K,
N = comp$N,
n = comp$n,
opchar = comp$opchar,
pi0 = pi0,
power = power,
ratio = comp$n[-1]/comp$n[1],
ratio_scenario = ratio_scenario,
summary = summary)
class(output) <- c("multiarm_des_ss_bern", class(output))
output
}
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