R/optimal_multitrial.R
In Sterniii3/drugdevelopR: Utility-Based Optimal Phase II/III Drug Development Planning
Defines functions
optimal_multitrial
Documented in
optimal_multitrial
#' Optimal phase II/III drug development planning where several phase III trials are performed for time-to-event endpoints
#'
#' The function \code{\link{optimal_multitrial}} of the drugdevelopR package enables planning of phase II/III drug development programs with time-to-event endpoints for programs with several phase III trials (Preussler et. al, 2019).
#' Its main output values are the optimal sample size allocation and optimal go/no-go decision rules.
#' The assumed true treatment effects can be assumed to be fixed (planning is then also possible via user friendly R Shiny App: \href{https://web.imbi.uni-heidelberg.de/multitrial/}{multitrial}) or can be modelled by a prior distribution.
#' The R Shiny application \href{https://web.imbi.uni-heidelberg.de/prior/}{prior} visualizes the prior distributions used in this package. Fast computing is enabled by parallel programming.
#'
#' @name optimal_multitrial
#'
#' @inheritParams optimal_multitrial_generic
#' @inheritParams optimal_tte_generic
#'
#' @inheritSection optimal_multitrial_generic Effect sizes
#'
#' @return
#' `r optimal_return_doc(type = "tte", setting = "multitrial")`
#'
#' @importFrom progressr progressor
#'
#'
#' @examples
#' # Activate progress bar (optional)
#' \dontrun{progressr::handlers(global = TRUE)}
#' # Optimize
#' \donttest{
#' optimal_multitrial(w = 0.3, # define parameters for prior
#' hr1 = 0.69, hr2 = 0.88, id1 = 210, id2 = 420, # (https://web.imbi.uni-heidelberg.de/prior/)
#' d2min = 20, d2max = 100, stepd2 = 5, # define optimization set for d2
#' hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05, # define optimization set for HRgo
#' alpha = 0.025, beta = 0.1, xi2 = 0.7, xi3 = 0.7, # drug development planning parameters
#' c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed and variable costs for phase II/III
#' K = Inf, N = Inf, S = -Inf, # set constraints
#' b1 = 1000, b2 = 2000, b3 = 3000, # expected benefit for each effect size
#' case = 1, strategy = TRUE, # chose Case and Strategy
#' fixed = TRUE, # true treatment effects are fixed/random
#' num_cl = 1) # number of cores for parallelized computing
#' }
#' @references
#' IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at \href{https://www.iqwig.de/ueber-uns/methoden/methodenpapier/}{https://www.iqwig.de/ueber-uns/methoden/methodenpapier/}, assessed last 15.05.19.
#'
#' Preussler, S., Kieser, M., and Kirchner, M. (2019). Optimal sample size allocation and go/no-go decision rules for phase II/III programs where several phase III trials are performed. Biometrical Journal, 61(2), 357-378.
#'
#' Schoenfeld, D. (1981). The asymptotic properties of nonparametric tests for comparing survival distributions. Biometrika, 68(1), 316-319.
#'
#' @export
optimal_multitrial <- function(w, hr1, hr2, id1, id2,
d2min, d2max, stepd2,
hrgomin, hrgomax, stephrgo,
alpha, beta, xi2, xi3,
c2, c3, c02, c03,
K = Inf, N = Inf, S = -Inf,
b1, b2, b3,
case, strategy = TRUE,
fixed = FALSE, num_cl = 1){
result <- result23 <- NULL
# spezifications for one phase III trial
steps1 = 1; stepm1 = 0.95; stepl1 = 0.85
steps2 <- stepm1
stepm2 <- stepl1
stepl2 <- 0
gamma <- 0
ymin <- -log(0.8)
alpha_in <- alpha
date <- Sys.time()
HRGO <- seq(hrgomin, hrgomax, stephrgo)
D2 <- seq(d2min, d2max, stepd2)
if(!is.numeric(strategy)){
if(case==1){
# Strategy 1alpha vs. Strategy 1/2,
STRATEGY = c(1, 2)
}
if(case==2){
# Strategy 1alpha^2 vs. Strategy 2/2 vs. Strategy 2/3 vs. Strategy 2/2( + 1)
STRATEGY = c(1, 2, 3, 23)
}
if(case==3){
# Strategy 1alpha^3 vs. Strategy 3/3 vs. Strategy 3/4
STRATEGY = c(1, 3, 4)
}
}else{
STRATEGY = strategy
}
HRgo <- NA_real_
Strategy <- NA_real_
cl <- parallel::makeCluster(getOption("cl.cores", num_cl)) #define cluster
parallel::clusterExport(cl, c("pmvnorm", "dmvnorm", "prior_tte", "Epgo_tte", "Epgo23", "Ed3_tte",
"EPsProg_tte", "EPsProg2", "EPsProg3", "EPsProg4", "EPsProg23",
"alpha", "beta",
"steps1", "steps2", "stepm1", "stepm2", "stepl1", "stepl2",
"K", "N", "S","gamma", "fixed", "case", "Strategy",
"xi2", "xi3", "c2", "c3", "c02", "c03",
"b1", "b2", "b3", "w", "HRgo", "ymin",
"hr1", "hr2", "id1", "id2"), envir = environment())
for(Strategy in STRATEGY){
ufkt <- d3fkt <- spfkt <- pgofkt <- K2fkt <- K3fkt <-
sp1fkt <- sp2fkt <- sp3fkt <- n2fkt <- n3fkt <- pgo3fkt <-
d33fkt <- n33fkt<- sp13fkt <- sp23fkt <- sp33fkt <- matrix(0, length(D2), length(HRGO))
pb <- progressr::progressor(steps = length(STRATEGY)*length(HRGO), label = "Optimization progress", message = "Optimization progress")
pb(paste("Performing optimization for strategy", Strategy), class = "sticky", amount = 0)
for(j in 1:length(HRGO)){
HRgo <- HRGO[j]
###################
# Strategy 1alpha #
###################
if(Strategy == 1){
if(case==1){
alpha <- alpha_in
}
if(case==2){
alpha <- alpha_in^2
}
if(case==3){
alpha <- alpha_in^3
}
}else{
alpha <- alpha_in
}
if(Strategy==1){
res <- parallel::parSapply(cl, D2, utility_tte, HRgo, w, hr1, hr2, id1, id2,
alpha, beta, xi2, xi3,
c2, c3, c02, c03,
K, N, S,
steps1, stepm1, stepl1,
b1, b2, b3,
gamma, fixed)
}
if(Strategy==2){
res <- parallel::parSapply(cl, D2, utility2, HRgo, w, hr1, hr2, id1, id2,
alpha, beta, xi2, xi3,
c2, c3, c02, c03,
K, N, S,
b1, b2, b3,
case, fixed)
}
if(Strategy==3){
res <- parallel::parSapply(cl, D2, utility3, HRgo, w, hr1, hr2, id1, id2,
alpha, beta, xi2, xi3,
c2, c3, c02, c03,
K, N, S,
b1, b2, b3,
case, fixed)
}
if(Strategy==23){
res <- parallel::parSapply(cl, D2, utility23, HRgo, w, hr1, hr2, id1, id2,
alpha, beta, xi2, xi3,
c2, c3, c02, c03,
b1, b2, b3)
}
if(Strategy==4){
res <- parallel::parSapply(cl, D2, utility4, HRgo, w, hr1, hr2, id1, id2,
alpha, beta, xi2, xi3,
c2, c3, c02, c03,
K, N, S,
b1, b2, b3,
case, fixed)
}
pb()
ufkt[, j] <- res[1, ]
d3fkt[, j] <- res[2, ]
spfkt[, j] <- res[3, ]
pgofkt[, j] <- res[4, ]
K2fkt[, j] <- res[5, ]
K3fkt[, j] <- res[6, ]
sp1fkt[, j] <- res[7, ]
sp2fkt[, j] <- res[8, ]
sp3fkt[, j] <- res[9, ]
n2fkt[, j] <- res[10, ]
n3fkt[, j] <- res[11, ]
if(Strategy==23){
pgo3fkt[, j] <- res[12, ]
d33fkt[, j] <- res[13, ]
n33fkt[, j] <- res[14, ]
sp13fkt[, j] <- res[15, ]
sp23fkt[, j] <- res[16, ]
sp33fkt[, j] <- res[17, ]
}
}
ind <- which(ufkt == max(ufkt), arr.ind <- TRUE)
I <- as.vector(ind[1, 1])
J <- as.vector(ind[1, 2])
Eud <- ufkt[I, J]
d3 <- d3fkt[I, J]
prob <- spfkt[I, J]
pg <- pgofkt[I, J]
k2 <- K2fkt[I, J]
k3 <- K3fkt[I, J]
prob1 <- sp1fkt[I, J]
prob2 <- sp2fkt[I, J]
prob3 <- sp3fkt[I, J]
n2 <- n2fkt[I,J]
n3 <- n3fkt[I,J]
if(Strategy==23){
d33 <- d33fkt[I, J]
pg3 <- pgo3fkt[I, J]
prob13 <- sp13fkt[I, J]
prob23 <- sp23fkt[I, J]
prob33 <- sp33fkt[I, J]
n33 <- n33fkt[I,J]
}else{
d33 <- 0
pg3 <- 0
prob13 <- 0
prob23 <- 0
prob33 <- 0
n33 <- 0
}
if(!fixed){
result <- rbind(result, data.frame(Case = case, Strategy = Strategy,
u = round(Eud,2), HRgo = HRGO[J], d2 = D2[I], d3 = d3, d = D2[I] + d3,
n2 = n2, n3 = n3, n = n2 + n3,
pgo = round(pg,2), sProg = round(prob,2),
w = w, hr1 = hr1, hr2 = hr2, id1 = id1, id2 = id2,
K = K, N = N, S = S, K2 = round(k2), K3 = round(k3),
sProg1 = round(prob1,2), sProg2 = round(prob2,2), sProg3 = round(prob3,2),
steps1 = round(steps1,2), stepm1 = round(stepm1,2), stepl1 = round(stepl1,2),
pgo3 = round(pg3,2), d33= d33, n33 = n33,
sProg13 = round(prob13,2), sProg23 = round(prob23,2), sProg33 = round(prob33,2),
alpha = alpha, beta = beta, xi2 = xi2, xi3 = xi3, c02 = c02,
c03 = c03, c2 = c2, c3 = c3, b1 = b1, b2 = b2, b3 = b3, gamma = gamma))
}else{
result <- rbind(result, data.frame(Case = case, Strategy = Strategy,
u = round(Eud,2), HRgo = HRGO[J], d2 = D2[I], d3 = d3, d = D2[I] + d3,
n2 = n2, n3 = n3, n = n2 + n3,
pgo = round(pg,2), sProg = round(prob,2),
hr = hr1,
K = K, N = N, S = S, K2 = round(k2), K3 = round(k3),
sProg1 = round(prob1,2), sProg2 = round(prob2,2), sProg3 = round(prob3,2),
steps1 = round(steps1,2), stepm1 = round(stepm1,2), stepl1 = round(stepl1,2),
alpha = alpha, beta = beta, xi2 = xi2, xi3 = xi3, c02 = c02,
c03 = c03, c2 = c2, c3 = c3, b1 = b1, b2 = b2, b3 = b3, gamma = gamma))
}
comment(result) <- c("\noptimization sequence HRgo:", HRGO,
"\noptimization sequence d2:", D2,
"\nonset date:", as.character(date),
"\nfinish date:", as.character(Sys.time()))
}
class(result) <- c("drugdevelopResult", class(result))
parallel::stopCluster(cl)
return(result)
}
Sterniii3/drugdevelopR documentation built on Jan. 26, 2024, 6:17 a.m.
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Defines functions optimal_multitrial
Documented in optimal_multitrial
#' Optimal phase II/III drug development planning where several phase III trials are performed for time-to-event endpoints
#'
#' The function \code{\link{optimal_multitrial}} of the drugdevelopR package enables planning of phase II/III drug development programs with time-to-event endpoints for programs with several phase III trials (Preussler et. al, 2019).
#' Its main output values are the optimal sample size allocation and optimal go/no-go decision rules.
#' The assumed true treatment effects can be assumed to be fixed (planning is then also possible via user friendly R Shiny App: \href{https://web.imbi.uni-heidelberg.de/multitrial/}{multitrial}) or can be modelled by a prior distribution.
#' The R Shiny application \href{https://web.imbi.uni-heidelberg.de/prior/}{prior} visualizes the prior distributions used in this package. Fast computing is enabled by parallel programming.
#'
#' @name optimal_multitrial
#'
#' @inheritParams optimal_multitrial_generic
#' @inheritParams optimal_tte_generic
#'
#' @inheritSection optimal_multitrial_generic Effect sizes
#'
#' @return
#' `r optimal_return_doc(type = "tte", setting = "multitrial")`
#'
#' @importFrom progressr progressor
#'
#'
#' @examples
#' # Activate progress bar (optional)
#' \dontrun{progressr::handlers(global = TRUE)}
#' # Optimize
#' \donttest{
#' optimal_multitrial(w = 0.3, # define parameters for prior
#' hr1 = 0.69, hr2 = 0.88, id1 = 210, id2 = 420, # (https://web.imbi.uni-heidelberg.de/prior/)
#' d2min = 20, d2max = 100, stepd2 = 5, # define optimization set for d2
#' hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05, # define optimization set for HRgo
#' alpha = 0.025, beta = 0.1, xi2 = 0.7, xi3 = 0.7, # drug development planning parameters
#' c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed and variable costs for phase II/III
#' K = Inf, N = Inf, S = -Inf, # set constraints
#' b1 = 1000, b2 = 2000, b3 = 3000, # expected benefit for each effect size
#' case = 1, strategy = TRUE, # chose Case and Strategy
#' fixed = TRUE, # true treatment effects are fixed/random
#' num_cl = 1) # number of cores for parallelized computing
#' }
#' @references
#' IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at \href{https://www.iqwig.de/ueber-uns/methoden/methodenpapier/}{https://www.iqwig.de/ueber-uns/methoden/methodenpapier/}, assessed last 15.05.19.
#'
#' Preussler, S., Kieser, M., and Kirchner, M. (2019). Optimal sample size allocation and go/no-go decision rules for phase II/III programs where several phase III trials are performed. Biometrical Journal, 61(2), 357-378.
#'
#' Schoenfeld, D. (1981). The asymptotic properties of nonparametric tests for comparing survival distributions. Biometrika, 68(1), 316-319.
#'
#' @export
optimal_multitrial <- function(w, hr1, hr2, id1, id2,
d2min, d2max, stepd2,
hrgomin, hrgomax, stephrgo,
alpha, beta, xi2, xi3,
c2, c3, c02, c03,
K = Inf, N = Inf, S = -Inf,
b1, b2, b3,
case, strategy = TRUE,
fixed = FALSE, num_cl = 1){
result <- result23 <- NULL
# spezifications for one phase III trial
steps1 = 1; stepm1 = 0.95; stepl1 = 0.85
steps2 <- stepm1
stepm2 <- stepl1
stepl2 <- 0
gamma <- 0
ymin <- -log(0.8)
alpha_in <- alpha
date <- Sys.time()
HRGO <- seq(hrgomin, hrgomax, stephrgo)
D2 <- seq(d2min, d2max, stepd2)
if(!is.numeric(strategy)){
if(case==1){
# Strategy 1alpha vs. Strategy 1/2,
STRATEGY = c(1, 2)
}
if(case==2){
# Strategy 1alpha^2 vs. Strategy 2/2 vs. Strategy 2/3 vs. Strategy 2/2( + 1)
STRATEGY = c(1, 2, 3, 23)
}
if(case==3){
# Strategy 1alpha^3 vs. Strategy 3/3 vs. Strategy 3/4
STRATEGY = c(1, 3, 4)
}
}else{
STRATEGY = strategy
}
HRgo <- NA_real_
Strategy <- NA_real_
cl <- parallel::makeCluster(getOption("cl.cores", num_cl)) #define cluster
parallel::clusterExport(cl, c("pmvnorm", "dmvnorm", "prior_tte", "Epgo_tte", "Epgo23", "Ed3_tte",
"EPsProg_tte", "EPsProg2", "EPsProg3", "EPsProg4", "EPsProg23",
"alpha", "beta",
"steps1", "steps2", "stepm1", "stepm2", "stepl1", "stepl2",
"K", "N", "S","gamma", "fixed", "case", "Strategy",
"xi2", "xi3", "c2", "c3", "c02", "c03",
"b1", "b2", "b3", "w", "HRgo", "ymin",
"hr1", "hr2", "id1", "id2"), envir = environment())
for(Strategy in STRATEGY){
ufkt <- d3fkt <- spfkt <- pgofkt <- K2fkt <- K3fkt <-
sp1fkt <- sp2fkt <- sp3fkt <- n2fkt <- n3fkt <- pgo3fkt <-
d33fkt <- n33fkt<- sp13fkt <- sp23fkt <- sp33fkt <- matrix(0, length(D2), length(HRGO))
pb <- progressr::progressor(steps = length(STRATEGY)*length(HRGO), label = "Optimization progress", message = "Optimization progress")
pb(paste("Performing optimization for strategy", Strategy), class = "sticky", amount = 0)
for(j in 1:length(HRGO)){
HRgo <- HRGO[j]
###################
# Strategy 1alpha #
###################
if(Strategy == 1){
if(case==1){
alpha <- alpha_in
}
if(case==2){
alpha <- alpha_in^2
}
if(case==3){
alpha <- alpha_in^3
}
}else{
alpha <- alpha_in
}
if(Strategy==1){
res <- parallel::parSapply(cl, D2, utility_tte, HRgo, w, hr1, hr2, id1, id2,
alpha, beta, xi2, xi3,
c2, c3, c02, c03,
K, N, S,
steps1, stepm1, stepl1,
b1, b2, b3,
gamma, fixed)
}
if(Strategy==2){
res <- parallel::parSapply(cl, D2, utility2, HRgo, w, hr1, hr2, id1, id2,
alpha, beta, xi2, xi3,
c2, c3, c02, c03,
K, N, S,
b1, b2, b3,
case, fixed)
}
if(Strategy==3){
res <- parallel::parSapply(cl, D2, utility3, HRgo, w, hr1, hr2, id1, id2,
alpha, beta, xi2, xi3,
c2, c3, c02, c03,
K, N, S,
b1, b2, b3,
case, fixed)
}
if(Strategy==23){
res <- parallel::parSapply(cl, D2, utility23, HRgo, w, hr1, hr2, id1, id2,
alpha, beta, xi2, xi3,
c2, c3, c02, c03,
b1, b2, b3)
}
if(Strategy==4){
res <- parallel::parSapply(cl, D2, utility4, HRgo, w, hr1, hr2, id1, id2,
alpha, beta, xi2, xi3,
c2, c3, c02, c03,
K, N, S,
b1, b2, b3,
case, fixed)
}
pb()
ufkt[, j] <- res[1, ]
d3fkt[, j] <- res[2, ]
spfkt[, j] <- res[3, ]
pgofkt[, j] <- res[4, ]
K2fkt[, j] <- res[5, ]
K3fkt[, j] <- res[6, ]
sp1fkt[, j] <- res[7, ]
sp2fkt[, j] <- res[8, ]
sp3fkt[, j] <- res[9, ]
n2fkt[, j] <- res[10, ]
n3fkt[, j] <- res[11, ]
if(Strategy==23){
pgo3fkt[, j] <- res[12, ]
d33fkt[, j] <- res[13, ]
n33fkt[, j] <- res[14, ]
sp13fkt[, j] <- res[15, ]
sp23fkt[, j] <- res[16, ]
sp33fkt[, j] <- res[17, ]
}
}
ind <- which(ufkt == max(ufkt), arr.ind <- TRUE)
I <- as.vector(ind[1, 1])
J <- as.vector(ind[1, 2])
Eud <- ufkt[I, J]
d3 <- d3fkt[I, J]
prob <- spfkt[I, J]
pg <- pgofkt[I, J]
k2 <- K2fkt[I, J]
k3 <- K3fkt[I, J]
prob1 <- sp1fkt[I, J]
prob2 <- sp2fkt[I, J]
prob3 <- sp3fkt[I, J]
n2 <- n2fkt[I,J]
n3 <- n3fkt[I,J]
if(Strategy==23){
d33 <- d33fkt[I, J]
pg3 <- pgo3fkt[I, J]
prob13 <- sp13fkt[I, J]
prob23 <- sp23fkt[I, J]
prob33 <- sp33fkt[I, J]
n33 <- n33fkt[I,J]
}else{
d33 <- 0
pg3 <- 0
prob13 <- 0
prob23 <- 0
prob33 <- 0
n33 <- 0
}
if(!fixed){
result <- rbind(result, data.frame(Case = case, Strategy = Strategy,
u = round(Eud,2), HRgo = HRGO[J], d2 = D2[I], d3 = d3, d = D2[I] + d3,
n2 = n2, n3 = n3, n = n2 + n3,
pgo = round(pg,2), sProg = round(prob,2),
w = w, hr1 = hr1, hr2 = hr2, id1 = id1, id2 = id2,
K = K, N = N, S = S, K2 = round(k2), K3 = round(k3),
sProg1 = round(prob1,2), sProg2 = round(prob2,2), sProg3 = round(prob3,2),
steps1 = round(steps1,2), stepm1 = round(stepm1,2), stepl1 = round(stepl1,2),
pgo3 = round(pg3,2), d33= d33, n33 = n33,
sProg13 = round(prob13,2), sProg23 = round(prob23,2), sProg33 = round(prob33,2),
alpha = alpha, beta = beta, xi2 = xi2, xi3 = xi3, c02 = c02,
c03 = c03, c2 = c2, c3 = c3, b1 = b1, b2 = b2, b3 = b3, gamma = gamma))
}else{
result <- rbind(result, data.frame(Case = case, Strategy = Strategy,
u = round(Eud,2), HRgo = HRGO[J], d2 = D2[I], d3 = d3, d = D2[I] + d3,
n2 = n2, n3 = n3, n = n2 + n3,
pgo = round(pg,2), sProg = round(prob,2),
hr = hr1,
K = K, N = N, S = S, K2 = round(k2), K3 = round(k3),
sProg1 = round(prob1,2), sProg2 = round(prob2,2), sProg3 = round(prob3,2),
steps1 = round(steps1,2), stepm1 = round(stepm1,2), stepl1 = round(stepl1,2),
alpha = alpha, beta = beta, xi2 = xi2, xi3 = xi3, c02 = c02,
c03 = c03, c2 = c2, c3 = c3, b1 = b1, b2 = b2, b3 = b3, gamma = gamma))
}
comment(result) <- c("\noptimization sequence HRgo:", HRGO,
"\noptimization sequence d2:", D2,
"\nonset date:", as.character(date),
"\nfinish date:", as.character(Sys.time()))
}
class(result) <- c("drugdevelopResult", class(result))
parallel::stopCluster(cl)
return(result)
}
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