Nothing
R/ClustRand.r
In MedianaDesigner: Power and Sample Size Calculations for Clinical Trials
Defines functions
ClustRandGLMEMR
ClustRandSingleCore
ClustRandReportDoc
ClustRand
AntiLogit
ComputePower
Documented in
ClustRand
ClustRandGLMEMR
ClustRandReportDoc
ClustRandSingleCore
ComputePower = function(data_frame, convergence, alpha) {
ncomps = ncol(data_frame)
nsims = nrow(data_frame)
power = rep(0, ncomps + 1)
outcomes = matrix(0, nsims, ncomps + 1)
for (i in 1:ncomps) {
outcomes[, i] = as.numeric(data_frame[, i] <= alpha)
outcomes[convergence[, i] == 0, i] = NA
power[i] = mean(outcomes[, i], na.rm = TRUE)
}
outcomes[, ncomps + 1] = as.numeric(rowSums(outcomes[, 1:ncomps]) >= 1)
power[ncomps + 1] = mean(outcomes[, ncomps + 1], na.rm = TRUE)
return(power)
}
AntiLogit = function(x) {
return(1 / (1 + exp(-x)))
}
ClustRand = function(parameters) {
# Error checks
if (typeof(parameters) != "list") stop("Function parameters must be a list of named values.", call. = FALSE)
if (is.null(parameters$random_seed)) {
random_seed = 49283
} else {
random_seed = ContinuousErrorCheck(parameters$random_seed,
1,
lower_values = 1,
lower_values_sign = c(">="),
upper_values = 100000,
upper_values_sign = c("<="),
"Seed for the random number generator (random_seed)",
c("Value"),
"int",
NA)
}
parameters$random_seed = random_seed
# Set the seed of R's random number generator.
# It also takes effect to Rcpp random generation functions.
# https://stackoverflow.com/questions/60119621/get-the-same-sample-of-integers-from-rcpp-as-base-r
suppressWarnings(RNGkind(sample.kind = "Rounding"))
set.seed(random_seed)
if (is.null(parameters$endpoint_type)) stop("Endpoint type (endpoint_type): Value must be specified.", call. = FALSE)
if (!tolower(parameters$endpoint_type) %in% tolower(c("normal", "binary"))) stop("Endpoint type (endpoint_type): Value must be Normal or Binary.", call. = FALSE)
if (tolower(parameters$endpoint_type) == "normal") endpoint_index = 1
if (tolower(parameters$endpoint_type) == "binary") endpoint_index = 2
parameters$endpoint_index = endpoint_index
if (is.null(parameters$method_type)) stop("Data analysis method (method_type): Value must be specified.", call. = FALSE)
if (!tolower(parameters$method_type) %in% tolower(c("gee", "glmem"))) stop("Data analysis method (method_type): Value must be GEE or GLMEM", call. = FALSE)
if (tolower(parameters$method_type) == "gee") method_index = 1
if (tolower(parameters$method_type) == "glmem") method_index = 2
parameters$method_index = method_index
if (is.null(parameters$direction)) {
parameters$direction_index = 1
} else {
if (!tolower(parameters$direction) %in% c("higher", "lower")) stop("Direction of favorable outcome (direction): Value must be specified.", call. = FALSE)
}
if (tolower(parameters$direction) == "higher") parameters$direction_index = 1
if (tolower(parameters$direction) == "lower") parameters$direction_index = 2
if (is.null(parameters$cluster_scheme)) stop("Cluster scheme (cluster_scheme): Value must be specified.", call. = FALSE)
if (!tolower(parameters$cluster_scheme) %in% tolower(c("fixed", "random"))) stop("Cluster scheme (cluster_scheme): Value must be Fixed or Random.", call. = FALSE)
if (tolower(parameters$cluster_scheme) == "fixed") cluster_index = 1
if (tolower(parameters$cluster_scheme) == "random") cluster_index = 2
parameters$cluster_index = cluster_index
if (is.null(parameters$sample_size)) stop("Number of completers in each trial arm (sample_size): Value must be specified.", call. = FALSE)
sample_size = ContinuousErrorCheck(parameters$sample_size,
NA,
lower_values = 0,
lower_values_sign = ">",
upper_values = 1000,
upper_values_sign = "<=",
"Number of completers in each trial arm (sample_size)",
NA,
"int",
NA)
narms = length(sample_size)
parameters$narms = narms
mult_test_index = 0
if (narms >= 3) {
mult_test_list = c("Bonferroni", "Holm", "Hochberg")
if (is.null(parameters$mult_test)) stop("Multiple testing procedure (mult_test): Value must be specified.", call. = FALSE)
if (!tolower(parameters$mult_test) %in% tolower(mult_test_list)) stop("Multiple testing procedure (mult_test): Value must be Bonferroni, Holm or Hochberg.", call. = FALSE)
for (i in 1:length(mult_test_list)) {
if (tolower(mult_test_list[i]) == tolower(parameters$mult_test)) mult_test_index = i
}
}
parameters$mult_test_index = mult_test_index
parameters$treatment_cluster_size_vector = rep(0, 2)
parameters$treatment_cluster_size_matrix = matrix(0, 2, 2)
parameters$treatment_cluster_cum_vector = rep(0, 2)
parameters$treatment_cluster_cum_matrix = matrix(0, 2, 2)
# Fixed cluster sizes
if (cluster_index == 1) {
# Vectors of cluster sizes in trial arms
if (is.null(parameters$control_cluster_size)) stop("Vector of cluster sizes in the control arm (control_cluster_size): Value must be specified.", call. = FALSE)
control_cluster_size = ContinuousErrorCheck(parameters$control_cluster_size,
NA,
lower_values = 5,
lower_values_sign = ">=",
upper_values = 100,
upper_values_sign = "<=",
"Vector of cluster sizes in the control arm (control_cluster_size)",
NA,
"int",
NA)
if (sum(parameters$control_cluster_size) != parameters$sample_size[1]) stop(
"Cluster sizes in the control arm (control_cluster_size) are incorrectly specified.", call. = FALSE)
if (is.null(parameters$treatment_cluster_size)) stop("Vector of cluster sizes in the treatment arm (treatment_cluster_size): Value must be specified.", call. = FALSE)
if (narms == 2) {
treatment_cluster_size = ContinuousErrorCheck(parameters$treatment_cluster_size,
NA,
lower_values = 5,
lower_values_sign = ">=",
upper_values = 100,
upper_values_sign = "<=",
"Vector of cluster sizes in the treatment arm (treatment_cluster_size)",
NA,
"int",
NA)
if (sum(parameters$treatment_cluster_size) != parameters$sample_size[2]) stop(
"Cluster sizes in the treatment arm (treatment_cluster_size) are incorrectly specified.", call. = FALSE)
parameters$treatment_cluster_size_vector = parameters$treatment_cluster_size
} else {
if (!is(parameters$treatment_cluster_size, "matrix")) stop(
"A matrix of cluster sizes in the treatment arms (treatment_cluster_size) must be specified.", call. = FALSE)
if (nrow(parameters$treatment_cluster_size) != narms - 1) stop(
"A matrix of cluster sizes in the treatment arms (treatment_cluster_size) must be specified.", call. = FALSE)
treatment_cluster_size = ContinuousErrorCheck(parameters$treatment_cluster_size,
NA,
lower_values = 5,
lower_values_sign = ">=",
upper_values = 100,
upper_values_sign = "<=",
"Matrix of cluster sizes in the treatment arms (treatment_cluster_size)",
NA,
"int",
NA)
for (i in 1:nrow(parameters$treatment_cluster_size)) if (sum(parameters$treatment_cluster_size[i, ]) != parameters$sample_size[i + 1]) stop(
"Cluster sizes in the treatment arms (treatment_cluster_size) are incorrectly specified.", call. = FALSE)
parameters$treatment_cluster_size_matrix = parameters$treatment_cluster_size
}
parameters$control_cluster_cum = 0
}
# Random cluster sizes
if (cluster_index == 2) {
if (is.null(parameters$control_cluster_proportion)) stop("Vector of relative cluster sizes in the control arm (control_cluster_proportion): Value must be specified.", call. = FALSE)
control_cluster_proportion = ContinuousErrorCheck(parameters$control_cluster_proportion,
NA,
lower_values = 0,
lower_values_sign = ">",
upper_values = 1,
upper_values_sign = "<",
"Vector of relative cluster sizes in the control arm (control_cluster_proportion)",
NA,
"double",
NA)
if (abs(sum(parameters$control_cluster_proportion)-1) > 0.0001) stop(
"Relative cluster sizes in the control arm (control_cluster_proportion) are incorrectly specified.", call. = FALSE)
if (narms == 2) {
treatment_cluster_proportion = ContinuousErrorCheck(parameters$treatment_cluster_proportion,
NA,
lower_values = 0,
lower_values_sign = ">",
upper_values = 1,
upper_values_sign = "<",
"Vector of relative cluster sizes in the treatment arm (treatment_cluster_proportion)",
NA,
"double",
NA)
if (abs(sum(parameters$treatment_cluster_proportion)-1) > 0.0001) stop(
"Relative cluster sizes in the control arm (treatment_cluster_proportion) are incorrectly specified.", call. = FALSE)
parameters$treatment_cluster_proportion_vector = parameters$treatment_cluster_proportion
} else {
if (!is(parameters$treatment_cluster_proportion, "matrix")) stop(
"A matrix of relative cluster sizes in the treatment arms (treatment_cluster_proportion) must be specified.", call. = FALSE)
if (nrow(parameters$treatment_cluster_proportion) != narms - 1) stop(
"A matrix of relative cluster sizes in the treatment arms (treatment_cluster_proportion) must be specified.", call. = FALSE)
treatment_cluster_proportion = ContinuousErrorCheck(parameters$treatment_cluster_proportion,
NA,
lower_values = 0,
lower_values_sign = ">",
upper_values = 1,
upper_values_sign = "<",
"Matrix of relative cluster sizes in the treatment arms (treatment_cluster_proportion)",
NA,
"double",
NA)
for (i in 1:(narms - 1)) {
if (abs(sum(parameters$treatment_cluster_proportion[i, ])-1) > 0.0001) stop(
"Relative cluster sizes in the treatment arms (treatment_cluster_proportion) are incorrectly specified.", call. = FALSE)
}
parameters$treatment_cluster_proportion_matrix = parameters$treatment_cluster_proportion
}
# Create vectors of cimulative proportions
parameters$control_cluster_cum = cumsum(parameters$control_cluster_proportion)
if (narms == 2) {
parameters$treatment_cluster_cum_vector = cumsum(parameters$treatment_cluster_proportion)
} else {
parameters$treatment_cluster_cum_matrix = matrix(0, narms - 1, ncol(parameters$treatment_cluster_proportion))
for (i in 1:(narms - 1)) {
parameters$treatment_cluster_cum_matrix[i, ] = cumsum(parameters$treatment_cluster_proportion[i, ])
}
}
parameters$control_cluster_size = 0
}
if (!is.null(parameters$nsims)) {
nsims = ContinuousErrorCheck(parameters$nsims,
1,
lower_values = c(1),
lower_values_sign = c(">="),
upper_values = c(10000),
upper_values_sign = c("<="),
"Number of simulations (nsims)",
c("Value"),
"int",
NA)
} else {
parameters$nsims = 1000 # nocov
}
if (!is.null(parameters$ncores)) {
# nocov start
# Maximum number of cores
max_ncores = parallel::detectCores()
ncores = ContinuousErrorCheck(parameters$ncores,
1,
lower_values = c(1),
lower_values_sign = c(">="),
upper_values = c(max_ncores),
upper_values_sign = c("<="),
"Number of cores for parallel calculations (ncores)",
c("Value"),
"int",
NA)
if (!is.doRGN && ncores > 1) {
warning("Please install the doRNG package to use multi-core simulation. Only one core will be used.")
ncores = 1
}
parameters$ncores = ncores
# nocov end
} else {
parameters$ncores = 1
}
# Number of simulations per core
parameters$nsims_per_core = ceiling(parameters$nsims / parameters$ncores)
# Compute descriptive statistics (arm-specific effects, cluster sizes) for each simulation run
if (!is.null(parameters$descriptive_statistics)) {
if (!is.logical(parameters$descriptive_statistics)) stop(
"Descriptive statistics flag (descriptive_statistics): Value must be TRUE or FALSE.", call. = FALSE)
} else {
parameters$descriptive_statistics = FALSE # nocov
}
if (!is.null(parameters$alpha)) {
alpha =
ContinuousErrorCheck(parameters$alpha,
1,
lower_values = c(0.001),
lower_values_sign = c(">"),
upper_values = c(0.5),
upper_values_sign = c("<"),
"One-sided Type I error rate (alpha)",
c("Value"),
"double",
NA)
} else {
parameters$alpha = 0.025
}
# Treatment effect assumptions
if (is.null(parameters$control_icc)) stop("Intracluster correlation coefficient in the control arm (control_icc): Value must be specified.", call. = FALSE)
control_icc =
ContinuousErrorCheck(parameters$control_icc,
1,
lower_values = 0,
lower_values_sign = ">",
upper_values = 1,
upper_values_sign = "<",
"Intracluster correlation coefficient in the control arm (control_icc)",
c("Value"),
"double",
NA)
if (is.null(parameters$treatment_icc)) stop("Intracluster correlation coefficient in the treatment arms (treatment_icc): Value must be specified.", call. = FALSE)
treatment_icc =
ContinuousErrorCheck(parameters$treatment_icc,
narms - 1,
lower_values = 0,
lower_values_sign = ">",
upper_values = 1,
upper_values_sign = "<",
"Intracluster correlation coefficient in the treatment arm (treatment_icc)",
c("Value"),
"double",
NA)
# Normal endpoint
if (endpoint_index == 1) {
if (is.null(parameters$control_between_cluster_sd)) stop("Between-cluster standard deviation in the control arm (control_sd): Value must be specified.", call. = FALSE)
control_between_cluster_sd =
ContinuousErrorCheck(parameters$control_between_cluster_sd,
1,
lower_values = c(0),
lower_values_sign = c(">"),
upper_values = c(NA),
upper_values_sign = c(NA),
"Between-cluster standard deviation in the control arm (control_between_cluster_sd)",
c("Value"),
"double",
NA)
if (is.null(parameters$treatment_between_cluster_sd)) stop("Between-cluster standard deviation in the treatment arms (treatment_sd): Value must be specified.", call. = FALSE)
treatment_between_cluster_sd =
ContinuousErrorCheck(parameters$treatment_between_cluster_sd,
narms - 1,
lower_values = c(0),
lower_values_sign = c(">"),
upper_values = c(NA),
upper_values_sign = c(NA),
"Between-cluster standard deviation in the treatment arm (treatment_between_cluster_sd)",
c("Value"),
"double",
NA)
# Within-cluster standard deviation in the control arm
parameters$control_within_cluster_sd = control_between_cluster_sd * (1 - control_icc) / control_icc
# Within-cluster standard deviation in the treatment arm
parameters$treatment_within_cluster_sd = treatment_between_cluster_sd * (1 - treatment_icc) / treatment_icc
if (is.null(parameters$control_mean)) stop("Mean effect in the control arm (control_mean): Value must be specified.", call. = FALSE)
control_mean =
ContinuousErrorCheck(parameters$control_mean,
1,
lower_values = c(NA),
lower_values_sign = c(NA),
upper_values = c(NA),
upper_values_sign = c(NA),
"Mean effect in the control arm (control_mean)",
c("Value"),
"double",
NA)
if (is.null(parameters$treatment_mean)) stop("Mean effect in the treatment arms (treatment_mean): Value must be specified.", call. = FALSE)
treatment_mean =
ContinuousErrorCheck(parameters$treatment_mean,
narms - 1,
lower_values = c(NA),
lower_values_sign = c(NA),
upper_values = c(NA),
upper_values_sign = c(NA),
"Mean effect in the treatment arm (treatment_mean)",
c("Value"),
"double",
NA)
parameters$control_alpha = 0
parameters$control_beta = 0
parameters$treatment_alpha = 0
parameters$treatment_beta = 0
parameters$control_rate = 0
parameters$treatment_rate = 0
}
# Binary endpoint
if (endpoint_index == 2) {
if (is.null(parameters$control_rate)) stop("Response rate in the control arm (control_rate): Value must be specified.", call. = FALSE)
control_rate =
ContinuousErrorCheck(parameters$control_rate,
1,
lower_values = 0,
lower_values_sign = ">",
upper_values = 1,
upper_values_sign = "<",
"Response rate in the control arm (control_rate)",
c("Value"),
"double",
NA)
if (is.null(parameters$treatment_rate)) stop("Response rate in the treatment arms (treatment_rate): Value must be specified.", call. = FALSE)
treatment_rate =
ContinuousErrorCheck(parameters$treatment_rate,
narms - 1,
lower_values = 0,
lower_values_sign = ">",
upper_values = 1,
upper_values_sign = "<",
"Response rate in the treatment arm (treatment_rate)",
c("Value"),
"double",
NA)
# Alpha and beta parameters of the beta distribution in the control arm
parameters$control_alpha = (1 / control_icc - 1) * control_rate
parameters$control_beta = (1 / control_icc - 1) * (1 - control_rate)
# Alpha and beta parameters of the beta distribution in the treatment arm
parameters$treatment_alpha = (1 / treatment_icc - 1) * treatment_rate
parameters$treatment_beta = (1 / treatment_icc - 1) * (1 - treatment_rate)
parameters$control_mean = 0
parameters$treatment_mean = 0
parameters$control_between_cluster_sd = 0
parameters$treatment_between_cluster_sd = 0
parameters$control_within_cluster_sd = 0
parameters$treatment_within_cluster_sd = 0
}
#############################################
parameters$means = 0
parameters$within_cluster_sds = 0
parameters$between_cluster_sds = 0
parameters$rates = 0
# All means and SDs
if (endpoint_index == 1) {
parameters$means = c(parameters$control_mean, parameters$treatment_mean)
parameters$within_cluster_sds = c(parameters$control_within_cluster_sd, parameters$treatment_within_cluster_sd)
parameters$between_cluster_sds = c(parameters$control_between_cluster_sd, parameters$treatment_between_cluster_sd)
}
# All rates
if (endpoint_index == 2) {
parameters$rates = c(parameters$control_rate, parameters$treatment_rate)
}
# Maximum number of iterations when fitting models
parameters$max_iterations = 100
# Minimum increment for stopping the model fitting process
parameters$min_increment = 0.001
# Parameters of multiple testing procedures
parameters$weight = rep(1 / (narms - 1), narms - 1)
parameters$transition = 0
#########################################################
# Run simulations on multple cores to compute operating characteristics
if (parameters$ncores > 1) {
# nocov start
cl = parallel::makeCluster(parameters$ncores)
# Export all functions in the global environment to each node
parallel::clusterExport(cl, ls(envir = .GlobalEnv))
doParallel::registerDoParallel(cl)
simulation_list = foreach(counter=(1:parameters$ncores), .packages = c("ClustRand")) %dorng% {
ClustRandSingleCore(parameters)
}
stopCluster(cl)
# Combine the simulation results across the cores
pval_results = NULL
coef_results = NULL
cluster_size_results = NULL
for (i in 1:parameters$ncores) {
pval_results = rbind(pval_results, simulation_list[[i]]$pval_results)
coef_results = rbind(coef_results, simulation_list[[i]]$coef_results)
cluster_size_results = c(cluster_size_results, simulation_list[[i]]$cluster_size_results)
}
# nocov end
} else {
simulations = ClustRandSingleCore(parameters)
pval_results = simulations$pval_results
coef_results = simulations$coef_results
cluster_size_results = simulations$cluster_size_results
}
pval_results = as.data.frame(pval_results)
if (parameters$descriptive_statistics) {
coef_results = as.data.frame(coef_results)
cluster_size_results = as.numeric(cluster_size_results)
}
sim_summary = list()
# GEE
if (parameters$method_index == 1) {
# Extract p-values for each treatment-control comparison
if (narms == 2) {
pval_convergence = pval_results[, 1]
sandwich = pval_results[, 2]
kc = pval_results[, 3]
md = pval_results[, 4]
# Compute overall power
sim_summary$power_sandwich = mean(sandwich[pval_convergence == 1] <= parameters$alpha)
sim_summary$power_kc = mean(kc[pval_convergence == 1] <= parameters$alpha)
sim_summary$power_md = mean(md[pval_convergence == 1] <= parameters$alpha)
if (parameters$descriptive_statistics) {
# Summary of random cluster size estimates
if (parameters$cluster_scheme == "Random") {
cluster_size = cluster_size_results
cluster_size_summary = rep(0, 5)
cluster_size_summary[1] = mean(cluster_size, na.rm = TRUE)
cluster_size_summary[2:5] = quantile(cluster_size, probs = c(0.025, 0.25, 0.75, 0.975), na.rm = TRUE)
sim_summary$cluster_size_summary = cluster_size_summary
}
coef_convergence = coef_results[, 1]
intercept = coef_results[, 2]
slope = coef_results[, 3]
if (parameters$direction_index == 2) {
intercept = -intercept
slope = -slope
}
# Compute effect estimates
nsims = nrow(coef_results)
effect = matrix(NA, nsims, narms)
for (i in 1:nsims) {
if (coef_convergence[i] == 1) {
if (endpoint_index == 1) {
effect[i, 1] = intercept[i]
effect[i, 2] = intercept[i] + slope[i]
}
if (endpoint_index == 2) { # nocov start
effect[i, 1] = AntiLogit(intercept[i])
effect[i, 2] = AntiLogit(intercept[i] + slope[i])
} # nocov end
}
}
# Compute the mean and 95% CI
eff_summary = matrix(0, 2, 5)
for (i in 1:2) {
eff_summary[i, 1] = mean(effect[, i], na.rm = TRUE)
eff_summary[i, 2:5] = quantile(effect[, i], probs = c(0.025, 0.25, 0.75, 0.975), na.rm = TRUE)
}
sim_summary$eff_summary = eff_summary
}
} else {
pval_convergence = pval_results[, seq(from = 1, to = 1 + (narms - 2) * 4, by = 4)]
sandwich = pval_results[, seq(from = 2, to = 2 + (narms - 2) * 4, by = 4)]
kc = pval_results[, seq(from = 3, to = 3 + (narms - 2) * 4, by = 4)]
md = pval_results[, seq(from = 4, to = 4 + (narms - 2) * 4, by = 4)]
# Compute treatment-specific and overall power
sim_summary$power_sandwich = ComputePower(sandwich, pval_convergence, parameters$alpha)
sim_summary$power_kc = ComputePower(kc, pval_convergence, parameters$alpha)
sim_summary$power_md = ComputePower(md, pval_convergence, parameters$alpha)
if (parameters$descriptive_statistics) {
# Summary of random cluster size estimates
if (parameters$cluster_scheme == "Random") {
cluster_size = cluster_size_results
cluster_size_summary = rep(0, 5)
cluster_size_summary[1] = mean(cluster_size, na.rm = TRUE)
cluster_size_summary[2:5] = quantile(cluster_size, probs = c(0.025, 0.25, 0.75, 0.975), na.rm = TRUE)
sim_summary$cluster_size_summary = cluster_size_summary
}
coef_convergence = coef_results[, seq(from = 1, to = 1 + (narms - 2) * 3, by = 3)]
intercept = coef_results[, seq(from = 2, to = 2 + (narms - 2) * 3, by = 3)]
slope = coef_results[, seq(from = 3, to = 3 + (narms - 2) * 3, by = 3)]
if (parameters$direction_index == 2) {
intercept = -intercept
slope = -slope
}
# Compute effect estimates
nsims = nrow(coef_results)
effect = matrix(NA, nsims, narms)
for (i in 1:nsims) {
if (coef_convergence[i, 1] == 1) {
if (endpoint_index == 1) effect[i, 1] = intercept[i, 1]
if (endpoint_index == 2) effect[i, 1] = AntiLogit(intercept[i, 1])
}
for (j in 2:narms) {
if (coef_convergence[i, j - 1] == 1) {
if (endpoint_index == 1) effect[i, j] = intercept[i, j - 1] + slope[i, j - 1]
if (endpoint_index == 2) effect[i, j] = AntiLogit(intercept[i, j - 1] + slope[i, j - 1])
}
}
}
# Compute the mean and 95% CI
eff_summary = matrix(0, narms, 5)
for (i in 1:narms) {
eff_summary[i, 1] = mean(effect[, i], na.rm = TRUE)
eff_summary[i, 2:5] = quantile(effect[, i], probs = c(0.025, 0.25, 0.75, 0.975), na.rm = TRUE)
}
sim_summary$eff_summary = eff_summary
}
}
}
# GLMEM
if (parameters$method_index == 2) {
# Extract p-values for each treatment-control comparison
if (narms == 2) {
pval_convergence = pval_results[, 1]
pval = pval_results[, 2]
# Compute overall power
sim_summary$power = mean(pval[pval_convergence == 1] <= parameters$alpha)
if (parameters$descriptive_statistics) {
# Summary of random cluster size estimates
if (parameters$cluster_scheme == "Random") {
cluster_size = cluster_size_results
cluster_size_summary = rep(0, 5)
cluster_size_summary[1] = mean(cluster_size, na.rm = TRUE)
cluster_size_summary[2:5] = quantile(cluster_size, probs = c(0.025, 0.25, 0.75, 0.975), na.rm = TRUE)
sim_summary$cluster_size_summary = cluster_size_summary
}
# Summary of effect estimates
coef_convergence = coef_results[, 1]
intercept = coef_results[, 2]
slope = coef_results[, 3]
if (parameters$direction_index == 2) {
intercept = -intercept
slope = -slope
}
nsims = nrow(coef_results)
effect = matrix(NA, nsims, narms)
for (i in 1:nsims) {
if (coef_convergence[i] == 1) {
if (endpoint_index == 1) { # nocov start
effect[i, 1] = intercept[i]
effect[i, 2] = intercept[i] + slope[i]
} # nocov end
if (endpoint_index == 2) {
effect[i, 1] = AntiLogit(intercept[i])
effect[i, 2] = AntiLogit(intercept[i] + slope[i])
}
}
}
eff_summary = matrix(0, narms, 5)
for (i in 1:narms) {
eff_summary[i, 1] = mean(effect[, i], na.rm = TRUE)
eff_summary[i, 2:5] = quantile(effect[, i], probs = c(0.025, 0.25, 0.75, 0.975), na.rm = TRUE)
}
sim_summary$eff_summary = eff_summary
}
} else {
pval_convergence = pval_results[, seq(from = 1, to = 1 + (narms - 2) * 2, by = 2)]
pval = pval_results[, seq(from = 2, to = 2 + (narms - 2) * 2, by = 2)]
# Compute treatment-specific and overall power
sim_summary$power = ComputePower(pval, pval_convergence, parameters$alpha)
if (parameters$descriptive_statistics) {
# Summary of random cluster size estimates
if (parameters$cluster_scheme == "Random") {
cluster_size = cluster_size_results
cluster_size_summary = rep(0, 5)
cluster_size_summary[1] = mean(cluster_size, na.rm = TRUE)
cluster_size_summary[2:5] = quantile(cluster_size, probs = c(0.025, 0.25, 0.75, 0.975), na.rm = TRUE)
sim_summary$cluster_size_summary = cluster_size_summary
}
# Summary of effect estimates
coef_convergence = coef_results[, seq(from = 1, to = 1 + (narms - 2) * 3, by = 3)]
intercept = coef_results[, seq(from = 2, to = 2 + (narms - 2) * 3, by = 3)]
slope = coef_results[, seq(from = 3, to = 3 + (narms - 2) * 3, by = 3)]
if (parameters$direction_index == 2) { # nocov start
intercept = -intercept
slope = -slope
} # nocov end
nsims = nrow(coef_results)
effect = matrix(NA, nsims, narms)
for (i in 1:nsims) {
if (coef_convergence[i, 1] == 1) {
if (endpoint_index == 1) effect[i, 1] = intercept[i, 1]
if (endpoint_index == 2) effect[i, 1] = AntiLogit(intercept[i, 1]) # nocov
}
for (j in 2:narms) {
if (coef_convergence[i, j - 1] == 1) {
if (endpoint_index == 1) effect[i, j] = intercept[i, j - 1] + slope[i, j - 1]
if (endpoint_index == 2) effect[i, j] = AntiLogit(intercept[i, j - 1] + slope[i, j - 1]) # nocov
}
}
}
eff_summary = matrix(0, narms, 5)
for (i in 1:narms) {
eff_summary[i, 1] = mean(effect[, i], na.rm = TRUE)
eff_summary[i, 2:5] = quantile(effect[, i], probs = c(0.025, 0.25, 0.75, 0.975), na.rm = TRUE)
}
sim_summary$eff_summary = eff_summary
}
}
}
results = list(parameters = parameters,
sim_summary = sim_summary,
pval_results = pval_results,
coef_results = coef_results,
cluster_size_results = cluster_size_results)
class(results) = "ClustRandResults"
return(results)
}
ClustRandReportDoc = function(results) {
#############################################################################
# Error checks
if (!is(results, "ClustRandResults")) stop("The object was not created by the ClustRand function", call. = FALSE)
#############################################################################
# Empty list of tables to be included in the report
item_list = list()
item_index = 1
table_index = 1
figure_index = 1
width = 6.5
height = 5
parameters = results$parameters
sim_summary = results$sim_summary
endpoint_index = parameters$endpoint_index
narms = parameters$narms
# Trial arms
trial_arms = "Control"
if (narms >= 3) {
for (i in 2:narms) trial_arms = c(trial_arms, paste0("Treatment ", i - 1))
} else {
trial_arms = c(trial_arms, "Treatment")
}
# All means and SDs
if (endpoint_index == 1) {
means = c(parameters$control_mean, parameters$treatment_mean)
}
# All rates
if (endpoint_index == 2) {
rates = c(parameters$control_rate, parameters$treatment_rate)
}
# Other parameters
between_cluster_sds = c(parameters$control_between_cluster_sd, parameters$treatment_between_cluster_sd)
iccs = c(parameters$control_icc, parameters$treatment_icc)
#############################################################################
report_title = "Cluster-randomized design"
item_list[[item_index]] = list(type = "paragraph", label = "Description", value = "The simulation report presents key operating characteristics of a cluster-randomized design for a Phase III clinical trial.")
item_index = item_index + 1
#############################################################################
column_names = c("Trial arm", "Sample size")
col1 = trial_arms
col2 = parameters$sample_size
data_frame = data.frame(col1, col2)
title = paste0("Table ", table_index, ". Number of completers")
footnote = "Completers are defined as patients who complete the trial and are included in the final analysis."
column_width = c(5, 1.5)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE, footnote)
item_index = item_index + 1
table_index = table_index + 1
#############################################################################
column_names = c("Parameter", "Value")
if (parameters$direction_index == 1) label = "A higher value of the endpoint indicates a more favorable outcome"
if (parameters$direction_index == 2) label = "A lower value of the endpoint indicates a more favorable outcome"
col1 = c("Endpoint type", "Direction of favorable outcome")
col2 = c(endpoint_list[endpoint_index], label)
data_frame = data.frame(col1, col2)
title = paste0("Table ", table_index, ". Primary efficacy endpoint")
column_width = c(3, 3.5)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
item_index = item_index + 1
table_index = table_index + 1
#############################################################################
if (parameters$cluster_index == 1) {
column_names = c("Trial arm", "Number of clusters", "Cluster sizes")
col1 = trial_arms
if (narms == 2) {
col2 = c(length(parameters$control_cluster_size), length(parameters$treatment_cluster_size))
col3 = c(paste0(parameters$control_cluster_size, collapse = ", "), paste0(parameters$treatment_cluster_size, collapse = ", "))
} else {
col2 = c(length(parameters$control_cluster_size), rep(ncol(parameters$treatment_cluster_size), narms - 1))
col3 = c(paste0(parameters$control_cluster_size, collapse = ", "))
for (i in 1:(narms - 1)) col3 = c(col3, paste0(parameters$treatment_cluster_size[i, ], collapse = ", "))
}
data_frame = data.frame(col1, col2, col3)
title = paste0("Table ", table_index, ". Cluster scheme parameters")
footnote = "A design with pre-defined cluster sizes is assumed."
column_width = c(1.5, 1.5, 3.5)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE, footnote)
item_index = item_index + 1
table_index = table_index + 1
}
if (parameters$cluster_index == 2) {
column_names = c("Trial arm", "Number of clusters", "Relative cluster sizes")
col1 = trial_arms
if (narms == 2) {
col2 = c(length(parameters$control_cluster_proportion), length(parameters$treatment_cluster_proportion))
col3 = c(paste0(parameters$control_cluster_proportion, collapse = ", "), paste0(parameters$treatment_cluster_proportion, collapse = ", "))
} else {
col2 = c(length(parameters$control_cluster_proportion), rep(ncol(parameters$treatment_cluster_proportion), narms - 1))
col3 = c(paste0(parameters$control_cluster_proportion, collapse = ", "))
for (i in 1:(narms - 1)) col3 = c(col3, paste0(parameters$treatment_cluster_proportion[i, ], collapse = ", "))
}
data_frame = data.frame(col1, col2, col3)
title = paste0("Table ", table_index, ". Cluster scheme parameters")
footnote = paste0("A design with random cluster sizes is assumed. The cluster sizes are generated using a generalized Bernoulli distribution based on the relative cluster sizes.")
column_width = c(1.5, 1.5, 3.5)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE, footnote)
item_index = item_index + 1
table_index = table_index + 1
}
#############################################################################
column_names = c("Trial arm", "Parameter", "Value")
col1 = NULL
col2 = NULL
col3 = NULL
for (i in 1:narms) {
if (endpoint_index == 1) {
col1 = c(col1, trial_arms[i])
col2 = c(col2, "Mean")
col3 = c(col3, means[i])
}
if (endpoint_index == 2) {
col1 = c(col1, trial_arms[i])
col2 = c(col2, "Rate (%)")
col3 = c(col3, 100 * rates[i])
}
}
data_frame = data.frame(col1, col2, col3)
title = paste0("Table ", table_index, ". Treatment effect assumptions")
column_width = c(1.5, 3.5, 1.5)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
item_index = item_index + 1
table_index = table_index + 1
#############################################################################
column_names = c("Trial arm", "Parameter", "Value")
col1 = NULL
col2 = NULL
col3 = NULL
for (i in 1:narms) {
if (parameters$endpoint_index == 1) {
col1 = c(col1, trial_arms[i], "")
col2 = c(col2, "Between-cluster standard deviation", "Intra-cluster correlation coefficient")
col3 = c(col3, between_cluster_sds[i], iccs[i])
}
if (parameters$endpoint_index == 2) {
col1 = c(col1, trial_arms[i])
col2 = c(col2, "Intra-cluster correlation coefficient")
col3 = c(col3, iccs[i])
}
}
data_frame = data.frame(col1, col2, col3)
title = paste0("Table ", table_index, ". Variability parameters")
column_width = c(1.5, 3.5, 1.5)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
item_index = item_index + 1
table_index = table_index + 1
#############################################################################
column_names = c("Parameter", "Value")
if (parameters$method_index == 1) method_type = "Generalized estimating equations (GEE)"
if (parameters$method_index == 2) method_type = "Generalized linear mixed effects model (GLMEM)"
col1 = c("Data analysis method")
col2 = c(method_type)
if (parameters$mult_test_index >= 1) {
col1 = c(col1, "Multiple testing procedure")
col2 = c(col2, parameters$mult_test)
}
col1 = c(col1, "One-sided Type I error rate", "Number of simulations")
col2 = c(col2, sprintf("%0.3f", sum(parameters$alpha)), sprintf("%d", parameters$nsims))
data_frame = data.frame(col1, col2)
title = paste0("Table ", table_index, ". Analysis and simulation parameters")
column_width = c(2.5, 4)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, TRUE)
item_index = item_index + 1
table_index = table_index + 1
#############################################################################
if (parameters$descriptive_statistics) {
column_names = c("Parameter", "Trial arm", "Statistic", "Value")
eff_summary = sim_summary$eff_summary
cluster_size_summary = sim_summary$cluster_size_summary
if (endpoint_index == 1) {
col1 = c("Mean", rep("", 3 * narms - 1))
col2 = NULL
col3 = NULL
col4 = NULL
for (i in 1:narms) {
col2 = c(col2, trial_arms[i], rep("", 2))
col3 = c(col3, "Mean", "25%P, 75%P", "2.5%P, 97.5%P")
col4 = c(col4, round(eff_summary[i, 1], 2), paste0(round(eff_summary[i, 3], 2), ", ", round(eff_summary[i, 4], 2)), paste0(round(eff_summary[i, 2], 2), ", ", round(eff_summary[i, 5], 2)))
}
}
if (endpoint_index == 2) {
col1 = c("Rate (%)", rep("", 3 * narms - 1))
col2 = NULL
col3 = NULL
col4 = NULL
for (i in 1:narms) {
col2 = c(col2, trial_arms[i], rep("", 2))
col3 = c(col3, "Mean", "25%P, 75%P", "2.5%P, 97.5%P")
col4 = c(col4, round(100 * eff_summary[i, 1], 1), paste0(round(100 * eff_summary[i, 3], 1), ", ", round(100 * eff_summary[i, 4], 1)), paste0(round(100 * eff_summary[i, 2], 1), ", ", round(100 * eff_summary[i, 5], 1)))
}
}
if (parameters$cluster_scheme == "Random") {
col1 = c(col1, "Cluster size", rep("", 2))
col2 = c(col2, "All trial arms", rep("", 2))
col3 = c(col3, "Mean", "25%P, 75%P", "2.5%P, 97.5%P")
col4 = c(col4, round(cluster_size_summary[1], 1), paste0(round(cluster_size_summary[3], 1), ", ", round(cluster_size_summary[4], 1)), paste0(round(cluster_size_summary[2], 1), ", ", round(cluster_size_summary[5], 1)))
}
data_frame = data.frame(col1, col2, col3, col4)
title = paste0("Table ", table_index, ". Simulation results: Descriptive statistics")
column_width = c(2, 1.5, 2, 1)
footnote = "Descriptive statistics computed from each simulation run: 2.5%P (2.5th percentile), 25%P (25th percentile), 75%P (75th percentile) and 97.5%P (97.5th percentile)."
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE, footnote)
item_index = item_index + 1
table_index = table_index + 1
}
#############################################################################
# GEE
if (parameters$method_index == 1) {
if (parameters$narms == 2) {
column_names = c("Analysis method", "Power (%)")
col1 = c("Standard analysis",
"Bias-corrected analysis (Kauermann-Carroll correction)",
"Bias-corrected analysis (Mancl-DeRouen correction)")
col2 = c(round(100 * sim_summary$power_sandwich, 1),
round(100 * sim_summary$power_kc, 1),
round(100 * sim_summary$power_md, 1))
data_frame = data.frame(col1, col2)
title = paste0("Table ", table_index, ". Simulation results: Power calculations")
column_width = c(5.5, 1)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
item_index = item_index + 1
table_index = table_index + 1
} else {
column_names = c("Comparison", "Analysis method", "Power (%)")
col1 = NULL
col2 = NULL
col3 = NULL
for (i in 1:narms) {
if (i < narms) comp = paste0(trial_arms[i + 1], " vs control") else comp = "Overall effect"
col1 = c(col1, comp, "", "")
col2 = c(col2, "Standard analysis",
"Bias-corrected analysis (Kauermann-Carroll correction)",
"Bias-corrected analysis (Mancl-DeRouen correction)")
col3 = c(col3, round(100 * sim_summary$power_sandwich[i], 1),
round(100 * sim_summary$power_kc[i], 1),
round(100 * sim_summary$power_md[i], 1))
}
data_frame = data.frame(col1, col2, col3)
title = paste0("Table ", table_index, ". Simulation results: Power calculations")
column_width = c(1.5, 4, 1)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
item_index = item_index + 1
table_index = table_index + 1
}
}
# GLMEM
if (parameters$method_index == 2) {
if (parameters$narms == 2) {
column_names = c("Comparison", "Power (%)")
col1 = "Treatment vs control"
col2 = round(100 * sim_summary$power, 1)
data_frame = data.frame(col1, col2)
title = paste0("Table ", table_index, ". Simulation results: Power calculations")
column_width = c(5.5, 1)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
item_index = item_index + 1
table_index = table_index + 1
} else {
column_names = c("Comparison", "Power (%)")
col1 = NULL
col2 = NULL
for (i in 1:narms) {
if (i < narms) comp = paste0(trial_arms[i + 1], " vs control") else comp = "Overall effect"
col1 = c(col1, comp)
col2 = c(col2, round(100 * sim_summary$power[i], 1))
}
data_frame = data.frame(col1, col2)
title = paste0("Table ", table_index, ". Simulation results: Power calculations")
column_width = c(5.5, 1)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
item_index = item_index + 1
table_index = table_index + 1
}
}
#############################################################################
report = item_list
doc = SaveReport(report, report_title)
return(doc)
}
# End of ClustRandReportDoc
ClustRandSingleCore = function(parameters) {
params_for_run = parameters
params_for_run$nsims = params_for_run$nsims_per_core
# GEE
if (params_for_run$method_index == 1) simulations = ClustRandGEEC(params_for_run)
# GLMEM
if (params_for_run$method_index == 2) simulations = ClustRandGLMEMR(params_for_run)
return(simulations)
}
ClustRandGLMEMR = function(parameters) {
nsims = parameters$nsims
narms = parameters$narms
control_cluster_size = parameters$control_cluster_size
if (narms == 2) treatment_size = length(parameters$treatment_cluster_size) else treatment_size = ncol(parameters$treatment_cluster_size)
pval_results = NULL
coef_results = NULL
cluster_size_results = NULL
for (sim in 1:nsims) {
# Random cluster sizes
if (parameters$cluster_index == 2) {
# Generate a vector of random cluster sizes
control_cluster_size = ExportRandomClusterSize(parameters$sample_size[1], parameters$control_cluster_cum)
}
control_size = length(control_cluster_size)
# Generate data for the common control arm
x_control = NULL
y_control = NULL
id_control = NULL
for (i in 1:control_size) {
# Normal endpoint
if (parameters$endpoint_index == 1) {
cluster_term = rnorm(n = 1, mean = 0, sd = parameters$between_cluster_sds[1])
control_sample = rnorm(n = control_cluster_size[i], mean = parameters$means[1] + cluster_term, sd = parameters$within_cluster_sds[1])
}
# Binary endpoint
if (parameters$endpoint_index == 2) {
cluster_term = rbeta(n = 1, shape1 = parameters$control_alpha, shape2 = parameters$control_beta)
control_sample = rbinom(n = control_cluster_size[i], size = 1, prob = cluster_term)
}
x_control = c(x_control, rep(0, control_cluster_size[i]))
y_control = c(y_control, control_sample)
id_control = c(id_control, rep(i, control_cluster_size[i]))
}
p = rep(NA, narms - 1)
convergence = rep(1, narms - 1)
intercept = rep(NA, narms - 1)
slope = rep(NA, narms - 1)
cluster_size = control_cluster_size
# Generate data for each treatment arm
for (k in 1:(narms - 1)) {
x = x_control
y = y_control
id = id_control
# Fixed cluster sizes
if (parameters$cluster_index == 1) {
if (narms == 2) treatment_cluster_size = parameters$treatment_cluster_size else treatment_cluster_size = parameters$treatment_cluster_size[k, ]
}
# Random cluster sizes
if (parameters$cluster_index == 2) {
if (narms == 2) proportions = parameters$treatment_cluster_cum_vector else proportions = parameters$treatment_cluster_cum_matrix[k, ] # nocov
# Generate a vector of random cluster sizes
treatment_cluster_size = ExportRandomClusterSize(parameters$sample_size[k + 1], proportions)
}
cluster_size = c(cluster_size, treatment_cluster_size)
treatment_size = length(treatment_cluster_size)
for (i in 1:treatment_size) {
# Normal endpoint
if (parameters$endpoint_index == 1) {
cluster_term = rnorm(n = 1, mean = 0, sd = parameters$between_cluster_sds[k + 1])
current_treatment_sample = rnorm(n = treatment_cluster_size[i], mean = parameters$means[k + 1] + cluster_term, sd = parameters$within_cluster_sds[k + 1])
}
# Binary endpoint
if (parameters$endpoint_index == 2) {
cluster_term = rbeta(n = 1, shape1 = parameters$treatment_alpha[k], shape2 = parameters$treatment_beta[k])
current_treatment_sample = rbinom(n = treatment_cluster_size[i], size = 1, prob = cluster_term)
}
x = c(x, rep(1, treatment_cluster_size[i]))
y = c(y, current_treatment_sample)
id = c(id, rep(control_size + i, treatment_cluster_size[i]))
}
# Direction of favorable outcome
if (parameters$direction_index == 2) {
if (parameters$endpoint_index == 1) y = -y
if (parameters$endpoint_index == 2) y = 1 - y
}
data_set = data.frame(x, y, id)
# Analyze the data for the current treatment-control comparison using generalized linear mixed-effects models
# Normal endpoint
if (parameters$endpoint_index == 1) {
result = tryCatch(
{
lmerTest::lmer(y ~ x + (1|id), data = data_set, REML = TRUE)
},
warning = function(cond) { # nocov start
w = -1
class(w) = "try-error"
return(w)
}) # nocov end
if (!inherits(result, "try-error")) {
model_fit = result
summary_fit = summary(model_fit, ddf = "Kenward-Roger")
# Estimated model parameters
if (nrow(summary_fit$coefficients) == 2) {
intercept[k] = summary_fit$coefficients[1, 1]
slope[k] = summary_fit$coefficients[2, 1]
delta = slope[k]
# One-sided p-value
if (delta > 0) p[k] = summary_fit$coefficients[2, 5] / 2 else p[k] = 1 - summary_fit$coefficients[2, 5] / 2
}
if (nrow(summary_fit$coefficients) == 1) { # nocov start
if (rownames(summary_fit$coefficients) == "(Intercept)") {
intercept[k] = summary_fit$coefficients[1, 1]
}
if (rownames(summary_fit$coefficients) == "x") {
slope[k] = summary_fit$coefficients[2, 1]
}
} # nocov end
} else {
convergence[k] = 0 # nocov
}
}
# Binary endpoint
if (parameters$endpoint_index == 2) {
result = tryCatch({
glmer(y ~ x + (1|id), data = data_set, family = binomial(link = 'logit'))
},
warning = function(cond) {
w = -1
class(w) = "try-error"
return(w)
})
if (!inherits(result, "try-error")) {
model_fit = result
summary_fit = summary(model_fit)
intercept[k] = summary_fit$coefficients[1, 1]
slope[k] = summary_fit$coefficients[2, 1]
delta = slope[k]
# One-sided p-value
if (delta > 0) p[k] = summary_fit$coefficients[2, 4] / 2 else p[k] = 1 - summary_fit$coefficients[2, 4] / 2
} else {
convergence[k] = 0
}
}
}
# Apply a multiplicity adjustment
if (parameters$mult_test_index >= 1) {
p = ExportTradMultAdj(parameters$mult_test_index, p, parameters$weight, parameters$transition)
}
# One-sided p-values
pval_vec = NULL
for (k in 1:(narms - 1)) pval_vec = c(pval_vec, convergence[k], p[k])
pval_results = rbind(pval_results, pval_vec)
# Descriptive statistics for each simulation run
if (parameters$descriptive_statistics) {
coef_vec = NULL
cluster_size_vec = NULL
for (k in 1:(narms - 1)) {
coef_vec = c(coef_vec, convergence[k], intercept[k], slope[k])
cluster_size_vec = c(cluster_size_vec, cluster_size)
}
coef_results = rbind(coef_results, coef_vec)
cluster_size_results = c(cluster_size_results, cluster_size_vec)
}
}
# End of simulations
return(list(pval_results = pval_results,
coef_results = coef_results,
cluster_size_results = cluster_size_results))
}
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Defines functions ClustRandGLMEMR ClustRandSingleCore ClustRandReportDoc ClustRand AntiLogit ComputePower
Documented in ClustRand ClustRandGLMEMR ClustRandReportDoc ClustRandSingleCore
ComputePower = function(data_frame, convergence, alpha) {
ncomps = ncol(data_frame)
nsims = nrow(data_frame)
power = rep(0, ncomps + 1)
outcomes = matrix(0, nsims, ncomps + 1)
for (i in 1:ncomps) {
outcomes[, i] = as.numeric(data_frame[, i] <= alpha)
outcomes[convergence[, i] == 0, i] = NA
power[i] = mean(outcomes[, i], na.rm = TRUE)
}
outcomes[, ncomps + 1] = as.numeric(rowSums(outcomes[, 1:ncomps]) >= 1)
power[ncomps + 1] = mean(outcomes[, ncomps + 1], na.rm = TRUE)
return(power)
}
AntiLogit = function(x) {
return(1 / (1 + exp(-x)))
}
ClustRand = function(parameters) {
# Error checks
if (typeof(parameters) != "list") stop("Function parameters must be a list of named values.", call. = FALSE)
if (is.null(parameters$random_seed)) {
random_seed = 49283
} else {
random_seed = ContinuousErrorCheck(parameters$random_seed,
1,
lower_values = 1,
lower_values_sign = c(">="),
upper_values = 100000,
upper_values_sign = c("<="),
"Seed for the random number generator (random_seed)",
c("Value"),
"int",
NA)
}
parameters$random_seed = random_seed
# Set the seed of R's random number generator.
# It also takes effect to Rcpp random generation functions.
# https://stackoverflow.com/questions/60119621/get-the-same-sample-of-integers-from-rcpp-as-base-r
suppressWarnings(RNGkind(sample.kind = "Rounding"))
set.seed(random_seed)
if (is.null(parameters$endpoint_type)) stop("Endpoint type (endpoint_type): Value must be specified.", call. = FALSE)
if (!tolower(parameters$endpoint_type) %in% tolower(c("normal", "binary"))) stop("Endpoint type (endpoint_type): Value must be Normal or Binary.", call. = FALSE)
if (tolower(parameters$endpoint_type) == "normal") endpoint_index = 1
if (tolower(parameters$endpoint_type) == "binary") endpoint_index = 2
parameters$endpoint_index = endpoint_index
if (is.null(parameters$method_type)) stop("Data analysis method (method_type): Value must be specified.", call. = FALSE)
if (!tolower(parameters$method_type) %in% tolower(c("gee", "glmem"))) stop("Data analysis method (method_type): Value must be GEE or GLMEM", call. = FALSE)
if (tolower(parameters$method_type) == "gee") method_index = 1
if (tolower(parameters$method_type) == "glmem") method_index = 2
parameters$method_index = method_index
if (is.null(parameters$direction)) {
parameters$direction_index = 1
} else {
if (!tolower(parameters$direction) %in% c("higher", "lower")) stop("Direction of favorable outcome (direction): Value must be specified.", call. = FALSE)
}
if (tolower(parameters$direction) == "higher") parameters$direction_index = 1
if (tolower(parameters$direction) == "lower") parameters$direction_index = 2
if (is.null(parameters$cluster_scheme)) stop("Cluster scheme (cluster_scheme): Value must be specified.", call. = FALSE)
if (!tolower(parameters$cluster_scheme) %in% tolower(c("fixed", "random"))) stop("Cluster scheme (cluster_scheme): Value must be Fixed or Random.", call. = FALSE)
if (tolower(parameters$cluster_scheme) == "fixed") cluster_index = 1
if (tolower(parameters$cluster_scheme) == "random") cluster_index = 2
parameters$cluster_index = cluster_index
if (is.null(parameters$sample_size)) stop("Number of completers in each trial arm (sample_size): Value must be specified.", call. = FALSE)
sample_size = ContinuousErrorCheck(parameters$sample_size,
NA,
lower_values = 0,
lower_values_sign = ">",
upper_values = 1000,
upper_values_sign = "<=",
"Number of completers in each trial arm (sample_size)",
NA,
"int",
NA)
narms = length(sample_size)
parameters$narms = narms
mult_test_index = 0
if (narms >= 3) {
mult_test_list = c("Bonferroni", "Holm", "Hochberg")
if (is.null(parameters$mult_test)) stop("Multiple testing procedure (mult_test): Value must be specified.", call. = FALSE)
if (!tolower(parameters$mult_test) %in% tolower(mult_test_list)) stop("Multiple testing procedure (mult_test): Value must be Bonferroni, Holm or Hochberg.", call. = FALSE)
for (i in 1:length(mult_test_list)) {
if (tolower(mult_test_list[i]) == tolower(parameters$mult_test)) mult_test_index = i
}
}
parameters$mult_test_index = mult_test_index
parameters$treatment_cluster_size_vector = rep(0, 2)
parameters$treatment_cluster_size_matrix = matrix(0, 2, 2)
parameters$treatment_cluster_cum_vector = rep(0, 2)
parameters$treatment_cluster_cum_matrix = matrix(0, 2, 2)
# Fixed cluster sizes
if (cluster_index == 1) {
# Vectors of cluster sizes in trial arms
if (is.null(parameters$control_cluster_size)) stop("Vector of cluster sizes in the control arm (control_cluster_size): Value must be specified.", call. = FALSE)
control_cluster_size = ContinuousErrorCheck(parameters$control_cluster_size,
NA,
lower_values = 5,
lower_values_sign = ">=",
upper_values = 100,
upper_values_sign = "<=",
"Vector of cluster sizes in the control arm (control_cluster_size)",
NA,
"int",
NA)
if (sum(parameters$control_cluster_size) != parameters$sample_size[1]) stop(
"Cluster sizes in the control arm (control_cluster_size) are incorrectly specified.", call. = FALSE)
if (is.null(parameters$treatment_cluster_size)) stop("Vector of cluster sizes in the treatment arm (treatment_cluster_size): Value must be specified.", call. = FALSE)
if (narms == 2) {
treatment_cluster_size = ContinuousErrorCheck(parameters$treatment_cluster_size,
NA,
lower_values = 5,
lower_values_sign = ">=",
upper_values = 100,
upper_values_sign = "<=",
"Vector of cluster sizes in the treatment arm (treatment_cluster_size)",
NA,
"int",
NA)
if (sum(parameters$treatment_cluster_size) != parameters$sample_size[2]) stop(
"Cluster sizes in the treatment arm (treatment_cluster_size) are incorrectly specified.", call. = FALSE)
parameters$treatment_cluster_size_vector = parameters$treatment_cluster_size
} else {
if (!is(parameters$treatment_cluster_size, "matrix")) stop(
"A matrix of cluster sizes in the treatment arms (treatment_cluster_size) must be specified.", call. = FALSE)
if (nrow(parameters$treatment_cluster_size) != narms - 1) stop(
"A matrix of cluster sizes in the treatment arms (treatment_cluster_size) must be specified.", call. = FALSE)
treatment_cluster_size = ContinuousErrorCheck(parameters$treatment_cluster_size,
NA,
lower_values = 5,
lower_values_sign = ">=",
upper_values = 100,
upper_values_sign = "<=",
"Matrix of cluster sizes in the treatment arms (treatment_cluster_size)",
NA,
"int",
NA)
for (i in 1:nrow(parameters$treatment_cluster_size)) if (sum(parameters$treatment_cluster_size[i, ]) != parameters$sample_size[i + 1]) stop(
"Cluster sizes in the treatment arms (treatment_cluster_size) are incorrectly specified.", call. = FALSE)
parameters$treatment_cluster_size_matrix = parameters$treatment_cluster_size
}
parameters$control_cluster_cum = 0
}
# Random cluster sizes
if (cluster_index == 2) {
if (is.null(parameters$control_cluster_proportion)) stop("Vector of relative cluster sizes in the control arm (control_cluster_proportion): Value must be specified.", call. = FALSE)
control_cluster_proportion = ContinuousErrorCheck(parameters$control_cluster_proportion,
NA,
lower_values = 0,
lower_values_sign = ">",
upper_values = 1,
upper_values_sign = "<",
"Vector of relative cluster sizes in the control arm (control_cluster_proportion)",
NA,
"double",
NA)
if (abs(sum(parameters$control_cluster_proportion)-1) > 0.0001) stop(
"Relative cluster sizes in the control arm (control_cluster_proportion) are incorrectly specified.", call. = FALSE)
if (narms == 2) {
treatment_cluster_proportion = ContinuousErrorCheck(parameters$treatment_cluster_proportion,
NA,
lower_values = 0,
lower_values_sign = ">",
upper_values = 1,
upper_values_sign = "<",
"Vector of relative cluster sizes in the treatment arm (treatment_cluster_proportion)",
NA,
"double",
NA)
if (abs(sum(parameters$treatment_cluster_proportion)-1) > 0.0001) stop(
"Relative cluster sizes in the control arm (treatment_cluster_proportion) are incorrectly specified.", call. = FALSE)
parameters$treatment_cluster_proportion_vector = parameters$treatment_cluster_proportion
} else {
if (!is(parameters$treatment_cluster_proportion, "matrix")) stop(
"A matrix of relative cluster sizes in the treatment arms (treatment_cluster_proportion) must be specified.", call. = FALSE)
if (nrow(parameters$treatment_cluster_proportion) != narms - 1) stop(
"A matrix of relative cluster sizes in the treatment arms (treatment_cluster_proportion) must be specified.", call. = FALSE)
treatment_cluster_proportion = ContinuousErrorCheck(parameters$treatment_cluster_proportion,
NA,
lower_values = 0,
lower_values_sign = ">",
upper_values = 1,
upper_values_sign = "<",
"Matrix of relative cluster sizes in the treatment arms (treatment_cluster_proportion)",
NA,
"double",
NA)
for (i in 1:(narms - 1)) {
if (abs(sum(parameters$treatment_cluster_proportion[i, ])-1) > 0.0001) stop(
"Relative cluster sizes in the treatment arms (treatment_cluster_proportion) are incorrectly specified.", call. = FALSE)
}
parameters$treatment_cluster_proportion_matrix = parameters$treatment_cluster_proportion
}
# Create vectors of cimulative proportions
parameters$control_cluster_cum = cumsum(parameters$control_cluster_proportion)
if (narms == 2) {
parameters$treatment_cluster_cum_vector = cumsum(parameters$treatment_cluster_proportion)
} else {
parameters$treatment_cluster_cum_matrix = matrix(0, narms - 1, ncol(parameters$treatment_cluster_proportion))
for (i in 1:(narms - 1)) {
parameters$treatment_cluster_cum_matrix[i, ] = cumsum(parameters$treatment_cluster_proportion[i, ])
}
}
parameters$control_cluster_size = 0
}
if (!is.null(parameters$nsims)) {
nsims = ContinuousErrorCheck(parameters$nsims,
1,
lower_values = c(1),
lower_values_sign = c(">="),
upper_values = c(10000),
upper_values_sign = c("<="),
"Number of simulations (nsims)",
c("Value"),
"int",
NA)
} else {
parameters$nsims = 1000 # nocov
}
if (!is.null(parameters$ncores)) {
# nocov start
# Maximum number of cores
max_ncores = parallel::detectCores()
ncores = ContinuousErrorCheck(parameters$ncores,
1,
lower_values = c(1),
lower_values_sign = c(">="),
upper_values = c(max_ncores),
upper_values_sign = c("<="),
"Number of cores for parallel calculations (ncores)",
c("Value"),
"int",
NA)
if (!is.doRGN && ncores > 1) {
warning("Please install the doRNG package to use multi-core simulation. Only one core will be used.")
ncores = 1
}
parameters$ncores = ncores
# nocov end
} else {
parameters$ncores = 1
}
# Number of simulations per core
parameters$nsims_per_core = ceiling(parameters$nsims / parameters$ncores)
# Compute descriptive statistics (arm-specific effects, cluster sizes) for each simulation run
if (!is.null(parameters$descriptive_statistics)) {
if (!is.logical(parameters$descriptive_statistics)) stop(
"Descriptive statistics flag (descriptive_statistics): Value must be TRUE or FALSE.", call. = FALSE)
} else {
parameters$descriptive_statistics = FALSE # nocov
}
if (!is.null(parameters$alpha)) {
alpha =
ContinuousErrorCheck(parameters$alpha,
1,
lower_values = c(0.001),
lower_values_sign = c(">"),
upper_values = c(0.5),
upper_values_sign = c("<"),
"One-sided Type I error rate (alpha)",
c("Value"),
"double",
NA)
} else {
parameters$alpha = 0.025
}
# Treatment effect assumptions
if (is.null(parameters$control_icc)) stop("Intracluster correlation coefficient in the control arm (control_icc): Value must be specified.", call. = FALSE)
control_icc =
ContinuousErrorCheck(parameters$control_icc,
1,
lower_values = 0,
lower_values_sign = ">",
upper_values = 1,
upper_values_sign = "<",
"Intracluster correlation coefficient in the control arm (control_icc)",
c("Value"),
"double",
NA)
if (is.null(parameters$treatment_icc)) stop("Intracluster correlation coefficient in the treatment arms (treatment_icc): Value must be specified.", call. = FALSE)
treatment_icc =
ContinuousErrorCheck(parameters$treatment_icc,
narms - 1,
lower_values = 0,
lower_values_sign = ">",
upper_values = 1,
upper_values_sign = "<",
"Intracluster correlation coefficient in the treatment arm (treatment_icc)",
c("Value"),
"double",
NA)
# Normal endpoint
if (endpoint_index == 1) {
if (is.null(parameters$control_between_cluster_sd)) stop("Between-cluster standard deviation in the control arm (control_sd): Value must be specified.", call. = FALSE)
control_between_cluster_sd =
ContinuousErrorCheck(parameters$control_between_cluster_sd,
1,
lower_values = c(0),
lower_values_sign = c(">"),
upper_values = c(NA),
upper_values_sign = c(NA),
"Between-cluster standard deviation in the control arm (control_between_cluster_sd)",
c("Value"),
"double",
NA)
if (is.null(parameters$treatment_between_cluster_sd)) stop("Between-cluster standard deviation in the treatment arms (treatment_sd): Value must be specified.", call. = FALSE)
treatment_between_cluster_sd =
ContinuousErrorCheck(parameters$treatment_between_cluster_sd,
narms - 1,
lower_values = c(0),
lower_values_sign = c(">"),
upper_values = c(NA),
upper_values_sign = c(NA),
"Between-cluster standard deviation in the treatment arm (treatment_between_cluster_sd)",
c("Value"),
"double",
NA)
# Within-cluster standard deviation in the control arm
parameters$control_within_cluster_sd = control_between_cluster_sd * (1 - control_icc) / control_icc
# Within-cluster standard deviation in the treatment arm
parameters$treatment_within_cluster_sd = treatment_between_cluster_sd * (1 - treatment_icc) / treatment_icc
if (is.null(parameters$control_mean)) stop("Mean effect in the control arm (control_mean): Value must be specified.", call. = FALSE)
control_mean =
ContinuousErrorCheck(parameters$control_mean,
1,
lower_values = c(NA),
lower_values_sign = c(NA),
upper_values = c(NA),
upper_values_sign = c(NA),
"Mean effect in the control arm (control_mean)",
c("Value"),
"double",
NA)
if (is.null(parameters$treatment_mean)) stop("Mean effect in the treatment arms (treatment_mean): Value must be specified.", call. = FALSE)
treatment_mean =
ContinuousErrorCheck(parameters$treatment_mean,
narms - 1,
lower_values = c(NA),
lower_values_sign = c(NA),
upper_values = c(NA),
upper_values_sign = c(NA),
"Mean effect in the treatment arm (treatment_mean)",
c("Value"),
"double",
NA)
parameters$control_alpha = 0
parameters$control_beta = 0
parameters$treatment_alpha = 0
parameters$treatment_beta = 0
parameters$control_rate = 0
parameters$treatment_rate = 0
}
# Binary endpoint
if (endpoint_index == 2) {
if (is.null(parameters$control_rate)) stop("Response rate in the control arm (control_rate): Value must be specified.", call. = FALSE)
control_rate =
ContinuousErrorCheck(parameters$control_rate,
1,
lower_values = 0,
lower_values_sign = ">",
upper_values = 1,
upper_values_sign = "<",
"Response rate in the control arm (control_rate)",
c("Value"),
"double",
NA)
if (is.null(parameters$treatment_rate)) stop("Response rate in the treatment arms (treatment_rate): Value must be specified.", call. = FALSE)
treatment_rate =
ContinuousErrorCheck(parameters$treatment_rate,
narms - 1,
lower_values = 0,
lower_values_sign = ">",
upper_values = 1,
upper_values_sign = "<",
"Response rate in the treatment arm (treatment_rate)",
c("Value"),
"double",
NA)
# Alpha and beta parameters of the beta distribution in the control arm
parameters$control_alpha = (1 / control_icc - 1) * control_rate
parameters$control_beta = (1 / control_icc - 1) * (1 - control_rate)
# Alpha and beta parameters of the beta distribution in the treatment arm
parameters$treatment_alpha = (1 / treatment_icc - 1) * treatment_rate
parameters$treatment_beta = (1 / treatment_icc - 1) * (1 - treatment_rate)
parameters$control_mean = 0
parameters$treatment_mean = 0
parameters$control_between_cluster_sd = 0
parameters$treatment_between_cluster_sd = 0
parameters$control_within_cluster_sd = 0
parameters$treatment_within_cluster_sd = 0
}
#############################################
parameters$means = 0
parameters$within_cluster_sds = 0
parameters$between_cluster_sds = 0
parameters$rates = 0
# All means and SDs
if (endpoint_index == 1) {
parameters$means = c(parameters$control_mean, parameters$treatment_mean)
parameters$within_cluster_sds = c(parameters$control_within_cluster_sd, parameters$treatment_within_cluster_sd)
parameters$between_cluster_sds = c(parameters$control_between_cluster_sd, parameters$treatment_between_cluster_sd)
}
# All rates
if (endpoint_index == 2) {
parameters$rates = c(parameters$control_rate, parameters$treatment_rate)
}
# Maximum number of iterations when fitting models
parameters$max_iterations = 100
# Minimum increment for stopping the model fitting process
parameters$min_increment = 0.001
# Parameters of multiple testing procedures
parameters$weight = rep(1 / (narms - 1), narms - 1)
parameters$transition = 0
#########################################################
# Run simulations on multple cores to compute operating characteristics
if (parameters$ncores > 1) {
# nocov start
cl = parallel::makeCluster(parameters$ncores)
# Export all functions in the global environment to each node
parallel::clusterExport(cl, ls(envir = .GlobalEnv))
doParallel::registerDoParallel(cl)
simulation_list = foreach(counter=(1:parameters$ncores), .packages = c("ClustRand")) %dorng% {
ClustRandSingleCore(parameters)
}
stopCluster(cl)
# Combine the simulation results across the cores
pval_results = NULL
coef_results = NULL
cluster_size_results = NULL
for (i in 1:parameters$ncores) {
pval_results = rbind(pval_results, simulation_list[[i]]$pval_results)
coef_results = rbind(coef_results, simulation_list[[i]]$coef_results)
cluster_size_results = c(cluster_size_results, simulation_list[[i]]$cluster_size_results)
}
# nocov end
} else {
simulations = ClustRandSingleCore(parameters)
pval_results = simulations$pval_results
coef_results = simulations$coef_results
cluster_size_results = simulations$cluster_size_results
}
pval_results = as.data.frame(pval_results)
if (parameters$descriptive_statistics) {
coef_results = as.data.frame(coef_results)
cluster_size_results = as.numeric(cluster_size_results)
}
sim_summary = list()
# GEE
if (parameters$method_index == 1) {
# Extract p-values for each treatment-control comparison
if (narms == 2) {
pval_convergence = pval_results[, 1]
sandwich = pval_results[, 2]
kc = pval_results[, 3]
md = pval_results[, 4]
# Compute overall power
sim_summary$power_sandwich = mean(sandwich[pval_convergence == 1] <= parameters$alpha)
sim_summary$power_kc = mean(kc[pval_convergence == 1] <= parameters$alpha)
sim_summary$power_md = mean(md[pval_convergence == 1] <= parameters$alpha)
if (parameters$descriptive_statistics) {
# Summary of random cluster size estimates
if (parameters$cluster_scheme == "Random") {
cluster_size = cluster_size_results
cluster_size_summary = rep(0, 5)
cluster_size_summary[1] = mean(cluster_size, na.rm = TRUE)
cluster_size_summary[2:5] = quantile(cluster_size, probs = c(0.025, 0.25, 0.75, 0.975), na.rm = TRUE)
sim_summary$cluster_size_summary = cluster_size_summary
}
coef_convergence = coef_results[, 1]
intercept = coef_results[, 2]
slope = coef_results[, 3]
if (parameters$direction_index == 2) {
intercept = -intercept
slope = -slope
}
# Compute effect estimates
nsims = nrow(coef_results)
effect = matrix(NA, nsims, narms)
for (i in 1:nsims) {
if (coef_convergence[i] == 1) {
if (endpoint_index == 1) {
effect[i, 1] = intercept[i]
effect[i, 2] = intercept[i] + slope[i]
}
if (endpoint_index == 2) { # nocov start
effect[i, 1] = AntiLogit(intercept[i])
effect[i, 2] = AntiLogit(intercept[i] + slope[i])
} # nocov end
}
}
# Compute the mean and 95% CI
eff_summary = matrix(0, 2, 5)
for (i in 1:2) {
eff_summary[i, 1] = mean(effect[, i], na.rm = TRUE)
eff_summary[i, 2:5] = quantile(effect[, i], probs = c(0.025, 0.25, 0.75, 0.975), na.rm = TRUE)
}
sim_summary$eff_summary = eff_summary
}
} else {
pval_convergence = pval_results[, seq(from = 1, to = 1 + (narms - 2) * 4, by = 4)]
sandwich = pval_results[, seq(from = 2, to = 2 + (narms - 2) * 4, by = 4)]
kc = pval_results[, seq(from = 3, to = 3 + (narms - 2) * 4, by = 4)]
md = pval_results[, seq(from = 4, to = 4 + (narms - 2) * 4, by = 4)]
# Compute treatment-specific and overall power
sim_summary$power_sandwich = ComputePower(sandwich, pval_convergence, parameters$alpha)
sim_summary$power_kc = ComputePower(kc, pval_convergence, parameters$alpha)
sim_summary$power_md = ComputePower(md, pval_convergence, parameters$alpha)
if (parameters$descriptive_statistics) {
# Summary of random cluster size estimates
if (parameters$cluster_scheme == "Random") {
cluster_size = cluster_size_results
cluster_size_summary = rep(0, 5)
cluster_size_summary[1] = mean(cluster_size, na.rm = TRUE)
cluster_size_summary[2:5] = quantile(cluster_size, probs = c(0.025, 0.25, 0.75, 0.975), na.rm = TRUE)
sim_summary$cluster_size_summary = cluster_size_summary
}
coef_convergence = coef_results[, seq(from = 1, to = 1 + (narms - 2) * 3, by = 3)]
intercept = coef_results[, seq(from = 2, to = 2 + (narms - 2) * 3, by = 3)]
slope = coef_results[, seq(from = 3, to = 3 + (narms - 2) * 3, by = 3)]
if (parameters$direction_index == 2) {
intercept = -intercept
slope = -slope
}
# Compute effect estimates
nsims = nrow(coef_results)
effect = matrix(NA, nsims, narms)
for (i in 1:nsims) {
if (coef_convergence[i, 1] == 1) {
if (endpoint_index == 1) effect[i, 1] = intercept[i, 1]
if (endpoint_index == 2) effect[i, 1] = AntiLogit(intercept[i, 1])
}
for (j in 2:narms) {
if (coef_convergence[i, j - 1] == 1) {
if (endpoint_index == 1) effect[i, j] = intercept[i, j - 1] + slope[i, j - 1]
if (endpoint_index == 2) effect[i, j] = AntiLogit(intercept[i, j - 1] + slope[i, j - 1])
}
}
}
# Compute the mean and 95% CI
eff_summary = matrix(0, narms, 5)
for (i in 1:narms) {
eff_summary[i, 1] = mean(effect[, i], na.rm = TRUE)
eff_summary[i, 2:5] = quantile(effect[, i], probs = c(0.025, 0.25, 0.75, 0.975), na.rm = TRUE)
}
sim_summary$eff_summary = eff_summary
}
}
}
# GLMEM
if (parameters$method_index == 2) {
# Extract p-values for each treatment-control comparison
if (narms == 2) {
pval_convergence = pval_results[, 1]
pval = pval_results[, 2]
# Compute overall power
sim_summary$power = mean(pval[pval_convergence == 1] <= parameters$alpha)
if (parameters$descriptive_statistics) {
# Summary of random cluster size estimates
if (parameters$cluster_scheme == "Random") {
cluster_size = cluster_size_results
cluster_size_summary = rep(0, 5)
cluster_size_summary[1] = mean(cluster_size, na.rm = TRUE)
cluster_size_summary[2:5] = quantile(cluster_size, probs = c(0.025, 0.25, 0.75, 0.975), na.rm = TRUE)
sim_summary$cluster_size_summary = cluster_size_summary
}
# Summary of effect estimates
coef_convergence = coef_results[, 1]
intercept = coef_results[, 2]
slope = coef_results[, 3]
if (parameters$direction_index == 2) {
intercept = -intercept
slope = -slope
}
nsims = nrow(coef_results)
effect = matrix(NA, nsims, narms)
for (i in 1:nsims) {
if (coef_convergence[i] == 1) {
if (endpoint_index == 1) { # nocov start
effect[i, 1] = intercept[i]
effect[i, 2] = intercept[i] + slope[i]
} # nocov end
if (endpoint_index == 2) {
effect[i, 1] = AntiLogit(intercept[i])
effect[i, 2] = AntiLogit(intercept[i] + slope[i])
}
}
}
eff_summary = matrix(0, narms, 5)
for (i in 1:narms) {
eff_summary[i, 1] = mean(effect[, i], na.rm = TRUE)
eff_summary[i, 2:5] = quantile(effect[, i], probs = c(0.025, 0.25, 0.75, 0.975), na.rm = TRUE)
}
sim_summary$eff_summary = eff_summary
}
} else {
pval_convergence = pval_results[, seq(from = 1, to = 1 + (narms - 2) * 2, by = 2)]
pval = pval_results[, seq(from = 2, to = 2 + (narms - 2) * 2, by = 2)]
# Compute treatment-specific and overall power
sim_summary$power = ComputePower(pval, pval_convergence, parameters$alpha)
if (parameters$descriptive_statistics) {
# Summary of random cluster size estimates
if (parameters$cluster_scheme == "Random") {
cluster_size = cluster_size_results
cluster_size_summary = rep(0, 5)
cluster_size_summary[1] = mean(cluster_size, na.rm = TRUE)
cluster_size_summary[2:5] = quantile(cluster_size, probs = c(0.025, 0.25, 0.75, 0.975), na.rm = TRUE)
sim_summary$cluster_size_summary = cluster_size_summary
}
# Summary of effect estimates
coef_convergence = coef_results[, seq(from = 1, to = 1 + (narms - 2) * 3, by = 3)]
intercept = coef_results[, seq(from = 2, to = 2 + (narms - 2) * 3, by = 3)]
slope = coef_results[, seq(from = 3, to = 3 + (narms - 2) * 3, by = 3)]
if (parameters$direction_index == 2) { # nocov start
intercept = -intercept
slope = -slope
} # nocov end
nsims = nrow(coef_results)
effect = matrix(NA, nsims, narms)
for (i in 1:nsims) {
if (coef_convergence[i, 1] == 1) {
if (endpoint_index == 1) effect[i, 1] = intercept[i, 1]
if (endpoint_index == 2) effect[i, 1] = AntiLogit(intercept[i, 1]) # nocov
}
for (j in 2:narms) {
if (coef_convergence[i, j - 1] == 1) {
if (endpoint_index == 1) effect[i, j] = intercept[i, j - 1] + slope[i, j - 1]
if (endpoint_index == 2) effect[i, j] = AntiLogit(intercept[i, j - 1] + slope[i, j - 1]) # nocov
}
}
}
eff_summary = matrix(0, narms, 5)
for (i in 1:narms) {
eff_summary[i, 1] = mean(effect[, i], na.rm = TRUE)
eff_summary[i, 2:5] = quantile(effect[, i], probs = c(0.025, 0.25, 0.75, 0.975), na.rm = TRUE)
}
sim_summary$eff_summary = eff_summary
}
}
}
results = list(parameters = parameters,
sim_summary = sim_summary,
pval_results = pval_results,
coef_results = coef_results,
cluster_size_results = cluster_size_results)
class(results) = "ClustRandResults"
return(results)
}
ClustRandReportDoc = function(results) {
#############################################################################
# Error checks
if (!is(results, "ClustRandResults")) stop("The object was not created by the ClustRand function", call. = FALSE)
#############################################################################
# Empty list of tables to be included in the report
item_list = list()
item_index = 1
table_index = 1
figure_index = 1
width = 6.5
height = 5
parameters = results$parameters
sim_summary = results$sim_summary
endpoint_index = parameters$endpoint_index
narms = parameters$narms
# Trial arms
trial_arms = "Control"
if (narms >= 3) {
for (i in 2:narms) trial_arms = c(trial_arms, paste0("Treatment ", i - 1))
} else {
trial_arms = c(trial_arms, "Treatment")
}
# All means and SDs
if (endpoint_index == 1) {
means = c(parameters$control_mean, parameters$treatment_mean)
}
# All rates
if (endpoint_index == 2) {
rates = c(parameters$control_rate, parameters$treatment_rate)
}
# Other parameters
between_cluster_sds = c(parameters$control_between_cluster_sd, parameters$treatment_between_cluster_sd)
iccs = c(parameters$control_icc, parameters$treatment_icc)
#############################################################################
report_title = "Cluster-randomized design"
item_list[[item_index]] = list(type = "paragraph", label = "Description", value = "The simulation report presents key operating characteristics of a cluster-randomized design for a Phase III clinical trial.")
item_index = item_index + 1
#############################################################################
column_names = c("Trial arm", "Sample size")
col1 = trial_arms
col2 = parameters$sample_size
data_frame = data.frame(col1, col2)
title = paste0("Table ", table_index, ". Number of completers")
footnote = "Completers are defined as patients who complete the trial and are included in the final analysis."
column_width = c(5, 1.5)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE, footnote)
item_index = item_index + 1
table_index = table_index + 1
#############################################################################
column_names = c("Parameter", "Value")
if (parameters$direction_index == 1) label = "A higher value of the endpoint indicates a more favorable outcome"
if (parameters$direction_index == 2) label = "A lower value of the endpoint indicates a more favorable outcome"
col1 = c("Endpoint type", "Direction of favorable outcome")
col2 = c(endpoint_list[endpoint_index], label)
data_frame = data.frame(col1, col2)
title = paste0("Table ", table_index, ". Primary efficacy endpoint")
column_width = c(3, 3.5)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
item_index = item_index + 1
table_index = table_index + 1
#############################################################################
if (parameters$cluster_index == 1) {
column_names = c("Trial arm", "Number of clusters", "Cluster sizes")
col1 = trial_arms
if (narms == 2) {
col2 = c(length(parameters$control_cluster_size), length(parameters$treatment_cluster_size))
col3 = c(paste0(parameters$control_cluster_size, collapse = ", "), paste0(parameters$treatment_cluster_size, collapse = ", "))
} else {
col2 = c(length(parameters$control_cluster_size), rep(ncol(parameters$treatment_cluster_size), narms - 1))
col3 = c(paste0(parameters$control_cluster_size, collapse = ", "))
for (i in 1:(narms - 1)) col3 = c(col3, paste0(parameters$treatment_cluster_size[i, ], collapse = ", "))
}
data_frame = data.frame(col1, col2, col3)
title = paste0("Table ", table_index, ". Cluster scheme parameters")
footnote = "A design with pre-defined cluster sizes is assumed."
column_width = c(1.5, 1.5, 3.5)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE, footnote)
item_index = item_index + 1
table_index = table_index + 1
}
if (parameters$cluster_index == 2) {
column_names = c("Trial arm", "Number of clusters", "Relative cluster sizes")
col1 = trial_arms
if (narms == 2) {
col2 = c(length(parameters$control_cluster_proportion), length(parameters$treatment_cluster_proportion))
col3 = c(paste0(parameters$control_cluster_proportion, collapse = ", "), paste0(parameters$treatment_cluster_proportion, collapse = ", "))
} else {
col2 = c(length(parameters$control_cluster_proportion), rep(ncol(parameters$treatment_cluster_proportion), narms - 1))
col3 = c(paste0(parameters$control_cluster_proportion, collapse = ", "))
for (i in 1:(narms - 1)) col3 = c(col3, paste0(parameters$treatment_cluster_proportion[i, ], collapse = ", "))
}
data_frame = data.frame(col1, col2, col3)
title = paste0("Table ", table_index, ". Cluster scheme parameters")
footnote = paste0("A design with random cluster sizes is assumed. The cluster sizes are generated using a generalized Bernoulli distribution based on the relative cluster sizes.")
column_width = c(1.5, 1.5, 3.5)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE, footnote)
item_index = item_index + 1
table_index = table_index + 1
}
#############################################################################
column_names = c("Trial arm", "Parameter", "Value")
col1 = NULL
col2 = NULL
col3 = NULL
for (i in 1:narms) {
if (endpoint_index == 1) {
col1 = c(col1, trial_arms[i])
col2 = c(col2, "Mean")
col3 = c(col3, means[i])
}
if (endpoint_index == 2) {
col1 = c(col1, trial_arms[i])
col2 = c(col2, "Rate (%)")
col3 = c(col3, 100 * rates[i])
}
}
data_frame = data.frame(col1, col2, col3)
title = paste0("Table ", table_index, ". Treatment effect assumptions")
column_width = c(1.5, 3.5, 1.5)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
item_index = item_index + 1
table_index = table_index + 1
#############################################################################
column_names = c("Trial arm", "Parameter", "Value")
col1 = NULL
col2 = NULL
col3 = NULL
for (i in 1:narms) {
if (parameters$endpoint_index == 1) {
col1 = c(col1, trial_arms[i], "")
col2 = c(col2, "Between-cluster standard deviation", "Intra-cluster correlation coefficient")
col3 = c(col3, between_cluster_sds[i], iccs[i])
}
if (parameters$endpoint_index == 2) {
col1 = c(col1, trial_arms[i])
col2 = c(col2, "Intra-cluster correlation coefficient")
col3 = c(col3, iccs[i])
}
}
data_frame = data.frame(col1, col2, col3)
title = paste0("Table ", table_index, ". Variability parameters")
column_width = c(1.5, 3.5, 1.5)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
item_index = item_index + 1
table_index = table_index + 1
#############################################################################
column_names = c("Parameter", "Value")
if (parameters$method_index == 1) method_type = "Generalized estimating equations (GEE)"
if (parameters$method_index == 2) method_type = "Generalized linear mixed effects model (GLMEM)"
col1 = c("Data analysis method")
col2 = c(method_type)
if (parameters$mult_test_index >= 1) {
col1 = c(col1, "Multiple testing procedure")
col2 = c(col2, parameters$mult_test)
}
col1 = c(col1, "One-sided Type I error rate", "Number of simulations")
col2 = c(col2, sprintf("%0.3f", sum(parameters$alpha)), sprintf("%d", parameters$nsims))
data_frame = data.frame(col1, col2)
title = paste0("Table ", table_index, ". Analysis and simulation parameters")
column_width = c(2.5, 4)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, TRUE)
item_index = item_index + 1
table_index = table_index + 1
#############################################################################
if (parameters$descriptive_statistics) {
column_names = c("Parameter", "Trial arm", "Statistic", "Value")
eff_summary = sim_summary$eff_summary
cluster_size_summary = sim_summary$cluster_size_summary
if (endpoint_index == 1) {
col1 = c("Mean", rep("", 3 * narms - 1))
col2 = NULL
col3 = NULL
col4 = NULL
for (i in 1:narms) {
col2 = c(col2, trial_arms[i], rep("", 2))
col3 = c(col3, "Mean", "25%P, 75%P", "2.5%P, 97.5%P")
col4 = c(col4, round(eff_summary[i, 1], 2), paste0(round(eff_summary[i, 3], 2), ", ", round(eff_summary[i, 4], 2)), paste0(round(eff_summary[i, 2], 2), ", ", round(eff_summary[i, 5], 2)))
}
}
if (endpoint_index == 2) {
col1 = c("Rate (%)", rep("", 3 * narms - 1))
col2 = NULL
col3 = NULL
col4 = NULL
for (i in 1:narms) {
col2 = c(col2, trial_arms[i], rep("", 2))
col3 = c(col3, "Mean", "25%P, 75%P", "2.5%P, 97.5%P")
col4 = c(col4, round(100 * eff_summary[i, 1], 1), paste0(round(100 * eff_summary[i, 3], 1), ", ", round(100 * eff_summary[i, 4], 1)), paste0(round(100 * eff_summary[i, 2], 1), ", ", round(100 * eff_summary[i, 5], 1)))
}
}
if (parameters$cluster_scheme == "Random") {
col1 = c(col1, "Cluster size", rep("", 2))
col2 = c(col2, "All trial arms", rep("", 2))
col3 = c(col3, "Mean", "25%P, 75%P", "2.5%P, 97.5%P")
col4 = c(col4, round(cluster_size_summary[1], 1), paste0(round(cluster_size_summary[3], 1), ", ", round(cluster_size_summary[4], 1)), paste0(round(cluster_size_summary[2], 1), ", ", round(cluster_size_summary[5], 1)))
}
data_frame = data.frame(col1, col2, col3, col4)
title = paste0("Table ", table_index, ". Simulation results: Descriptive statistics")
column_width = c(2, 1.5, 2, 1)
footnote = "Descriptive statistics computed from each simulation run: 2.5%P (2.5th percentile), 25%P (25th percentile), 75%P (75th percentile) and 97.5%P (97.5th percentile)."
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE, footnote)
item_index = item_index + 1
table_index = table_index + 1
}
#############################################################################
# GEE
if (parameters$method_index == 1) {
if (parameters$narms == 2) {
column_names = c("Analysis method", "Power (%)")
col1 = c("Standard analysis",
"Bias-corrected analysis (Kauermann-Carroll correction)",
"Bias-corrected analysis (Mancl-DeRouen correction)")
col2 = c(round(100 * sim_summary$power_sandwich, 1),
round(100 * sim_summary$power_kc, 1),
round(100 * sim_summary$power_md, 1))
data_frame = data.frame(col1, col2)
title = paste0("Table ", table_index, ". Simulation results: Power calculations")
column_width = c(5.5, 1)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
item_index = item_index + 1
table_index = table_index + 1
} else {
column_names = c("Comparison", "Analysis method", "Power (%)")
col1 = NULL
col2 = NULL
col3 = NULL
for (i in 1:narms) {
if (i < narms) comp = paste0(trial_arms[i + 1], " vs control") else comp = "Overall effect"
col1 = c(col1, comp, "", "")
col2 = c(col2, "Standard analysis",
"Bias-corrected analysis (Kauermann-Carroll correction)",
"Bias-corrected analysis (Mancl-DeRouen correction)")
col3 = c(col3, round(100 * sim_summary$power_sandwich[i], 1),
round(100 * sim_summary$power_kc[i], 1),
round(100 * sim_summary$power_md[i], 1))
}
data_frame = data.frame(col1, col2, col3)
title = paste0("Table ", table_index, ". Simulation results: Power calculations")
column_width = c(1.5, 4, 1)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
item_index = item_index + 1
table_index = table_index + 1
}
}
# GLMEM
if (parameters$method_index == 2) {
if (parameters$narms == 2) {
column_names = c("Comparison", "Power (%)")
col1 = "Treatment vs control"
col2 = round(100 * sim_summary$power, 1)
data_frame = data.frame(col1, col2)
title = paste0("Table ", table_index, ". Simulation results: Power calculations")
column_width = c(5.5, 1)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
item_index = item_index + 1
table_index = table_index + 1
} else {
column_names = c("Comparison", "Power (%)")
col1 = NULL
col2 = NULL
for (i in 1:narms) {
if (i < narms) comp = paste0(trial_arms[i + 1], " vs control") else comp = "Overall effect"
col1 = c(col1, comp)
col2 = c(col2, round(100 * sim_summary$power[i], 1))
}
data_frame = data.frame(col1, col2)
title = paste0("Table ", table_index, ". Simulation results: Power calculations")
column_width = c(5.5, 1)
item_list[[item_index]] = CreateTable(data_frame, column_names, column_width, title, FALSE)
item_index = item_index + 1
table_index = table_index + 1
}
}
#############################################################################
report = item_list
doc = SaveReport(report, report_title)
return(doc)
}
# End of ClustRandReportDoc
ClustRandSingleCore = function(parameters) {
params_for_run = parameters
params_for_run$nsims = params_for_run$nsims_per_core
# GEE
if (params_for_run$method_index == 1) simulations = ClustRandGEEC(params_for_run)
# GLMEM
if (params_for_run$method_index == 2) simulations = ClustRandGLMEMR(params_for_run)
return(simulations)
}
ClustRandGLMEMR = function(parameters) {
nsims = parameters$nsims
narms = parameters$narms
control_cluster_size = parameters$control_cluster_size
if (narms == 2) treatment_size = length(parameters$treatment_cluster_size) else treatment_size = ncol(parameters$treatment_cluster_size)
pval_results = NULL
coef_results = NULL
cluster_size_results = NULL
for (sim in 1:nsims) {
# Random cluster sizes
if (parameters$cluster_index == 2) {
# Generate a vector of random cluster sizes
control_cluster_size = ExportRandomClusterSize(parameters$sample_size[1], parameters$control_cluster_cum)
}
control_size = length(control_cluster_size)
# Generate data for the common control arm
x_control = NULL
y_control = NULL
id_control = NULL
for (i in 1:control_size) {
# Normal endpoint
if (parameters$endpoint_index == 1) {
cluster_term = rnorm(n = 1, mean = 0, sd = parameters$between_cluster_sds[1])
control_sample = rnorm(n = control_cluster_size[i], mean = parameters$means[1] + cluster_term, sd = parameters$within_cluster_sds[1])
}
# Binary endpoint
if (parameters$endpoint_index == 2) {
cluster_term = rbeta(n = 1, shape1 = parameters$control_alpha, shape2 = parameters$control_beta)
control_sample = rbinom(n = control_cluster_size[i], size = 1, prob = cluster_term)
}
x_control = c(x_control, rep(0, control_cluster_size[i]))
y_control = c(y_control, control_sample)
id_control = c(id_control, rep(i, control_cluster_size[i]))
}
p = rep(NA, narms - 1)
convergence = rep(1, narms - 1)
intercept = rep(NA, narms - 1)
slope = rep(NA, narms - 1)
cluster_size = control_cluster_size
# Generate data for each treatment arm
for (k in 1:(narms - 1)) {
x = x_control
y = y_control
id = id_control
# Fixed cluster sizes
if (parameters$cluster_index == 1) {
if (narms == 2) treatment_cluster_size = parameters$treatment_cluster_size else treatment_cluster_size = parameters$treatment_cluster_size[k, ]
}
# Random cluster sizes
if (parameters$cluster_index == 2) {
if (narms == 2) proportions = parameters$treatment_cluster_cum_vector else proportions = parameters$treatment_cluster_cum_matrix[k, ] # nocov
# Generate a vector of random cluster sizes
treatment_cluster_size = ExportRandomClusterSize(parameters$sample_size[k + 1], proportions)
}
cluster_size = c(cluster_size, treatment_cluster_size)
treatment_size = length(treatment_cluster_size)
for (i in 1:treatment_size) {
# Normal endpoint
if (parameters$endpoint_index == 1) {
cluster_term = rnorm(n = 1, mean = 0, sd = parameters$between_cluster_sds[k + 1])
current_treatment_sample = rnorm(n = treatment_cluster_size[i], mean = parameters$means[k + 1] + cluster_term, sd = parameters$within_cluster_sds[k + 1])
}
# Binary endpoint
if (parameters$endpoint_index == 2) {
cluster_term = rbeta(n = 1, shape1 = parameters$treatment_alpha[k], shape2 = parameters$treatment_beta[k])
current_treatment_sample = rbinom(n = treatment_cluster_size[i], size = 1, prob = cluster_term)
}
x = c(x, rep(1, treatment_cluster_size[i]))
y = c(y, current_treatment_sample)
id = c(id, rep(control_size + i, treatment_cluster_size[i]))
}
# Direction of favorable outcome
if (parameters$direction_index == 2) {
if (parameters$endpoint_index == 1) y = -y
if (parameters$endpoint_index == 2) y = 1 - y
}
data_set = data.frame(x, y, id)
# Analyze the data for the current treatment-control comparison using generalized linear mixed-effects models
# Normal endpoint
if (parameters$endpoint_index == 1) {
result = tryCatch(
{
lmerTest::lmer(y ~ x + (1|id), data = data_set, REML = TRUE)
},
warning = function(cond) { # nocov start
w = -1
class(w) = "try-error"
return(w)
}) # nocov end
if (!inherits(result, "try-error")) {
model_fit = result
summary_fit = summary(model_fit, ddf = "Kenward-Roger")
# Estimated model parameters
if (nrow(summary_fit$coefficients) == 2) {
intercept[k] = summary_fit$coefficients[1, 1]
slope[k] = summary_fit$coefficients[2, 1]
delta = slope[k]
# One-sided p-value
if (delta > 0) p[k] = summary_fit$coefficients[2, 5] / 2 else p[k] = 1 - summary_fit$coefficients[2, 5] / 2
}
if (nrow(summary_fit$coefficients) == 1) { # nocov start
if (rownames(summary_fit$coefficients) == "(Intercept)") {
intercept[k] = summary_fit$coefficients[1, 1]
}
if (rownames(summary_fit$coefficients) == "x") {
slope[k] = summary_fit$coefficients[2, 1]
}
} # nocov end
} else {
convergence[k] = 0 # nocov
}
}
# Binary endpoint
if (parameters$endpoint_index == 2) {
result = tryCatch({
glmer(y ~ x + (1|id), data = data_set, family = binomial(link = 'logit'))
},
warning = function(cond) {
w = -1
class(w) = "try-error"
return(w)
})
if (!inherits(result, "try-error")) {
model_fit = result
summary_fit = summary(model_fit)
intercept[k] = summary_fit$coefficients[1, 1]
slope[k] = summary_fit$coefficients[2, 1]
delta = slope[k]
# One-sided p-value
if (delta > 0) p[k] = summary_fit$coefficients[2, 4] / 2 else p[k] = 1 - summary_fit$coefficients[2, 4] / 2
} else {
convergence[k] = 0
}
}
}
# Apply a multiplicity adjustment
if (parameters$mult_test_index >= 1) {
p = ExportTradMultAdj(parameters$mult_test_index, p, parameters$weight, parameters$transition)
}
# One-sided p-values
pval_vec = NULL
for (k in 1:(narms - 1)) pval_vec = c(pval_vec, convergence[k], p[k])
pval_results = rbind(pval_results, pval_vec)
# Descriptive statistics for each simulation run
if (parameters$descriptive_statistics) {
coef_vec = NULL
cluster_size_vec = NULL
for (k in 1:(narms - 1)) {
coef_vec = c(coef_vec, convergence[k], intercept[k], slope[k])
cluster_size_vec = c(cluster_size_vec, cluster_size)
}
coef_results = rbind(coef_results, coef_vec)
cluster_size_results = c(cluster_size_results, cluster_size_vec)
}
}
# End of simulations
return(list(pval_results = pval_results,
coef_results = coef_results,
cluster_size_results = cluster_size_results))
}
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