#' Power simulations for cluster-randomized trials: Parallel Designs, Binary Outcome
#'
#' @description
#' \loadmathjax
#'
#'
#' This function uses Monte Carlo methods (simulations) to estimate
#' power for cluster-randomized trials. Users
#' can modify a variety of parameters to suit the simulations to their
#' desired experimental situation.
#'
#' Users must specify the desired number of simulations, number of subjects per
#' cluster, number of clusters per arm, and two of the following three
#' parameters: expected probability of the outcome in one group, expected
#' probability of the outcome in the second group,
#' and expected difference in probabilities between groups.
#' Default values are provided for significance level, analytic method,
#' progress updates, and whether the simulated data sets are retained.
#'
#'
#' @param nsim Number of datasets to simulate; accepts integer. Required.
#'
#' @param nsubjects Number of subjects per cluster; accepts either a scalar
#' (implying equal cluster sizes for the two groups), a vector of length two
#' (equal cluster sizes within arm), or a vector of length \code{sum(nclusters)}
#' (unequal cluster sizes within arm). Required.
#'
#' @param nclusters Number of clusters per treatment group; accepts a single integer
#' (if there are the same number of clusters in each arm) or a vector of 2 integers
#' (if nsubjects differs between arms). If a vector of cluster sizes >2 is provided in
#' \code{nsubjects}, \code{sum(nclusters)} must match the \code{nsubjects} vector length.
#' Required.
#'
#' @param p1 Expected probability of outcome in first group.
#' @param p2 Expected probability of outcome in second group.
#'
#' @param sigma_b_sq Between-cluster variance; if sigma_b_sq2 is not specified,
#' between-cluster variances are assumed to be equal in the two arms. Accepts numeric. Required.
#' @param sigma_b_sq2 Between-cluster variance for clusters in second group. Only required if
#' between-cluster variances differ between treatment arms.
#'
#'
#' @param alpha Significance level; default = 0.05.
#' @param method Data analysis method, either generalized linear mixed effects model (GLMM)
#' or generalized estimating equations (GEE). Accepts c('glmm', 'gee'); default = 'glmm'. Required.
#' @param quiet When set to FALSE, displays simulation progress and estimated completion
#' time, default = TRUE.
#' @param allSimData Option to include a list of all simulated datasets in the output object.
#' Default = \code{FALSE}.
#' @param nofit Option to skip model fitting and analysis and instead return a dataframe with
#' the simulated datasets. Default = \code{FALSE}.
#' @param allSimData Option to output list of all simulated datasets; default = FALSE.
#' @param nofit Option to skip model fitting and analysis and only return the simulated data.
#' Default = \code{FALSE}.
#' @param seed Option to set the seed. Default is NA.
#' @param poorFitOverride Option to override \code{stop()} if more than 25\%
#' of fits fail to converge.
#' @param lowPowerOverride Option to override \code{stop()} if the power
#' is less than 0.5 after the first 50 simulations and every ten simulations
#' thereafter. On function execution stop, the actual power is printed in the
#' stop message. Default = FALSE. When TRUE, this check is ignored and the
#' calculated power is returned regardless of value.
#' @param timelimitOverride Logical. When FALSE, stops execution if the estimated completion time
#' is more than 2 minutes. Defaults to TRUE.
#' @param irgtt Logical. Default = FALSE. Is the experimental design an
#' individually randomized group treatment trial? For details,
#' see ?cps.irgtt.binary.
#'
#' @return If \code{nofit = F}, a list with the following components:
#' \itemize{
#' \item Character string indicating total number of simulations, simulation type,
#' and number of convergent models
#' \item Number of simulations
#' \item Data frame with columns "Power" (estimated statistical power),
#' "lower.95.ci" (lower 95% confidence interval bound),
#' "upper.95.ci" (upper 95% confidence interval bound),
#' "Alpha" (probability of committing a Type I error or rejecting a true null),
#' "Beta" (probability of committing a Type II error or failing to reject a false null).
#' Note that non-convergent models are returned for review,
#' but not included in this calculation.
#' \item Analytic method used for power estimation
#' \item Significance level
#' \item Vector containing user-defined cluster sizes
#' \item Vector containing user-defined number of clusters
#' \item Data frame reporting sigma_b_sq for each group
#' \item Vector containing user-supplied outcome probability and estimated odds ratio
#' \item Data frame containing three estimates of ICC
#' \item Data frame with columns:
#' "Estimate" (Estimate of treatment effect for a given simulation),
#' "Std.err" (Standard error for treatment effect estimate),
#' "Test.statistic" (z-value (for GLMM) or Wald statistic (for GEE)),
#' "p.value",
#' "converge" (Did simulated model converge?)
#' \item If allSimData = TRUE, list of data frames, each containing: "y" (Simulated response value),
#' "trt" (Indicator for treatment group), "clust" (Indicator for cluster)
#' \item List of warning messages produced by non-convergent models;
#' Includes model number for cross-referencing against \code{model.estimates}
#' \item Logical vector reporting whether models converged.
#' }
#'
#' If \code{nofit = T}, a data frame of the simulated data sets, containing:
#'
#' \itemize{
#' \item "arm" (Indicator for treatment arm)
#' \item "cluster" (Indicator for cluster)
#' \item "y1" ... "yn" (Simulated response value for each of the \code{nsim} data sets).
#' }
#'
#'
#' @details
#'
#' The data generating model for observation \mjseqn{j} in cluster \mjseqn{i} is:
#'
#' \mjsdeqn{y_{ij} \sim \code{Bernoulli}(\frac{e^{p_1 + b_i}}{1 + e^{p_1 + b_i} }) }
#' for the first group or arm, where \mjseqn{b_i \sim N(0,\sigma_b^2)},
#' while for the second group,
#' \mjsdeqn{y_{ij} \sim \code{Bernoulli}(\frac{e^{p_2 + b_i}}{1 + e^{p_2 + b_i} }) }
#' where \mjseqn{b_i \sim N(0,\sigma_{b_2}^2)}; if
#' \mjseqn{\sigma_{b_2}^2} is not used, then the second group uses
#' \mjseqn{b_i \sim N(0,\sigma_b^2)}.
#'
#' All random terms are generated independent of one another.
#'
#'
#' Non-convergent models are not included in the calculation of exact confidence
#' intervals.
#'
#'
#' @seealso
#'
#' An intracluster correlation coefficient (ICC) for binary outcome data is
#' neither a natural parameter of the data generating model nor a function
#' of its parameters. Several methods for calculation have been suggested
#' (Wu, Crespi, and Wong, 2012). We provide several versions of ICCs for
#' comparison. These can be accessed in the \code{bincalcICC()} function.
#'
#'
#'
#' @section Testing details:
#' This function has been verified against reference values from the NIH's GRT
#' Sample Size Calculator, PASS11, \code{CRTsize::n4prop}, and
#' \code{clusterPower::cpa.binary}.
#'
#' @author Alexander R. Bogdan, Alexandria C. Sakrejda
#' (\email{acbro0@@umass.edu}), and Ken Kleinman
#' (\email{ken.kleinman@@gmail.com})
#' #'
#' @references Elridge, S., Ukoumunne, O. & Carlin, J. The Intra-Cluster Correlation
#' Coefficient in Cluster Randomized Trials:
#' A Review of Definitions. International Statistical Review (2009), 77, 3, 378-394.
#' doi: 10.1111/j.1751-5823.2009.00092.x
#' @references Snjiders, T. & Bosker, R. Multilevel Analysis: an Introduction to Basic and
#' Advanced Multilevel Modelling. London, 1999: Sage.
#' @references Wu S, Crespi CM, Wong WK. Comparison of Methods for Estimating Intraclass
#' Correlation Coefficient for Binary Responses in Cancer Prevention Cluster Randomized
#' Trials. Contemp Clin Trials. 2012; 33(5): 869-880. doi:10.1016/j.cct.2012.05.004
#' London: Arnold; 2000.
#'
#' @examples
#'
#' # Estimate power for a trial with 10 clusters in each arm, 20 subjects in
#' # each cluster, with a probability of 0.8 in the first arm and 0.5 in the
#' # second arm, with a sigma_b_sq = 1 in the first arm sigma_b_sq = 1.2 in
#' # the second arm.
#'
#' \dontrun{
#' binary.sim = cps.binary(nsim = 100, nsubjects = 20,
#' nclusters = 10, p1 = 0.8,
#' p2 = 0.5, sigma_b_sq = 1,
#' sigma_b_sq2 = 1.2, alpha = 0.05,
#' method = 'glmm', allSimData = FALSE)
#' }
#'
#' # Estimate power for a trial just as above, except that in the first arm,
#' # the clusters have 10 subjects in 9 of the 10 clusters and 100 in the tenth
#' # cluster, while in the second arm all clusters have 20 subjects.
#'
#' \dontrun{
#' binary.sim2 = cps.binary(nsim = 100,
#' nsubjects = c(c(rep(10,9),100), rep(20,10)),
#' nclusters = 10, p1 = 0.8,
#' p2 = 0.5, sigma_b_sq = 1,
#' sigma_b_sq2 = 1.2, alpha = 0.05,
#' method = 'gee', allSimData = FALSE)
#' }
#'
#'
#'
#' @export
# Define function
cps.binary = function(nsim = NULL,
nsubjects = NULL,
nclusters = NULL,
p1 = NULL,
p2 = NULL,
sigma_b_sq = NULL,
sigma_b_sq2 = NULL,
alpha = 0.05,
method = 'glmm',
quiet = FALSE,
allSimData = FALSE,
seed = NA,
nofit = FALSE,
poorFitOverride = FALSE,
lowPowerOverride = FALSE,
timelimitOverride = TRUE,
irgtt = FALSE) {
if (!is.na(seed)) {
set.seed(seed = seed)
}
# Create objects to collect iteration-specific values
est.vector <- NULL
se.vector <- NULL
stat.vector <- NULL
pval.vector <- NULL
converge.ind <- NULL
converge.vector <- NULL
icc2.vector <- NULL
lmer.icc.vector <- NULL
converge.vector <- NULL
simulated.datasets <- list()
warning.list <- list()
converge <- NULL
# Create progress bar
prog.bar = progress::progress_bar$new(
format = "(:spin) [:bar] :percent eta :eta",
total = nsim,
clear = FALSE,
width = 100
)
prog.bar$tick(0)
# Define wholenumber function
is.wholenumber = function(x, tol = .Machine$double.eps ^ 0.5)
abs(x - round(x)) < tol
# Define expit function
expit = function(x)
1 / (1 + exp(-x))
# Validate NSIM, NSUBJECTS, NCLUSTERS
sim.data.arg.list = list(nsim, nsubjects, nclusters, sigma_b_sq)
sim.data.args = unlist(lapply(sim.data.arg.list, is.null))
if (sum(sim.data.args) > 0) {
stop(
"NSIM, NSUBJECTS, NCLUSTERS & sigma_b_sq must all be specified. Please review your input values."
)
}
min1.warning = " must be an integer greater than or equal to 1"
if (!is.wholenumber(nsim) || nsim < 1) {
stop(paste0("NSIM", min1.warning))
}
if (!is.wholenumber(nsubjects) || nsubjects < 1) {
stop(paste0("NSUBJECTS", min1.warning))
}
if (!is.wholenumber(nclusters) || nclusters < 1) {
stop(paste0("NCLUSTERS", min1.warning))
}
if (length(nclusters) > 2) {
stop(
"NCLUSTERS can only be a vector of length 1 (equal # of clusters per group) or 2 (unequal # of clusters per group)"
)
}
# Set cluster sizes for arm (if not already specified)
if (length(nclusters) == 1) {
if (irgtt == TRUE) {
nclusters[2] = nclusters[1]
nclusters[1] = 1
} else {
nclusters[2] = nclusters[1]
}
}
# Set sample sizes for each cluster (if not already specified)
if (length(nsubjects) == 1) {
nsubjects[1:sum(nclusters)] = nsubjects
}
if (length(nsubjects) == 2) {
nsubjects = c(rep(nsubjects[1], nclusters[1]), rep(nsubjects[2], nclusters[2]))
}
if (nclusters[1] == nclusters[2] &&
length(nsubjects) == nclusters[1]) {
nsubjects = rep(nsubjects, 2)
}
if (length(nclusters) == 2 &&
length(nsubjects) != 1 &&
length(nsubjects) != sum(nclusters)) {
stop(
"A cluster size must be specified for each cluster. If all cluster sizes are equal, please provide a single value for NSUBJECTS"
)
}
if (irgtt == FALSE) {
# Validate sigma_b_sq, sigma_b_sq2
min0.warning = " must be a numeric value greater than 0"
if (!is.numeric(sigma_b_sq) || sigma_b_sq <= 0) {
stop("sigma_b_sq", min0.warning)
}
if (!is.null(sigma_b_sq2) && sigma_b_sq2 <= 0) {
stop("sigma_b_sq2", min0.warning)
}
}
# Set between-cluster variances
if (is.null(sigma_b_sq2)) {
sigma_b_sq[2] = sigma_b_sq
} else{
sigma_b_sq[2] = sigma_b_sq2
}
# Validate P1, P2
parm1.arg.list = list(p1, p2)
parm1.args = unlist(lapply(parm1.arg.list, is.null))
if (sum(parm1.args) > 1) {
stop("Both terms must be specified: p1, p2")
}
# Validate ALPHA, METHOD, QUIET, allSimData
if (!is.numeric(alpha) || alpha < 0) {
stop("ALPHA", min0.warning)
} else if (alpha > 1) {
stop("ALPHA must be a numeric value between 0 - 1")
}
if (!is.element(method, c('glmm', 'gee'))) {
stop(
"METHOD must be either 'glmm' (Generalized Linear Mixed Model)
or 'gee'(Generalized Estimating Equation)"
)
}
if (!is.logical(quiet)) {
stop(
"QUIET must be either TRUE (No progress information shown) or FALSE (Progress information shown)"
)
}
if (!is.logical(allSimData)) {
stop(
"allSimData must be either TRUE (Output all simulated data sets) or FALSE (No simulated data output"
)
}
# Calculate ICC1 (sigma_b_sq / (sigma_b_sq + pi^2/3))
icc1 = mean(sapply(1:2, function(x)
sigma_b_sq[x] / (sigma_b_sq[x] + pi ^ 2 / 3)))
# Create indicators for arm & cluster
trt = c(rep(1, length.out = sum(nsubjects[1:nclusters[1]])),
rep(2, length.out = sum(nsubjects[(nclusters[1] + 1):(nclusters[1] + nclusters[2])])))
trt <- as.factor(trt)
clust = unlist(lapply(1:sum(nclusters), function(x)
rep(x, length.out = nsubjects[x])))
clust <- as.factor(clust)
# Calculate log odds for each group
logit.p1 = log(p1 / (1 - p1))
logit.p2 = log(p2 / (1 - p2))
# for irgtt option
index <- 1
### Create simulation loop
while (sum(converge.vector == TRUE) != nsim) {
# Generate between-cluster effects for arm 1 and arm 2
randint.0 = stats::rnorm(nclusters[1], mean = 0, sd = sqrt(sigma_b_sq[1]))
randint.1 = stats::rnorm(nclusters[2], mean = 0, sd = sqrt(sigma_b_sq[2]))
# Create arm 1 y-value
y0.intercept = unlist(lapply(1:nclusters[1], function(x)
rep(randint.0[x], length.out = nsubjects[x])))
y0.linpred = y0.intercept + logit.p1
y0.prob = expit(y0.linpred)
y0 = unlist(lapply(y0.prob, function(x)
stats::rbinom(1, 1, x)))
if (length(table(y0)) != 2) {
warning(print(
"y0 is completely seperated. Repeating the random draw 1 time."
))
randint.0 = stats::rnorm(nclusters[1],
mean = 0,
sd = sqrt(sigma_b_sq[1]))
y0.intercept = unlist(lapply(1:nclusters[1], function(x)
rep(randint.0[x], length.out = nsubjects[x])))
y0.linpred = y0.intercept + logit.p1
y0.prob = expit(y0.linpred)
y0 = unlist(lapply(y0.prob, function(x)
stats::rbinom(1, 1, x)))
}
# Create arm 2 y-value
y1.intercept = unlist(lapply(1:nclusters[2], function(x)
rep(randint.1[x], length.out = nsubjects[nclusters[1] + x])))
y1.linpred = y1.intercept + logit.p2
y1.prob = expit(y1.linpred)
y1 = unlist(lapply(y1.prob, function(x)
stats::rbinom(1, 1, x)))
if (length(table(y1)) != 2) {
warning(print(
"y1 is completely seperated. Repeating the random draw 1 time."
))
randint.1 = stats::rnorm(nclusters[2],
mean = 0,
sd = sqrt(sigma_b_sq[2]))
y1.intercept = unlist(lapply(1:nclusters[2], function(x)
rep(randint.1[x], length.out = nsubjects[nclusters[1] + x])))
y1.linpred = y1.intercept + logit.p2
y1.prob = expit(y1.linpred)
y1 = unlist(lapply(y1.prob, function(x)
stats::rbinom(1, 1, x)))
}
# Create single response vector
y = c(y0, y1)
# Create and store data frame for simulated dataset
sim.dat = data.frame(y = y, trt = trt, clust = clust)
if (allSimData == TRUE && nofit == FALSE) {
simulated.datasets = append(simulated.datasets, list(sim.dat))
}
# option to return simulated data only
if (nofit == TRUE) {
if (!exists("nofitop")) {
nofitop <- data.frame(trt = trt,
clust = clust,
y1 = y)
} else {
nofitop[, length(nofitop) + 1] <- y
}
if (length(nofitop) == (nsim + 2)) {
temp1 <- seq(1:nsim)
temp2 <- paste0("y", temp1)
colnames(nofitop) <- c("arm", "cluster", temp2)
}
if (length(nofitop) != (nsim + 2)) {
next()
}
return(nofitop)
}
# Calculate ICC2 ([P(Yij = 1, Yih = 1)] - pij * pih) / sqrt(pij(1 - pij) * pih(1 - pih))
#icc2 = (mean(y0.prob) * mean(y1.prob) - p1*p2) / sqrt((p1 * (1 - p1)) * p2 * (1 - p2))
icc2 = (mean(y0.prob) - p1) * (mean(y1.prob) - p2) / sqrt((p1 * (1 - p1)) * p2 * (1 - p2))
# ^Equation above #11 (no number); Eldridge, Ukoumunne & Carlin, 2009 (p.386)
icc2.vector = append(icc2.vector, icc2)
# Calculate LMER.ICC (lmer: sigma_b_sq / (sigma_b_sq + sigma))
if (irgtt == FALSE) {
lmer.mod = lme4::glmer(
y ~ trt + (1 | clust),
data = sim.dat,
family = stats::binomial(link = 'logit')
)
lmer.vcov <-
as.numeric(as.data.frame(lme4::VarCorr(lmer.mod))[, 4:5])
icc.val <- lmer.vcov[1] / (lmer.vcov[1] + lmer.vcov[2])
lmer.icc.vector <- append(lmer.icc.vector, icc.val)
}
# Set warnings to OFF
# Note: Warnings will still be stored in 'warning.list'
options(warn = -1)
start.time = Sys.time()
# Fit GLMM (lmer)
if (method == 'glmm') {
if (irgtt == TRUE) {
my.mod <-
try(MASS::glmmPQL(
y ~ trt,
random = ~ 0 + trt | clust,
data = sim.dat,
family = stats::binomial(link = 'logit')
))
if (class(my.mod) == "try-error") {
glmm.values <- NA
est.vector[index] <- NA
se.vector[index] <- NA
stat.vector[index] <- NA
pval.vector[index] <- NA
converge.vector[index] <- FALSE
} else {
glmm.values <- summary(my.mod)$tTable
est.vector[index] <- glmm.values['trt2', 'Value']
se.vector[index] <- glmm.values['trt2', 'Std.Error']
stat.vector[index] <- glmm.values['trt2', 't-value']
pval.vector[index] <- glmm.values['trt2', 'p-value']
converge.vector[index] <- TRUE
}
index <- index + 1
} else {
my.mod = try(lme4::glmer(
y ~ trt + (1 | clust),
data = sim.dat,
family = stats::binomial(link = 'logit')
))
model.converge = try(my.mod)
converge.ind = is.null(model.converge@optinfo$conv$lme4$messages)
converge.vector = append(converge.vector, converge.ind)
if (!isTRUE(converge.ind)) {
model.id = paste0("Model ", length(converge.vector))
warning.list[model.id] = list(model.converge@optinfo$conv$lme4$messages)
glmm.values = NA
est.vector = append(est.vector, NA)
se.vector = append(se.vector, NA)
stat.vector = append(stat.vector, NA)
pval.vector = append(pval.vector, NA)
} else {
glmm.values = summary(my.mod)$coefficient
est.vector = append(est.vector, glmm.values['trt2', 'Estimate'])
se.vector = append(se.vector, glmm.values['trt2', 'Std. Error'])
stat.vector = append(stat.vector, glmm.values['trt2', 'z value'])
pval.vector = append(pval.vector, glmm.values['trt2', 'Pr(>|z|)'])
}
}
if (poorFitOverride == FALSE &&
length(converge.vector) > 50 &&
sum(converge.vector == FALSE, na.rm = TRUE) > (nsim * 0.25)) {
stop("more than 25% of simulations are singular fit: check model specifications")
}
}
# Set warnings to ON
# Note: Warnings will still be stored in 'warning.list'
options(warn = 0)
# Fit GEE (geeglm)
if (method == "gee") {
sim.dat = dplyr::arrange(sim.dat, clust)
if (irgtt == FALSE) {
my.mod = geepack::geeglm(
y ~ trt,
data = sim.dat,
family = stats::binomial(link = 'logit'),
id = clust,
corstr = "exchangeable"
)
} else {
my.mod = geepack::geeglm(
y ~ trt + (0 + trt | clust),
data = sim.dat,
family = stats::binomial(link = 'logit'),
id = clust,
corstr = "exchangeable"
)
}
gee.values = summary(my.mod)$coefficients
est.vector = append(est.vector, gee.values['trt2', 'Estimate'])
se.vector = append(se.vector, gee.values['trt2', 'Std.err'])
stat.vector = append(stat.vector, gee.values['trt2', 'Wald'])
pval.vector = append(pval.vector, gee.values['trt2', 'Pr(>|W|)'])
converge.vector = append(converge.vector, ifelse(summary(my.mod)$error == 0, TRUE, FALSE))
}
# Print simulation start message
if (length(est.vector) == 1) {
avg.iter.time = as.numeric(difftime(Sys.time(), start.time, units = 'secs'))
time.est = avg.iter.time * (nsim - 1) / 60
hr.est = time.est %/% 60
min.est = round(time.est %% 60, 3)
if (quiet == FALSE) {
message(
paste0(
'Begin simulations :: Start Time: ',
Sys.time(),
' :: Estimated completion time: ',
hr.est,
'Hr:',
min.est,
'Min'
)
)
}
if (min.est > 2 && timelimitOverride == FALSE) {
stop(paste0(
"Estimated completion time: ",
hr.est,
'Hr:',
min.est,
'Min'
))
}
}
# Update simulation progress information
if (quiet == FALSE) {
prog.bar$update(sum(converge.vector == TRUE) / nsim)
Sys.sleep(1 / 100)
}
# stop the loop if power is <0.5
if (lowPowerOverride == FALSE && length(pval.vector) > 50) {
sig.val.temp <-
ifelse(pval.vector < alpha, 1, 0)
pval.power.temp <-
sum(sig.val.temp, na.rm = TRUE) / length(pval.vector)
if (pval.power.temp < 0.5) {
stop(
paste(
"Calculated power is < ",
pval.power.temp,
". Set lowPowerOverride == TRUE to run the simulations anyway.",
sep = ""
)
)
}
}
}
# Print simulation complete message
if (quiet == FALSE && sum(converge.vector) == nsim) {
message(paste0("Simulations Complete! Time Completed: ", Sys.time()))
}
# Governor to prevent infinite non-convergence loop
converge.ratio <-
sum(converge.vector == FALSE) / sum(converge.vector == TRUE)
if (converge.ratio > 4.0 && converge.ratio != Inf) {
stop(
"WARNING! The number of non-convergent models exceeds the number of convergent models by a factor of 4. Consider reducing sigma_b_sq"
)
}
## Output objects
# Create object containing summary statement
if (irgtt == FALSE) {
summary.message = paste0(
"Monte Carlo Power Estimation based on ",
nsim,
" Simulations: Simple Design, Binary Outcome. Note: ",
sum(converge.vector == FALSE),
" additional models were fitted to account for non-convergent simulations."
)
} else {
summary.message = paste0(
"Monte Carlo Power Estimation based on ",
nsim,
" Simulations: IRGTT Design, Binary Outcome. Note: Models fit using penalized quasi-likelihood."
)
}
# Create method object
long.method = switch(method, glmm = 'Generalized Linear Mixed Model',
gee = 'Generalized Estimating Equation')
# Store model estimate output in data frame
cps.model.est = data.frame(
Estimate = as.vector(unlist(est.vector)),
Std.err = as.vector(unlist(se.vector)),
Test.statistic = as.vector(unlist(stat.vector)),
p.value = as.vector(unlist(pval.vector)),
converge = as.vector(unlist(converge.vector))
)
# Calculate and store power estimate & confidence intervals
if (!is.na(any(cps.model.est$converge))) {
cps.model.temp <- dplyr::filter(cps.model.est, converge == TRUE)
} else {
cps.model.temp <- cps.model.est
}
power.parms <- confintCalc(nsim = nsim,
alpha = alpha,
p.val = cps.model.temp[, 'p.value'])
# Create object containing inputs
p1.p2.or = round(p1 / (1 - p1) / (p2 / (1 - p2)), 3)
p2.p1.or = round(p2 / (1 - p2) / (p1 / (1 - p1)), 3)
inputs = t(data.frame(
'Arm1' = c("probability" = p1, "odds.ratio" = p1.p2.or),
'Arm2' = c("probability" = p2, 'odds.ratio' = p2.p1.or)
))
# Create object containing group-specific cluster sizes
cluster.sizes = list('Arm1' = nsubjects[1:nclusters[1]],
'Arm2' = nsubjects[(nclusters[1] + 1):(nclusters[1] + nclusters[2])])
# Create object containing number of clusters
n.clusters = t(data.frame(
"Arm1" = c("n.clust" = nclusters[1]),
"Arm2" = c("n.clust" = nclusters[2])
))
if (irgtt == FALSE) {
# Create object containing estimated ICC values
ICC = round(t(data.frame(
'P_h' = c('ICC' = icc1),
'P_c' = c('ICC' = mean(icc2.vector, na.rm = TRUE)),
'lmer' = c('ICC' = mean(lmer.icc.vector, na.rm = TRUE))
)), 3)
# Create object containing all ICC values
# Note: P_h is a single calculated value. No vector to be appended.
icc.list = data.frame('P_c' = icc2.vector,
'lmer' = lmer.icc.vector)
}
# Create object containing group-specific variance parameters
var.parms = t(data.frame(
'Arm1' = c('sigma_b_sq' = sigma_b_sq[1]),
'Arm2' = c('sigma_b_sq' = sigma_b_sq[2])
))
# Check & governor for inclusion of simulated datasets
# Note: If number of non-convergent models exceeds 5% of NSIM,
# override allSimData and output all simulated data sets
if (allSimData == FALSE &&
(sum(converge.vector == FALSE) < sum(converge.vector == TRUE) * 0.05)) {
simulated.datasets = NULL
}
# Create list containing all output (class 'crtpwr') and return
if (irgtt == FALSE) {
complete.output = structure(
list(
"overview" = summary.message,
"nsim" = nsim,
"power" = power.parms,
"method" = long.method,
"alpha" = alpha,
"cluster.sizes" = cluster.sizes,
"n.clusters" = n.clusters,
"variance.parms" = var.parms,
"inputs" = inputs,
"ICC" = ICC,
"icc.list" = icc.list,
"model.estimates" = cps.model.est,
"sim.data" = simulated.datasets,
"warning.list" = warning.list,
"convergence" = converge.vector
),
class = "crtpwr"
)
} else {
complete.output = structure(
list(
"overview" = summary.message,
"nsim" = nsim,
"power" = power.parms,
"method" = long.method,
"alpha" = alpha,
"cluster.sizes" = cluster.sizes,
"n.clusters" = n.clusters,
"variance.parms" = var.parms,
"inputs" = inputs,
"model.estimates" = cps.model.est,
"sim.data" = simulated.datasets,
"warning.list" = warning.list,
"convergence" = converge.vector
),
class = "crtpwr"
)
}
return(complete.output)
}
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