#' Power simulations for cluster-randomized trials: Parallel Designs, Normal Outcome
#'
#' @description
#' \loadmathjax
#'
#' This function uses Monte Carlo methods (simulations) to estimate
#' power for parallel design cluster-randomized trials with normal outcomes. 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, expected means of the arms, and two of
#' the following: ICC, within-cluster variance, or between-cluster variance.
#' Defaults are provided for significance level, analytic method, progress
#' updates, and whether the simulated data sets are retained.
#'
#' Users have the option of specifying different variance parameters for each
#' arm, different numbers of clusters for each treatment group, and different numbers
#' of units within each cluster.
#'
#' Non-convergent models are not included in the calculation of exact confidence
#' intervals.
#'
#' @section Testing details:
#' This function has been verified, where possible, against reference values from the NIH's GRT
#' Sample Size Calculator, PASS11, \code{CRTsize::n4means}, and
#' \code{clusterPower::cpa.normal}.
#'
#' @param nsim Number of datasets to simulate; accepts integer. Required.
#'
#' @param nclusters Number of clusters per condition; accepts single integer (implying equal numbers of clusters in the two groups)
#' or vector of length 2 (unequal number of clusters per arm). 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 mu Mean in the first arm; accepts numeric, default 0. Required..
#'
#' @param mu2 Mean in the second arm; accepts numeric. Required.
#'
#' At least 2 of the following must be specified:
#'
#' @param ICC Intra-cluster correlation coefficient; accepts a value between 0 and 1.
#'
#' @param sigma_sq Within-cluster variance; accepts numeric.
#'
#' @param sigma_b_sq Between-cluster variance; accepts numeric.
#'
#'
#' The defaults for the following are all NA, implying equal variance parameters
#' for the two groups. If one of the following is given, variance parameters differ
#' between treatment groups, and at least 2 of the following
#' must be specified:
#'
#' @param ICC2 Intra-cluster correlation coefficient for clusters in the second arm.
#'
#' @param sigma_sq2 Within-cluster variance for clusters in the second arm.
#'
#' @param sigma_b_sq2 Between-cluster variance for clusters in the second arm.
#'
#' Optional parameters:
#'
#' @param alpha Significance level; default = 0.05.
#'
#' @param method Analytical method, either Generalized Linear Mixed Effects Model (GLMM, default) or
#' Generalized Estimating Equation (GEE). Accepts c('glmm', 'gee').
#'
#' @param quiet When set to FALSE, displays simulation progress and estimated completion time; default is FALSE.
#'
#' @param allSimData Option to include a list of all simulated datasets in the output object.
#' Default = \code{FALSE}.
#'
#' @param seed Option to set the seed. Default, NA, selects a seed based on the system clock.
#'
#' @param irgtt Logical. Default = FALSE. Is the experimental design an individually randomized
#' group treatment trial? For details, see ?cps.irgtt.normal.
#'
#' @param poorFitOverride Option to override \code{stop()} if more than 25\%
#' of fits fail to converge.
#'
#' @param nofit Option to skip model fitting and analysis and instead return a dataframe with
#' the simulated datasets. Default = \code{FALSE}.
#'
#' @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.
#'
#' @return If \code{nofit = F}, a list with the following components:
#' \itemize{
#' \item Character string indicating total number of simulations and simulation type
#' \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 or \mjseqn{\alpha} 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 in each arm
#' \item Data frame reporting ICC, variance parameters, and means for each arm
#' \item Vector containing expected group means based on user inputs
#' \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 the model converge?)
#' \item If \code{allSimData = TRUE}, a list of data frames, each containing:
#' "y" (Simulated response value),
#' "trt" (Indicator for arm),
#' "clust" (Indicator for cluster)
#' }
#'
#' If \code{nofit = T}, a data frame of the simulated data sets, containing:
#' \itemize{
#' \item "arm" (Indicator for treatment arm)
#' \item "clust" (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{i} in cluster \mjseqn{j} is:
#' \mjsdeqn{y_{ij} \sim N(\mu + b_i, \sigma^2) }
#' 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 N(\mu_2 + b_i, \sigma_2^2) }
#' where \mjseqn{b_i \sim N(0,\sigma_{b_2}^2)}; if none of
#' \mjseqn{\sigma_2^2, \sigma_{b_2}^2} or \code{ICC2} are used, then the second group uses
#' \mjseqn{b_i \sim N(0,\sigma_b^2)}
#' and \mjseqn{y_{ij} \sim N(\mu_2 + b_i, \sigma^2)} .
#'
#' All random terms are generated independent of one another.
#'
#'
#' For calls without \mjseqn{\sigma_2^2, \sigma_{b_2}^2} or \code{ICC2}, and using
#' \code{method="glmm"} the fitted model is:
#' \mjsdeqn{y_{ij}|b_i = \mu + \beta_1 x_{ij} + b_i + e_{ij}}
#'
#' with \mjseqn{\beta_1 = \mu_2 - \mu},
#' treatment group indicator \mjseqn{x_{ij} = 0} for the first group, with
#' \mjseqn{b_i \sim N(0, \sigma_b^2)} and \mjseqn{e_{ij} \sim N(0,\sigma^2)}.
#' In this case, both the random effects distribution and the residual distribution are the same for both
#' conditions.
#'
#' Otherwise, for \code{method="glmm"} the fitted model is:
#' \mjsdeqn{y_{ij}|b_i = \mu + \beta_1 x_{ij}
#' + b_i I(x_{ij}=0) + e_{ij} I(x_{ij}=0)
#' + g_i I(x_{ij}=1) + f_{ij} I(x_{ij}=1)
#' }
#'
#' with \mjseqn{\beta_1}, \mjseqn{x_{ij}, b_i}, and \mjseqn{e_{ij}} as above, with
#' \mjseqn{g_i \sim N(0, \sigma_{b_2}^2)} and \mjseqn{f \sim N(0,\sigma_2^2)}, the
#' random effects and residual distribution in the second group.
#'
#' @examples
#'
#' # Estimate power for a trial with 10 clusters in each arm and 25 subjects in each
#' # cluster, with an ICC of .3, sigma squared of 20 (implying sigma_b^2 of 8.57143)
#' # in each group, with arm means of 1 and 4.75 in the two groups, using 100 simulated
#' # data sets. The resulting estimated power should be 0.78.
#'
#' \dontrun{
#'
#' normal.sim = cps.normal(nsim = 100, nsubjects = 25, nclusters = 10, mu = 1,
#' mu2 = 4.75, ICC = 0.3, sigma_sq = 20, seed = 123)
#' }
#'
#'
#'
#' # Estimate power for a trial with 5 clusters in one arm, those clusters having 25 subjects
#' # each, 25 clusters in the other arm, those clusters having 5 subjects each, the first arm
#' # having a sigma squared of 20 and sigma_b squared of 8.57143, and the second a sigma squared
#' # of 9 and a sigma_b squared of 1, with estimated arm means of 1 and 4.75 in the first and
#' # second groups, respectively, using 100 simulated data sets analyzed by the GEE method.
#' # The estimated power should be 0.79, assuming seed = 123.
#'
#' \dontrun{
#' normal.sim2 = cps.normal(nsim = 100, nclusters = c(5,25), nsubjects = c(25,5), mu = 1,
#' mu2 = 4.75, sigma_sq = 20,sigma_b_sq = 8.8571429, sigma_sq2 = 9, sigma_b_sq2 = 1,
#' method = "gee", seed = 123)
#' }
#'
#'
#' # Estimate power for a trial with 5 clusters in one arm, those clusters having
#' # 4, 5, 6, 7, 7, and 7 subjects each, and 10 clusters in the other arm,
#' # those clusters having 5 subjects each, with sigma_b_sq = .3 and and ICC of .3 in both arms.
#' # We have estimated arm means of 1 and 2 in the first and second arms, respectively, and we use
#' # 100 simulated data sets analyzed by the GLMM method.
#'
#' \dontrun{
#' normal.sim2 = cps.normal(nsim = 100, nclusters = c(6,10),
#' nsubjects = list(c(4, 5, 6, 7, 7, 7), rep(5, times = 10)),
#' mu = 1, mu2 = 2, sigma_b_sq = .3, ICC = .3, method = "glmm",
#' seed = 1)
#' }
#'
#' # The resulting estimated power (if you set seed = 1) should be about 0.76.
#'
#' # Estimate power for a trial with 3 clusters in one arm,
#' # those clusters having 25, 35, and 45 subjects each, and 10 clusters
#' # in the other arm, those clusters having 5 subjects each, the first arm
#' # having a sigma squared of 20 and sigma_b squared of 8.57143, and the second a sigma squared
#' # of 9 and a sigma_b squared of 1, with estimated arm means of 1 and 4.75 in the first and
#' # second groups, respectively, using 100 simulated data sets analyzed by the GLMM method.
#'
#' \dontrun{
#'
#' normal.sim2 <- cps.normal(nsim = 100, nclusters = c(3,10),
#' nsubjects = c(25, 35, 45, rep(5, times = 10)),
#' mu = 1, mu2 = 4.75, sigma_sq = 20, sigma_b_sq = 8.8571429,
#' sigma_sq2 = 9, sigma_b_sq2 = 1, method = "glmm")
#' }
#'
#' # The resulting estimated power (if you set seed = 1) should be about 0.71.
#'
#'
#' @author Alexander R. Bogdan, Alexandria C. Sakrejda
#' (\email{acbro0@@umass.edu}), and Ken Kleinman
#' (\email{ken.kleinman@@gmail.com})
#'
#'
#'
#'
#'
#' @export
cps.normal = function(nsim = NA,
nclusters = NA,
nsubjects = NA,
mu = 0,
mu2 = NA,
ICC = NA,
sigma_sq = NA,
sigma_b_sq = NA,
ICC2 = NA,
sigma_sq2 = NA,
sigma_b_sq2 = NA,
alpha = 0.05,
method = 'glmm',
quiet = FALSE,
allSimData = FALSE,
seed = NA,
poorFitOverride = FALSE,
timelimitOverride = TRUE,
lowPowerOverride = FALSE,
irgtt = FALSE,
nofit = FALSE) {
converge <- NULL
# option for reproducibility
if (!is.na(seed)) {
set.seed(seed = seed)
}
# Create vectors to collect iteration-specific values
est.vector = rep(NA, length = nsim)
se.vector = rep(NA, length = nsim)
stat.vector = rep(NA, length = nsim)
pval.vector = rep(NA, length = nsim)
# This container keeps track of how many models failed to converge
converge.vector <- rep(NA, length = nsim)
simulated.datasets = list()
# initialize progress bar
prog.bar = progress::progress_bar$new(
format = "(:spin) [:bar] :percent eta :eta",
total = nsim,
clear = FALSE,
width = 100
)
prog.bar$tick(0)
# Validate NSIM, NCLUSTERS, NSUBJECTS
sim.data.arg.list = list(nsim, nclusters, nsubjects)
sim.data.args = unlist(lapply(sim.data.arg.list, is.na))
if (sum(sim.data.args) > 0) {
stop("NSIM, NCLUSTERS, & NSUBJECTS 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(nclusters) || nclusters < 1) {
stop(paste0("NCLUSTERS", min1.warning))
}
if (is.list(nsubjects)) {
temp <- unlist(nsubjects)
} else {
temp <- nsubjects
}
if (!is.wholenumber(temp) || temp < 1) {
stop(paste0("NSUBJECTS", min1.warning))
}
if (length(nclusters) > 2) {
stop(
"NCLUSTERS can only be a scalar (equal # of clusters per group) or a vector of length 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"
)
}
## Create variance parameters
# sigma_b_sq, sigma_sq, ICC
if (!is.na(c(ICC, sigma_sq)) && is.na(sigma_b_sq)) {
sigma_b_sq = ICC * sigma_sq / (1 - ICC)
}
if (!is.na(c(ICC, sigma_b_sq)) && is.na(sigma_sq)) {
sigma_sq = sigma_b_sq / ICC - sigma_b_sq
}
if (!is.na(c(sigma_sq, sigma_b_sq)) && is.na(ICC)) {
ICC = sigma_b_sq / (sigma_b_sq + sigma_sq)
}
# sigma_b_sq2, sigma_sq2, ICC2
if (!is.na(c(ICC2, sigma_sq2)) && is.na(sigma_b_sq2)) {
sigma_b_sq2 = ICC2 * sigma_sq2 / (1 - ICC2)
}
if (!is.na(c(ICC2, sigma_b_sq2)) && is.na(sigma_sq2)) {
sigma_sq2 = sigma_b_sq2 / ICC2 - sigma_b_sq2
}
if (!is.na(c(sigma_sq2, sigma_b_sq2)) && is.na(ICC2)) {
ICC2 = sigma_b_sq2 / (sigma_b_sq2 + sigma_sq2)
}
# Set within/between cluster variances & ICC for arm (if not already specified)
if (isTRUE(is.na(sigma_sq2))) {
sigma_sq2 <- sigma_sq
}
if (isTRUE(is.na(sigma_b_sq2))) {
sigma_b_sq2 <- sigma_b_sq
}
if (isTRUE(is.na(ICC2))) {
ICC2 <- ICC
}
# Validate mu, mu2, ALPHA
if (is.na(mu) || is.na(mu2)) {
stop("MU and MU2 are required.")
}
min0.warning = " must be numeric."
if (!is.numeric(mu) || !is.numeric(mu2)) {
stop("MU and MU2", min0.warning)
}
if (!is.numeric(alpha) || alpha < 0 || alpha > 1) {
stop("ALPHA must be a numeric value between 0 - 1")
}
# Validate ICC, sigma_sq, sigma_b_sq, ICC2, sigma_sq2, sigma_b_sq2
parm1.arg.list = list(ICC, sigma_sq, sigma_b_sq)
parm1.args = unlist(lapply(parm1.arg.list, is.na))
if (sum(parm1.args) > 1) {
stop("At least two of the following terms must be specified: ICC, sigma_sq, sigma_b_sq")
}
if (round(ICC, 2) != round((sigma_b_sq / (sigma_b_sq + sigma_sq)), 2)) {
stop("At least one of the following terms has been misspecified: ICC, sigma_sq, sigma_b_sq")
}
parm2.arg.list = list(ICC2, sigma_sq2, sigma_b_sq2)
parm2.args = unlist(lapply(parm2.arg.list, is.na))
if (sum(parm2.args) > 1 && sum(parm2.args) != 3) {
stop(
"At least two of the following terms must be provided to simulate arm-specific
variances: ICC2, sigma_sq2, sigma_b_sq2"
)
}
if (round(ICC2, 2) != round((sigma_b_sq2 / (sigma_b_sq2 + sigma_sq2)), 2)) {
stop(
"At least one of the following terms has been misspecified: ICC2, sigma_sq2, sigma_b_sq2"
)
}
# Validate METHOD, QUIET, ALL.SIM.DATA
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(
"ALL.SIM.DATA must be either TRUE (Output all simulated data sets) or FALSE (No simulated data output"
)
}
# Create indicators for arm & cluster
if (is.list(nsubjects)){
nsubjects <- unlist(nsubjects)
}
trt = c(rep(1, length.out = sum(nsubjects[1:nclusters[1]])),
rep(2, length.out = sum(nsubjects[(nclusters[1] + 1):(nclusters[1] + nclusters[2])])))
clust = unlist(lapply(1:sum(nclusters), function(x)
rep(x, length.out = nsubjects[x])))
# Create simulation loop
for (i in 1:nsim) {
# Generate between-cluster effects
randint.0 = stats::rnorm(nclusters[1], mean = 0, sd = sqrt(sigma_b_sq))
randint.1 = stats::rnorm(nclusters[2], mean = 0, sd = sqrt(sigma_b_sq2))
# Create y-value for the first arm
y0.bclust = unlist(lapply(1:nclusters[1], function(x)
rep(randint.0[x], length.out = nsubjects[x])))
y0.wclust = unlist(lapply(nsubjects[1:nclusters[1]], function(x)
stats::rnorm(
x, mean = mu, sd = sqrt(sigma_sq)
)))
y.0 = y0.bclust + y0.wclust
# Create y-value for the second arm
y1.bclust = unlist(lapply(1:nclusters[2], function(x)
rep(randint.1[x], length.out = nsubjects[nclusters[1] + x])))
y1.wclust = unlist(lapply(nsubjects[(nclusters[1] + 1):(nclusters[1] + nclusters[2])],
function(x)
stats::rnorm(
x, mean = mu2, sd = sqrt(sigma_sq2)
)))
y.1 = y1.bclust + y1.wclust
# Create single response vector
y = c(y.0, y.1)
# Create data frame for simulated dataset
sim.dat = data.frame(y = y, trt = trt, clust = clust)
if (allSimData == TRUE) {
simulated.datasets[[i]] = sim.dat
}
# option to return simulated data only
if (nofit == TRUE) {
if (i == 1) {
nofitop <- data.frame(trt = trt,
clust = clust,
y1 = y)
} else {
nofitop[, i + 2] <- y
}
if (i != nsim) {
next()
}
if (i == nsim) {
temp1 <- seq(1:nsim)
temp2 <- paste0("y", temp1)
colnames(nofitop) <- c("arm", "clust", temp2)
return(nofitop)
}
}
#set start time
start.time = Sys.time()
# trt and clust are re-coded as trt2 and clust2 to work nicely with lme.
# Fit GLMM (lmer)
if (method == 'glmm') {
if (irgtt == TRUE) {
if (sigma_sq != sigma_sq2 && sigma_b_sq != sigma_b_sq2) {
trt2 <- unlist(trt)
clust2 <- unlist(clust)
my.mod <-
try(nlme::lme(
y ~ as.factor(trt2),
random = ~ 0 + as.factor(trt2) | clust2,
weights = nlme::varIdent(form = ~ 1 |
as.factor(trt2)),
method = "ML",
control = nlme::lmeControl(opt = 'optim')
),
silent = TRUE)
glmm.values <- summary(my.mod)$tTable
# get the overall p-values (>Chisq)
null.mod <-
try(nlme::lme(
y ~ 1,
random = ~ 0 + as.factor(trt2) | clust2,
weights = nlme::varIdent(form = ~ 1 |
as.factor(trt2)),
method = "ML",
control = nlme::lmeControl(opt = 'optim')
),
silent = TRUE)
pval.vector[i] = glmm.values['as.factor(trt2)2', 'p-value']
est.vector[i] = glmm.values['as.factor(trt2)2', 'Value']
se.vector[i] = glmm.values['as.factor(trt2)2', 'Std.Error']
stat.vector[i] = glmm.values['as.factor(trt2)2', 't-value']
converge.vector[i] <-
ifelse(isTRUE(class(my.mod) == "try-error"), FALSE, TRUE)
}
if (sigma_sq == sigma_sq2 && sigma_b_sq != sigma_b_sq2) {
my.mod <-
lmerTest::lmer(y ~ trt + (0 + as.factor(trt) | clust),
REML = FALSE,
data = sim.dat)
# get the overall p-values (>Chisq)
null.mod <-
stats::update.formula(my.mod, y ~ 1 + (0 + as.factor(trt) |
clust))
glmm.values[i] = summary(my.mod)$coefficients
pval.vector[i] = glmm.values['trt', 'Pr(>|t|)']
est.vector[i] = glmm.values['trt', 'Estimate']
se.vector[i] = glmm.values['trt', 'Std. Error']
stat.vector[i] = glmm.values['trt', 't value']
converge.vector[i] = ifelse(any(
grepl("singular",
my.mod@optinfo$conv$lme4$messages)
) == FALSE, TRUE, FALSE)
# option to stop the function early if fits are singular
if (poorFitOverride == FALSE && converge.vector[i] == FALSE) {
if (sum(converge.vector == FALSE, na.rm = TRUE) > (nsim * .25)) {
stop(
"more than 25% of simulations are singular fit: check model specifications"
)
}
}
}
#if not IRGTT, then the following:
} else {
if (sigma_sq != sigma_sq2 && sigma_b_sq != sigma_b_sq2) {
trt2 <- unlist(trt)
clust2 <- unlist(clust)
oldw <- getOption("warn")
options(warn = -1)
my.mod <-
try(nlme::lme(
y ~ as.factor(trt2),
random = ~ 0 + as.factor(trt2) | clust2,
weights = nlme::varIdent(form = ~ 1 |
as.factor(trt2)),
method = "ML",
control = nlme::lmeControl(opt = 'optim')
),
silent = TRUE)
if (class(my.mod) != "try-error") {
glmm.values <- summary(my.mod)$tTable
# get the overall p-values (>Chisq)
null.mod <-
try(nlme::lme(
y ~ 1,
random = ~ 0 + as.factor(trt2) | clust2,
weights = nlme::varIdent(form = ~ 1 |
as.factor(trt2)),
method = "ML",
control = nlme::lmeControl(opt = 'optim')
),
silent = TRUE)
options(warn = oldw)
pval.vector[i] = glmm.values['as.factor(trt2)2', 'p-value']
est.vector[i] = glmm.values['as.factor(trt2)2', 'Value']
se.vector[i] = glmm.values['as.factor(trt2)2', 'Std.Error']
stat.vector[i] = glmm.values['as.factor(trt2)2', 't-value']
}
converge.vector[i] <-
ifelse(isTRUE(class(my.mod) == "try-error"), FALSE, TRUE)
}
if (sigma_sq == sigma_sq2 && sigma_b_sq != sigma_b_sq2) {
my.mod <-
lmerTest::lmer(y ~ trt + (0 + as.factor(trt) | clust),
REML = FALSE,
data = sim.dat)
# get the overall p-values (>Chisq)
null.mod <-
stats::update.formula(my.mod, y ~ 1 + (0 + as.factor(trt) |
clust))
glmm.values = summary(my.mod)$coefficients
pval.vector[i] = glmm.values['trt', 'Pr(>|t|)']
est.vector[i] = glmm.values['trt', 'Estimate']
se.vector[i] = glmm.values['trt', 'Std. Error']
stat.vector[i] = glmm.values['trt', 't value']
converge.vector[i] = ifelse(any(
grepl("singular",
my.mod@optinfo$conv$lme4$messages)
) == FALSE, TRUE, FALSE)
# option to stop the function early if fits are singular
if (poorFitOverride == FALSE) {
if (sum(converge.vector == FALSE, na.rm = TRUE) > (nsim * .25)) {
stop(
"more than 25% of simulations are singular fit: check model specifications"
)
}
}
}
if (sigma_sq != sigma_sq2 && sigma_b_sq == sigma_b_sq2) {
trt2 <- unlist(trt)
clust2 <- unlist(clust)
oldw <- getOption("warn")
options(warn = -1)
my.mod <-
try(nlme::lme(
y ~ as.factor(trt2),
random = ~ 1 + as.factor(trt2) | clust2,
weights = nlme::varIdent(form = ~ 1 |
as.factor(trt2)),
method = "ML",
control = nlme::lmeControl(opt = 'optim')
),
silent = TRUE)
glmm.values <- summary(my.mod)$tTable
# get the overall p-values (>Chisq)
null.mod <-
try(nlme::lme(
y ~ 1,
random = ~ 1 + as.factor(trt2) | clust2,
weights = nlme::varIdent(form = ~ 1 |
as.factor(trt2)),
method = "ML",
control = nlme::lmeControl(opt = 'optim')
),
silent = TRUE)
options(warn = oldw)
pval.vector[i] = glmm.values['as.factor(trt2)2', 'p-value']
est.vector[i] = glmm.values['as.factor(trt2)2', 'Value']
se.vector[i] = glmm.values['as.factor(trt2)2', 'Std.Error']
stat.vector[i] = glmm.values['as.factor(trt2)2', 't-value']
converge.vector[i] <-
ifelse(isTRUE(class(my.mod) == "try-error"), FALSE, TRUE)
}
if (sigma_sq == sigma_sq2 && sigma_b_sq == sigma_b_sq2) {
my.mod <- lmerTest::lmer(y ~ trt + (1 | clust), REML = FALSE,
data = sim.dat)
# get the overall p-values (>Chisq)
null.mod <- update.formula(my.mod, y ~ 1 + (1 | clust))
glmm.values = summary(my.mod)$coefficients
pval.vector[i] = glmm.values['trt', 'Pr(>|t|)']
est.vector[i] = glmm.values['trt', 'Estimate']
se.vector[i] = glmm.values['trt', 'Std. Error']
stat.vector[i] = glmm.values['trt', 't value']
converge.vector[i] = ifelse(any(
grepl("singular",
my.mod@optinfo$conv$lme4$messages)
) == TRUE, FALSE, TRUE)
# option to stop the function early if fits are singular
if (poorFitOverride == FALSE) {
if (sum(converge.vector == FALSE, na.rm = TRUE) > (nsim * .25)) {
stop(
"more than 25% of simulations are singular fit: check model specifications"
)
}
}
}
}
}
# Fit GEE (geeglm)
# Note: there is no option for GEE with irgtt
if (method == 'gee') {
sim.dat = dplyr::arrange(sim.dat, clust)
my.mod = geepack::geeglm(y ~ trt,
data = sim.dat,
id = clust,
corstr = "exchangeable")
gee.values = summary(my.mod)$coefficients
est.vector[i] = gee.values['trt', 'Estimate']
se.vector[i] = gee.values['trt', 'Std.err']
stat.vector[i] = gee.values['trt', 'Wald']
pval.vector[i] = gee.values['trt', 'Pr(>|W|)']
converge.vector[i] <- ifelse(summary(my.mod)$error == 0, TRUE, FALSE)
}
# stop the loop if power is <0.5
if (lowPowerOverride == FALSE && i > 50 && (i %% 10 == 0)) {
sig.val.temp <-
ifelse(pval.vector < alpha, 1, 0)
pval.power.temp <- sum(sig.val.temp, na.rm = TRUE) / i
if (pval.power.temp < 0.5) {
stop(
paste(
"Calculated power is < ",
pval.power.temp,
". Set lowPowerOverride == TRUE to run the simulations anyway.",
sep = ""
)
)
}
}
# Update simulation progress information
if (quiet == FALSE) {
if (i == 1) {
avg.iter.time = as.numeric(difftime(Sys.time(), start.time, units = 'secs'))
time.est = avg.iter.time * (nsim - 1) / 60
hr.est = time.est %/% 60
min.est = round(time.est %% 60, 3)
if (min.est > 2 && timelimitOverride == FALSE){
stop(paste0("Estimated completion time: ",
hr.est,
'Hr:',
min.est,
'Min'
))
}
message(
paste0(
'Begin simulations :: Start Time: ',
Sys.time(),
' :: Estimated completion time: ',
hr.est,
'Hr:',
min.est,
'Min'
)
)
}
# Iterate progress bar
prog.bar$update(i / nsim)
Sys.sleep(1 / 100)
if (i == nsim) {
total.est = as.numeric(difftime(Sys.time(), start.time, units = 'secs'))
hr.est = total.est %/% 3600
min.est = total.est %/% 60
sec.est = round(total.est %% 60, 3)
message(
paste0(
"Simulations Complete! Time Completed: ",
Sys.time(),
"\nTotal Runtime: ",
hr.est,
'Hr:',
min.est,
'Min:',
sec.est,
'Sec'
)
)
}
}
}
## Output objects
# Create object containing summary statement
if (irgtt == FALSE) {
summary.message = paste0(
"Monte Carlo Power Estimation based on ",
nsim,
" Simulations: Parallel Design, Continuous Outcome"
)
} else {
summary.message = paste0(
"Monte Carlo Power Estimation based on ",
nsim,
" Simulations: IRGTT Design, Continuous Outcome"
)
}
# Create method object
long.method = switch(method, glmm = 'Generalized Linear Mixed Model',
gee = 'Generalized Estimating Equation')
# Store simulation 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
cps.model.temp <- dplyr::filter(cps.model.est, converge == TRUE)
power.parms <- confintCalc(alpha = alpha,
nsim = nsim,
p.val = cps.model.temp[, 'p.value'])
# Create object containing group-specific cluster sizes
cluster.sizes = list('Arm.1' = nsubjects[1:nclusters[1]],
'Arm.2' = nsubjects[(nclusters[1] + 1):(nclusters[1] + nclusters[2])])
# Create object containing number of clusters
n.clusters = t(data.frame(
"Arm.1" = c("n.clust" = nclusters[1]),
"Arm.2" = c("n.clust" = nclusters[2])
))
# Create object containing group-specific variance parameters
var.parms = t(data.frame(
'Arm.1' = c(
'ICC' = ICC[1],
'sigma_sq' = sigma_sq[1],
'sigma_b_sq' = sigma_b_sq[1],
'mu' = mu
),
'Arm.2' = c(
'ICC' = ICC2,
'sigma_sq' = sigma_sq2,
'sigma_b_sq' = sigma_b_sq2,
'mu' = mu2
)
))
fail <- unlist(converge.vector)
# Create list containing all output (class 'crtpwr') and return
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,
"means" = c(mu, mu2),
"model.estimates" = cps.model.est,
"convergence" = fail,
"sim.data" = simulated.datasets
),
class = 'crtpwr'
)
return(complete.output)
}
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