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adding DID function accounting for loss to follow-up, need to see if …

…documentation should go in man or in vignette
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jm3594 committed May 13, 2019
1 parent 57af36c commit 06a7ce993bb3874664953f0ed8639fb3b8b9ca36
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  1. +1 −0 NAMESPACE
  2. +200 −0 R/crtpwr.2meanD.ltf.R
  3. +100 −0 man/crtpwr.2meanD.ltf.Rd
@@ -19,6 +19,7 @@ export(createMissingVarianceParam)
export(crtpwr.2mean)
export(crtpwr.2meanCA)
export(crtpwr.2meanD)
export(crtpwr.2meanD.ltf)
export(crtpwr.2meanM)
export(crtpwr.2prop)
export(crtpwr.2propD)
@@ -0,0 +1,200 @@
#' Power calculations for difference-in-difference cluster randomized trials accounting for loss to and gain at follow-up, continuous outcome
#'
#' Compute the power of a difference-in-difference cluster randomized trial design with a continuous outcome,
#' accounting for potential loss to or gain at follow-up, or determine parameters to obtain a target power.
#'
#' Exactly one of \code{alpha}, \code{power}, \code{nclusters}, \code{nsubjects},
#' \code{d}, \code{icc}, \code{rho_c}, \code{rho_s}, and \code{vart}
#' must be passed as \code{NA}. Note that \code{alpha} and\code{power}
#' have non-\code{NA} defaults, so if those are the parameters of
#' interest they must be explicitly passed as \code{NA}.
#'
#' @section Note:
#' This function was inspired by work from Stephane Champely (pwr.t.test) and
#' Peter Dalgaard (power.t.test). As with those functions, 'uniroot' is used to
#' solve power equation for unknowns, so you may see
#' errors from it, notably about inability to bracket the root when
#' invalid arguments are given.
#'
#' @section Authors:
#' @section Authors:
#' Jonathan Moyer (\email{jon.moyer@@gmail.com}), Ken Kleinman (\email{ken.kleinman@@gmail.com})
#'
#' @param alpha The level of significance of the test, the probability of a
#' Type I error.
#' @param power The power of the test, 1 minus the probability of a Type II
#' error.
#' @param nclusters The number of clusters per condition at baseline. It must be greater than 1.
#' @param nsubjects The number of subjects per cluster at baseline.
#' @param d The difference in mean change between conditions (i.e. "difference-in-difference").
#' @param icc The intraclass correlation.
#' @param rho_c The correlation between baseline and post-test outcomes at the
#' cluster level. This value can be used in both cross-sectional and cohort
#' designs. If this quantity is unknown, a value of 0 is a conservative estimate.
#' @param rho_s The correlation between baseline and post-test outcomes at the
#' subject level assuming the a cohort design with no loss or gain to follow-up. Entering a value
#' of 0 for this parameter is equivalent to a cross-sectional design and automatically sets \code{ltf_0}, \code{ltf_1},
#' \code{gtf_0}, and \code{gtf_1} all to 1.
#' @param vart The total variation of the outcome (the sum of within- and between-cluster variation).
#' @param ltf A length 2 vector indicating the proportion lost to follow-up per cluster in terms of \code{nsubjects}
#' in the control and treatment arms. The first element corresponds to the proportion lost in the control
#' group, while the second element correponds to the proportion lost in the treatment group. Entering a scalar
#' for \code{ltf} will set both elements of the vector to that value. If \code{rho_s} is 0 then both elements
#' will be set to 1.
#' @param gtf A length 2 vector indicating the proportion gained at follow-up per cluster in terms of \code{nsubjects}
#' in the control and treatment arms. The first element corresponds to the proportion gained in the control
#' group, while the second element correponds to the proportion gained in the treatment group. By default, \code{gtf}
#' is set to \code{ltf}. Entering a scalar for \code{gtf} will set both elements of the vector to that value.
#' If \code{rho_s} is 0 then both elements will be set to 1.
#' @param tol Numerical tolerance used in root finding. The default provides
#' at least four significant digits.
#' @return The computed argument.
#' @examples
#' # Find the number of clusters per condition needed for a trial with alpha = 0.05,
#' # power = 0.80, nsubjects = 20, d = 0.50 units, icc = 0.05, rho_c = 0.50, rho_s = 0.70,
#' # and vart = 1 square unit if 50 percent of subjects in each cluster are lost to follow-up
#' # and replaced.
#' crtpwr.2meanD.ltf(nsubjects = 100 , d = 0.5, icc = 0.05, rho_c = 0.50, rho_s = 0.70, vart = 1,ltf=0.5)
#' #
#' # The result, nclusters = 8.099772, suggests 9 clusters per condition should be used.
#'
#' @references Rutterford C, Copas A, Eldridge S. (2015) Methods for sample size
#' determination in cluster randomized trials. Int J Epidemiol. 44(3):1051-1067.
#' @references Teerenstra S, Eldridge S, Graff M, de Hoop E, Borm, GF. (2012) A simple
#' sample size formula for analysis of covariance in cluster randomized trials.
#' Statist Med. 31:2169-2178
#'
#' @export
#'

crtpwr.2meanD.ltf <- function(alpha = 0.05, power = 0.80, nclusters = NA,
nsubjects = NA, d = NA, icc = NA,
rho_c = NA, rho_s = NA, vart = NA,
ltf = c(0,0), gtf = ltf,
tol = .Machine$double.eps^0.25){

if(!is.na(nclusters) && nclusters <= 1) {
stop("'nclusters' must be greater than 1.")
}

if(!is.na(nsubjects) && nsubjects <= 1) {
stop("'nsubjects' must be greater than 1.")
}

# rho_s = 0 corresponds to a cross-sectional design in which ltfs and gtfs equal 1
if(!is.na(rho_s) && rho_s == 0) {
ltf <- gtf <- c(1,1)
}

if(length(ltf) > 2 | length(gtf) > 2){
stop("'ltf' and 'gtf' cannot contain have length greater than 2.")
}

if(length(ltf) == 1){
ltf <- c(ltf,ltf)
}

if(length(gtf) == 1){
gtf <- c(gtf,gtf)
}

# list of needed inputs
needlist <- list(alpha, power, nclusters, nsubjects, d, icc, rho_c, rho_s, vart)
neednames <- c("alpha", "power", "nclusters", "nsubjects", "d", "icc",
"rho_c", "rho_s", "vart")
needind <- which(unlist(lapply(needlist, is.na)))
# check to see that exactly one needed param is NA

if (length(needind) != 1) {
neederror = "Exactly one of 'alpha', 'power', 'nclusters', 'nsubjects', 'd', 'icc', 'rho_c', 'rho_s', and 'vart' must be NA."
stop(neederror)
}

target <- neednames[needind]

# evaluate power
pwr <- quote({

varc <- icc*rho_c*vart
varct <- icc*(1-rho_c)*vart
vars <- (1-icc)*rho_s*vart
varst <- (1-icc)*(1-rho_s)*vart

# ltf[1], gtf[1] are loss, gain to follow-up in control arm
# ltf[2], gtf[2] are loss, gain to follow-up in treatment arm
eta <- (1-ltf[1])/(1-ltf[1]+gtf[1]) + (1-ltf[2])/(1-ltf[2]+gtf[2]) - 1
rho_s_star <- rho_s - 0.25*( 1/(1-ltf[1]+gtf[1]) + 1/(1-ltf[2]+gtf[2]) - 2*(eta*vars+varst)/(vars+varst) )

vardid <- 4*( varct/nclusters + (1-rho_s_star)*(vars+varst)/(nclusters*nsubjects) )

tcrit <- qt(alpha/2, 2*(nclusters - 1), lower.tail = FALSE)

ncp <- abs(d)/sqrt(vardid)

pt(tcrit, 2*(nclusters - 1), ncp, lower.tail = FALSE)#+
#pt(-tcrit, 2*(nclusters - 1), ncp, lower.tail = TRUE)
})

# calculate alpha
if (is.na(alpha)) {
alpha <- stats::uniroot(function(alpha) eval(pwr) - power,
interval = c(1e-10, 1 - 1e-10),
tol = tol)$root
}

# calculate power
if (is.na(power)) {
power <- eval(pwr)
}

# calculate nclusters
if (is.na(nclusters)) {
nclusters <- stats::uniroot(function(nclusters) eval(pwr) - power,
interval = c(2 + 1e-10, 1e+07),
tol = tol, extendInt = "upX")$root
}

# calculate nsubjects
if (is.na(nsubjects)) {
nsubjects <- stats::uniroot(function(nsubjects) eval(pwr) - power,
interval = c(2 + 1e-10, 1e+07),
tol = tol, extendInt = "upX")$root
}

# calculate d
if (is.na(d)) {
d <- stats::uniroot(function(d) eval(pwr) - power,
interval = c(1e-07, 1e+07),
tol = tol, extendInt = "upX")$root
}

# calculate icc
if (is.na(icc)){
icc <- stats::uniroot(function(icc) eval(pwr) - power,
interval = c(1e-07, 1 - 1e-07),
tol = tol)$root
}

# calculate rho_c
if (is.na(rho_c)){
rho_c <- stats::uniroot(function(rho_c) eval(pwr) - power,
interval = c(1e-07, 1 - 1e-07),
tol = tol)$root
}

# calculate rho_s
if (is.na(rho_s)){
rho_s <- stats::uniroot(function(rho_s) eval(pwr) - power,
interval = c(1e-07, 1 - 1e-07),
tol = tol)$root
}

# calculate vart
if (is.na(vart)) {
vart <- stats::uniroot(function(vart) eval(pwr) - power,
interval = c(1e-07, 1e+07),
tol = tol, extendInt = "downX")$root
}

structure(get(target), names = target)
}

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