R/qrjm.R
In AntoineBbi/BQt: BQt: Bayesian Quantile regression for joint modeling
Defines functions
qrjm
Documented in
qrjm
#' \code{qrjm} fits quantile regression joint model
#'
#' Function using JAGS via jagsUI package to estimate the quantile regression joint model assuming asymmetric Laplace distribution for residual error.
#' Joint modeling concerns longitudinal data and time-to-event
#'
#'
#' @param formFixed formula for fixed part of longitudinal submodel with response variable
#' @param formRandom formula for random part of longitudinal submodel without response variable
#' @param formGroup formula specifying the cluster variable (e.g. = ~ subject)
#' @param formSurv survival formula as formula in survival package for latency submodel
#' @param survMod specifying the baseline risk function for Cox proportional hazard model (only "weibull" is available until now)
#' @param param shared association including in joint modeling: the classical shared random effects or the current value denoting by "sharedRE" (default) or "value", respectively.
#' @param timeVar string specify the names of time variable (time of repeated measurements)
#' @param data dataset of observed variables
#' @param tau the quantile(s) to be estimated. This must be a number between 0 and 1, otherwise the execution is stopped. If more than one quantile is specified, rounding off to the 4th decimal must give non–duplicated values of \code{tau}, otherwise the execution is stopped.
#' @param RE_ind Boolean denoting if the random effects are assumed independent ; default is \code{FALSE}
#' @param n.chains the number of parallel chains for the model; default is 1.
#' @param n.iter integer specifying the total number of iterations; default is 10000
#' @param n.burnin integer specifying how many of n.iter to discard as burn-in ; default is 5000
#' @param n.thin integer specifying the thinning of the chains; default is 1
#' @param n.adapt integer specifying the number of iterations to use for adaptation; default is 5000
#' @param precision variance by default for vague prior distribution
#' @param C value used in the zero trick; default is 1000.
#' @param save_va If TRUE (is FALSE by default), the draws of auxilary variable W is returned by the function
#' @param save_jagsUI If TRUE (by default), the output of jagsUI package is returned by the function
#' @param parallel see jagsUI::jags() function
#'
#'
#' @return A \code{BQt} object is a list with the following elements:
#' \describe{
#' \item{\code{mean}}{list of posterior mean for each parameter}
#' \item{\code{median}}{list of posterior median for each parameter}
#' \item{\code{modes}}{list of posterior mode for each parameter}
#' \item{\code{StErr}}{list of standard error for each parameter}
#' \item{\code{StDev}}{list of standard deviation for each parameter}
#' \item{\code{ICs}}{list of the credibility interval at 0.95 for each parameters excepted for covariance parameters in covariance matrix of random effects. Otherwise, use save_jagsUI=TRUE to have the associated quantiles.}
#' \item{\code{data}}{data included in argument}
#' \item{\code{sims.list}}{list of the MCMC chains of the parameters and random effects}
#' \item{\code{control}}{list of arguments giving details about the estimation}
#' \item{\code{random_effect}}{list for each quantile including both posterior mean and posterior standard deviation of subject-specific random effects}
#' \item{\code{out_jagsUI}}{only if \code{save_jagsUI=TRUE} in argument: list including posterior mean, median, quantiles (2.5%, 25%, 50%, 75%, 97.5%), standart deviation for each parameter and each random effect.
#' Moreover, this list also returns the MCMC draws, the Gelman and Rubin diagnostics (see output of jagsUI objects)}
#' }
#'
#' @author Antoine Barbieri
#'
#' @import jagsUI lqmm survival
#'
#' @export
#'
#' @references Ming Yang, Sheng Luo, and Stacia DeSantis (2019).
#' \emph{Bayesian quantile regression joint models: Inference and dynamic predictions}.
#' Statistical Methods in Medical Research, 28(8):2524-2537. doi: 10.1177/0962280218784757.
#'
#' @examples
#'
#' \dontrun{
#' #---- use the data 'aids' from joineR package
#' data("aids", package = "joineR")
#'
#' #---- Fit quantile regression joint model for the first quartile
#' qrjm_25 <- qrjm(formFixed = CD4 ~ obstime,
#' formRandom = ~ obstime,
#' formGroup = ~ id,
#' formSurv = Surv(time, death) ~ drug + gender + prevOI + AZT,
#' survMod = "weibull",
#' param = "value",
#' timeVar= "obstime",
#' data = aids,
#' tau = 0.25)
#'
#' #---- Visualize the trace for beta parameters
#' jagsUI::traceplot(qrjm_25$out_jagsUI, parameters = "beta" )
#'
#' #---- Get the estimated coefficients : posterior means
#' qrjm_25$mean
#'
#' #---- Summary of output
#' BQt::summary.BQt(qrjm_25)
#' }
#'
qrjm <- function(formFixed,
formRandom,
formGroup,
formSurv,
survMod = "weibull",
param = "value",
timeVar,
data,
tau,
RE_ind = FALSE,
n.chains = 3,
n.iter = 10000,
n.burnin = 5000,
n.thin = 5,
n.adapt = 5000,
precision = 10,
C = 1000,
save_jagsUI = TRUE,
save_va = FALSE,
parallel = FALSE){
# #
# # -- To do
# # verify with value.IG
# # add a stopping convergence criteria
# # initialize the values of parameter chains and to fix the intercept to test the convergence of beta's parameter.
# #
#
#-- data management
# control
lag = 0
#--- longitudinal part
data_long <- data[unique(c(all.vars(formGroup),all.vars(formFixed),all.vars(formRandom)))]
y <- data_long[all.vars(formFixed)][, 1]
mfX <- model.frame(formFixed, data = data_long)
X <- model.matrix(formFixed, mfX)
mfU <- model.frame(formRandom, data = data_long)
U <- model.matrix(formRandom, mfU)
id <- as.integer(data_long[all.vars(formGroup)][,1])
offset <- as.vector(c(1, 1 + cumsum(tapply(id, id, length))))
I <- length(unique(id))
if(!("id" %in% colnames(data_long)))
data_long <- cbind(data_long, id = id)
# use lqmm function to initiated values
cat("> Initialisation of longitudinal parameter values using 'lqmm' package. \n")
tmp_model <- lqmm::lqmm(fixed = formFixed,
random = formRandom,
group = id,
tau = tau,
data = data_long)
# prior beta parameters
priorMean.beta <- coef(tmp_model)
priorTau.beta <- diag(rep(1/10,length(priorMean.beta)))
bis <- as.matrix(lqmm::ranef(tmp_model))
bis[abs(bis)<.0001] <- 0
initial.values <- list(b = bis,
beta = priorMean.beta,
sigma = tmp_model$scale)
# list of data jags
jags.data <- list(y = y,
X = X,
U = U,
tau = tau,
ncX = ncol(X),
ncU = ncol(U),
I = I,
offset = offset,
priorMean.beta = priorMean.beta,
priorTau.beta = priorTau.beta,
priorA.sigma = 1/precision,
priorB.sigma = 1/precision
)
if(jags.data$ncU==1)
RE_ind <- TRUE
if(RE_ind){
jags.data <- c(jags.data,
list(priorA.Sigma2 = 1/precision,
priorB.Sigma2 = 1/precision
)
)
initial.values$prec.Sigma2 <- 1/VarCorr(tmp_model)
}else{
jags.data <- c(jags.data,
list(priorR.Sigma2 = diag(rep(1/precision, ncol(U))),
priorK.Sigma2 = ncol(U),
mu0 = rep(0, ncol(U))
)
)
initial.values$prec.Sigma2 <- diag(1/lqmm::VarCorr(tmp_model))
}
#--- survival part
tmp <- data[c(all.vars(formGroup),all.vars(formSurv))]
tmp <- unique(tmp)
Time <- tmp[all.vars(formSurv)][, 1] # matrix of observed time such as Time=min(Tevent,Tcens)
event <- tmp[all.vars(formSurv)][, 2] # vector of event indicator (delta)
nTime <- length(Time) # number of subject having Time
zeros <- numeric(nTime) # for zero trick in Bayesian procedure
# design matrice
mfZ <- model.frame(formSurv, data = tmp)
Z <- model.matrix(formSurv, mfZ)
# use survival::coxph function to initiated values
cat("> Initialisation of survival parameter values using 'survival' package. \n")
tmp_model <- survival::coxph(formSurv,
data = tmp,
x = TRUE)
# Complete the jags data
priorMean.alpha <- c(0, tmp_model$coefficients)
priorTau.alpha <- diag(c(1/precision, 1/(precision*diag(tmp_model$var))))
jags.data <- c(jags.data,
list(C = C,
zeros = numeric(nTime),
Time = Time,
event = event,
Z = Z,
ncZ = ncol(Z),
priorMean.alpha = priorMean.alpha,
priorTau.alpha = priorTau.alpha,
priorTau.alphaA = 1/precision)
)
# initialisation values of survival parameters
initial.values$alpha <- c(0, tmp_model$coefficients)
# if(survMod=="weibull")
# initial.values$shape <- 1
if(param=="value")
initial.values$alpha.assoc <- 0
if(param=="sharedRE")
initial.values$alpha.assoc <- rep(0, ncol(U))
#--- shared current value case
data.id <- data_long[!duplicated(id), ]
if (!timeVar %in% names(data_long))
stop("\n'timeVar' does not correspond to one of the columns in formulas")
if (param %in% c("value")) {
data.id[[timeVar]] <- pmax(Time - lag, 0)
mfX.id <- model.frame(formFixed, data = data.id)
Xtime <- model.matrix(formFixed, mfX.id)
mfU.id <- model.frame(formRandom, data = data.id)
Utime <- model.matrix(formRandom, mfU.id)
# if (one.RE)
# Utime <- cbind(Utime, rep(0, nrow(Utime)))
jags.data <- c(jags.data, list(Xtime = Xtime, Utime = Utime))
#-- approxitmation of the intergral via the Gaussian quadrature (Gauss Kronrod rule)
gaussKronrod <-
function (k = 15) {
sk <- c(-0.949107912342758524526189684047851, -0.741531185599394439863864773280788, -0.405845151377397166906606412076961, 0,
0.405845151377397166906606412076961, 0.741531185599394439863864773280788, 0.949107912342758524526189684047851, -0.991455371120812639206854697526329,
-0.864864423359769072789712788640926, -0.586087235467691130294144838258730, -0.207784955007898467600689403773245, 0.207784955007898467600689403773245,
0.586087235467691130294144838258730, 0.864864423359769072789712788640926, 0.991455371120812639206854697526329)
wk15 <- c(0.063092092629978553290700663189204, 0.140653259715525918745189590510238, 0.190350578064785409913256402421014,
0.209482141084727828012999174891714, 0.190350578064785409913256402421014, 0.140653259715525918745189590510238, 0.063092092629978553290700663189204,
0.022935322010529224963732008058970, 0.104790010322250183839876322541518, 0.169004726639267902826583426598550, 0.204432940075298892414161999234649,
0.204432940075298892414161999234649, 0.169004726639267902826583426598550, 0.104790010322250183839876322541518, 0.022935322010529224963732008058970)
wk7 <- c(0.129484966168869693270611432679082, 0.279705391489276667901467771423780, 0.381830050505118944950369775488975,
0.417959183673469387755102040816327, 0.381830050505118944950369775488975, 0.279705391489276667901467771423780, 0.129484966168869693270611432679082)
if (k == 7)
list(sk = sk[1:7], wk = wk7)
else
list(sk = sk, wk = wk15)
}
wk <- gaussKronrod()$wk
sk <- gaussKronrod()$sk
K <- length(sk)
P <- Time/2
st <- outer(P, sk + 1)
id.GK <- rep(seq_along(Time), each = K)
data.id2 <- data.id[id.GK, ]
data.id2[[timeVar]] <- c(t(st))
mfX <- model.frame(formFixed, data = data.id2)
mfU <- model.frame(formRandom, data = data.id2)
Xs <- model.matrix(formFixed, mfX)
Us <- model.matrix(formRandom, mfU)
jags.data <- c(jags.data, list(K = K, P = P, st = st, wk = wk, Xs = Xs, Us = Us))
}
#---- Model for JAGS
# model to consider
model <- switch(paste(survMod, RE_ind, param, sep = "/"),
# wishart distribution when RE are considered dependent
`weibull/FALSE/value` = jags_qrjm.weib.value,
# inverse gamma distribution when RE are considered independent
`weibull/TRUE/value` = jags_qrjm.weib.value.IG,
# wishart distribution when RE are considered dependent
`weibull/FALSE/sharedRE` = jags_qrjm.weib.sharedRE,
# inverse gamma distribution when RE are considered independent
`weibull/TRUE/sharedRE` = jags_qrjm.weib.sharedRE.IG
)
# parameters to save in the sampling step
parms_to_save <- c("alpha", "alpha.assoc", "beta", "sigma", "b", "covariance.b")
if(save_va)
parms_to_save <- c(parms_to_save, "va1")
# complement given survMod
if(survMod == "weibull"){
jags.data <- c(jags.data, list(priorA.shape = 1/precision, priorB.shape = 1/precision))
parms_to_save <- c(parms_to_save, "shape")
}
# # initial values to improve chain convergence
# initial.values <- list(gamma = priorMean.gamma,
# alpha = priorMean.alpha,
# shape = 3)
#-- write jags model in txt from R function
working.directory = getwd()
write.model.jags(model = model,
name_model = "jags_qrjm",
intitled = file.path(working.directory, "JagsModel.txt"),
Data = jags.data,
param = param)
#---- use JAGS sampler
# if (!require("rjags"))
# stop("'rjags' is required.\n")
if(n.chains==3)
inits <- list(initial.values,
initial.values,
initial.values)
if(n.chains==2)
inits <- list(initial.values,
initial.values)
if(n.chains==1)
inits <- initial.values
# using jagsUI
out_jags = jagsUI::jags(data = jags.data,
parameters.to.save = parms_to_save,
model.file = "JagsModel.txt",
inits = inits,
n.chains = n.chains,
parallel = parallel,
n.adapt = n.adapt,
n.iter = n.iter,
n.burnin = n.burnin,
n.thin = n.thin,
DIC = F)
file.remove(file.path(working.directory, "JagsModel.txt"))
#---- output building
#-- MCMClist management
#- arguments
out <- list(data = data)
out$control <- list(formFixed = formFixed,
formRandom = formRandom,
formGroup = formGroup,
formSurv = formSurv,
timeVar = timeVar,
tau = tau,
call_function = "qrjm",
I = I,
C = C,
param = param,
survMod = survMod,
n.chains = n.chains,
parallel = parallel,
n.adapt = n.adapt,
n.iter = n.iter,
n.burnin = n.burnin,
n.thin = n.thin,
RE_ind = RE_ind,
event = event,
Time = Time)
#- other outputs
# sims.list output
out$sims.list <- out_jags$sims.list
out$sims.list$b <- NULL
if(save_va)
out$sims.list$va1 <- NULL
# random effect output
out$random_effect <- list(postMeans = out_jags$mean$b,
postSd = out_jags$sd$b)
colnames(out$random_effect$postMeans) <- colnames(U)
colnames(out$random_effect$postSd) <- colnames(U)
# median : Posterior median of parameters
out$median <- out_jags$q50
out$median$b <- NULL
# mean : Posterior mean of parameters
out$mean <- out_jags$mean
out$mean$b <- NULL
# modes of parameters
out$modes <- lapply(out$sims.list, function(x) {
m <- function(x) {
d <- density(x, bw = "nrd", adjust = 3, n = 1000)
d$x[which.max(d$y)]
}
if (is.matrix(x))
as.array(apply(x, 2, m))
else{
if(is.array(x))
apply(x, c(2,3), m)
else m(x)
}
})
# standard error of parameters
out$StErr <- lapply(out$sims.list, function(x) {
f <- function(x) {
acf.x <- drop(acf(x, lag.max = 0.4 * length(x), plot = FALSE)$acf)[-1]
acf.x <- acf.x[seq_len(rle(acf.x > 0)$lengths[1])]
ess <- length(x)/(1 + 2 * sum(acf.x))
sqrt(var(x)/ess)
}
if (is.matrix(x))
as.array(apply(x, 2, f))
else{
if(is.array(x))
apply(x, c(2,3), f)
else f(x)
}
})
# standard deviation of parameters
out$StDev <- out_jags$sd
out$StDev$b <- NULL
# Rhat : Gelman & Rubin diagnostic
out$Rhat <- out_jags$Rhat
out$Rhat$b <- NULL
# clean regarding auxilary variable (information avalaible in jagsUI output)
if(save_va)
out$median$va1 <- out$mean$va1 <- out$StDev$va1 <- out$Rhat$va1 <- NULL
# names
names(out$mean$beta) <-
names(out$median$beta) <-
names(out$modes$beta) <-
names(out$StErr$beta) <-
names(out$Rhat$beta) <-
names(out$StDev$beta) <- colnames(X)
if(RE_ind){
names(out$mean$covariance.b) <-
names(out$median$covariance.b) <-
names(out$modes$covariance.b) <-
names(out$StErr$covariance.b) <-
names(out$Rhat$covariance.b) <-
names(out$StDev$covariance.b) <- colnames(U)
}else{
colnames(out$mean$covariance.b) <-
rownames(out$mean$covariance.b) <-
colnames(out$median$covariance.b) <-
rownames(out$median$covariance.b) <-
colnames(out$modes$covariance.b) <-
rownames(out$modes$covariance.b) <-
colnames(out$Rhat$covariance.b) <-
rownames(out$Rhat$covariance.b) <-
colnames(out$StErr$covariance.b) <-
rownames(out$StErr$covariance.b) <-
colnames(out$StDev$covariance.b) <-
rownames(out$StDev$covariance.b) <- colnames(U)
}
names(out$mean$alpha) <-
names(out$median$alpha) <-
names(out$modes$alpha) <-
names(out$Rhat$alpha) <-
names(out$StErr$alpha) <-
names(out$StDev$alpha) <- colnames(Z)
# credible intervalles
out$CIs$beta <- cbind(as.vector(t(out_jags$q2.5$beta)),
as.vector(t(out_jags$q97.5$beta)))
rownames(out$CIs$beta) <- colnames(X)
colnames(out$CIs$beta) <- c("2.5%", "97.5%")
out$CIs$sigma <- c(out_jags$q2.5$sigma,
out_jags$q97.5$sigma)
names(out$CIs$sigma) <- c("2.5%", "97.5%")
out$CIs$shape <- c(out_jags$q2.5$shape,
out_jags$q97.5$shape)
names(out$CIs$shape) <- c("2.5%", "97.5%")
if(param %in% c("value")){
out$CIs$alpha.assoc <- c(out_jags$q2.5$alpha.assoc,
out_jags$q97.5$alpha.assoc)
names(out$CIs$alpha.assoc) <- c("2.5%", "97.5%")
}
if(param %in% c("sharedRE")){
if(jags.data$ncU>1){
out$CIs$alpha.assoc <- cbind(as.vector(t(out_jags$q2.5$alpha.assoc)),
as.vector(t(out_jags$q97.5$alpha.assoc)))
rownames(out$CIs$alpha.assoc) <- colnames(U)
colnames(out$CIs$alpha.assoc) <- c("2.5%", "97.5%")
}else{
out$CIs$alpha.assoc <- c(out_jags$q2.5$alpha.assoc,
out_jags$q97.5$alpha.assoc)
names(out$CIs$alpha.assoc) <- c("2.5%", "97.5%")
}
}
out$CIs$alpha <- cbind(as.vector(t(out_jags$q2.5$alpha)),
as.vector(t(out_jags$q97.5$alpha)))
rownames(out$CIs$alpha) <- colnames(Z)
colnames(out$CIs$alpha) <- c("2.5%", "97.5%")
# only for diagonal elements of covariance matrix of random effects
out$CIs$variances.b <- cbind(as.vector(diag(out_jags$q2.5$covariance.b)),
as.vector(diag(out_jags$q97.5$covariance.b)))
rownames(out$CIs$variances.b) <- colnames(U)
colnames(out$CIs$variances.b) <- c("2.5%", "97.5%")
# save jags output if requires
if(save_jagsUI)
out$out_jagsUI <- out_jags
#---- End of the function defining the class and retruning the output
class(out) <- "BQt"
out
}
AntoineBbi/BQt documentation built on June 25, 2022, 3:32 p.m.
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Defines functions qrjm
Documented in qrjm
#' \code{qrjm} fits quantile regression joint model
#'
#' Function using JAGS via jagsUI package to estimate the quantile regression joint model assuming asymmetric Laplace distribution for residual error.
#' Joint modeling concerns longitudinal data and time-to-event
#'
#'
#' @param formFixed formula for fixed part of longitudinal submodel with response variable
#' @param formRandom formula for random part of longitudinal submodel without response variable
#' @param formGroup formula specifying the cluster variable (e.g. = ~ subject)
#' @param formSurv survival formula as formula in survival package for latency submodel
#' @param survMod specifying the baseline risk function for Cox proportional hazard model (only "weibull" is available until now)
#' @param param shared association including in joint modeling: the classical shared random effects or the current value denoting by "sharedRE" (default) or "value", respectively.
#' @param timeVar string specify the names of time variable (time of repeated measurements)
#' @param data dataset of observed variables
#' @param tau the quantile(s) to be estimated. This must be a number between 0 and 1, otherwise the execution is stopped. If more than one quantile is specified, rounding off to the 4th decimal must give non–duplicated values of \code{tau}, otherwise the execution is stopped.
#' @param RE_ind Boolean denoting if the random effects are assumed independent ; default is \code{FALSE}
#' @param n.chains the number of parallel chains for the model; default is 1.
#' @param n.iter integer specifying the total number of iterations; default is 10000
#' @param n.burnin integer specifying how many of n.iter to discard as burn-in ; default is 5000
#' @param n.thin integer specifying the thinning of the chains; default is 1
#' @param n.adapt integer specifying the number of iterations to use for adaptation; default is 5000
#' @param precision variance by default for vague prior distribution
#' @param C value used in the zero trick; default is 1000.
#' @param save_va If TRUE (is FALSE by default), the draws of auxilary variable W is returned by the function
#' @param save_jagsUI If TRUE (by default), the output of jagsUI package is returned by the function
#' @param parallel see jagsUI::jags() function
#'
#'
#' @return A \code{BQt} object is a list with the following elements:
#' \describe{
#' \item{\code{mean}}{list of posterior mean for each parameter}
#' \item{\code{median}}{list of posterior median for each parameter}
#' \item{\code{modes}}{list of posterior mode for each parameter}
#' \item{\code{StErr}}{list of standard error for each parameter}
#' \item{\code{StDev}}{list of standard deviation for each parameter}
#' \item{\code{ICs}}{list of the credibility interval at 0.95 for each parameters excepted for covariance parameters in covariance matrix of random effects. Otherwise, use save_jagsUI=TRUE to have the associated quantiles.}
#' \item{\code{data}}{data included in argument}
#' \item{\code{sims.list}}{list of the MCMC chains of the parameters and random effects}
#' \item{\code{control}}{list of arguments giving details about the estimation}
#' \item{\code{random_effect}}{list for each quantile including both posterior mean and posterior standard deviation of subject-specific random effects}
#' \item{\code{out_jagsUI}}{only if \code{save_jagsUI=TRUE} in argument: list including posterior mean, median, quantiles (2.5%, 25%, 50%, 75%, 97.5%), standart deviation for each parameter and each random effect.
#' Moreover, this list also returns the MCMC draws, the Gelman and Rubin diagnostics (see output of jagsUI objects)}
#' }
#'
#' @author Antoine Barbieri
#'
#' @import jagsUI lqmm survival
#'
#' @export
#'
#' @references Ming Yang, Sheng Luo, and Stacia DeSantis (2019).
#' \emph{Bayesian quantile regression joint models: Inference and dynamic predictions}.
#' Statistical Methods in Medical Research, 28(8):2524-2537. doi: 10.1177/0962280218784757.
#'
#' @examples
#'
#' \dontrun{
#' #---- use the data 'aids' from joineR package
#' data("aids", package = "joineR")
#'
#' #---- Fit quantile regression joint model for the first quartile
#' qrjm_25 <- qrjm(formFixed = CD4 ~ obstime,
#' formRandom = ~ obstime,
#' formGroup = ~ id,
#' formSurv = Surv(time, death) ~ drug + gender + prevOI + AZT,
#' survMod = "weibull",
#' param = "value",
#' timeVar= "obstime",
#' data = aids,
#' tau = 0.25)
#'
#' #---- Visualize the trace for beta parameters
#' jagsUI::traceplot(qrjm_25$out_jagsUI, parameters = "beta" )
#'
#' #---- Get the estimated coefficients : posterior means
#' qrjm_25$mean
#'
#' #---- Summary of output
#' BQt::summary.BQt(qrjm_25)
#' }
#'
qrjm <- function(formFixed,
formRandom,
formGroup,
formSurv,
survMod = "weibull",
param = "value",
timeVar,
data,
tau,
RE_ind = FALSE,
n.chains = 3,
n.iter = 10000,
n.burnin = 5000,
n.thin = 5,
n.adapt = 5000,
precision = 10,
C = 1000,
save_jagsUI = TRUE,
save_va = FALSE,
parallel = FALSE){
# #
# # -- To do
# # verify with value.IG
# # add a stopping convergence criteria
# # initialize the values of parameter chains and to fix the intercept to test the convergence of beta's parameter.
# #
#
#-- data management
# control
lag = 0
#--- longitudinal part
data_long <- data[unique(c(all.vars(formGroup),all.vars(formFixed),all.vars(formRandom)))]
y <- data_long[all.vars(formFixed)][, 1]
mfX <- model.frame(formFixed, data = data_long)
X <- model.matrix(formFixed, mfX)
mfU <- model.frame(formRandom, data = data_long)
U <- model.matrix(formRandom, mfU)
id <- as.integer(data_long[all.vars(formGroup)][,1])
offset <- as.vector(c(1, 1 + cumsum(tapply(id, id, length))))
I <- length(unique(id))
if(!("id" %in% colnames(data_long)))
data_long <- cbind(data_long, id = id)
# use lqmm function to initiated values
cat("> Initialisation of longitudinal parameter values using 'lqmm' package. \n")
tmp_model <- lqmm::lqmm(fixed = formFixed,
random = formRandom,
group = id,
tau = tau,
data = data_long)
# prior beta parameters
priorMean.beta <- coef(tmp_model)
priorTau.beta <- diag(rep(1/10,length(priorMean.beta)))
bis <- as.matrix(lqmm::ranef(tmp_model))
bis[abs(bis)<.0001] <- 0
initial.values <- list(b = bis,
beta = priorMean.beta,
sigma = tmp_model$scale)
# list of data jags
jags.data <- list(y = y,
X = X,
U = U,
tau = tau,
ncX = ncol(X),
ncU = ncol(U),
I = I,
offset = offset,
priorMean.beta = priorMean.beta,
priorTau.beta = priorTau.beta,
priorA.sigma = 1/precision,
priorB.sigma = 1/precision
)
if(jags.data$ncU==1)
RE_ind <- TRUE
if(RE_ind){
jags.data <- c(jags.data,
list(priorA.Sigma2 = 1/precision,
priorB.Sigma2 = 1/precision
)
)
initial.values$prec.Sigma2 <- 1/VarCorr(tmp_model)
}else{
jags.data <- c(jags.data,
list(priorR.Sigma2 = diag(rep(1/precision, ncol(U))),
priorK.Sigma2 = ncol(U),
mu0 = rep(0, ncol(U))
)
)
initial.values$prec.Sigma2 <- diag(1/lqmm::VarCorr(tmp_model))
}
#--- survival part
tmp <- data[c(all.vars(formGroup),all.vars(formSurv))]
tmp <- unique(tmp)
Time <- tmp[all.vars(formSurv)][, 1] # matrix of observed time such as Time=min(Tevent,Tcens)
event <- tmp[all.vars(formSurv)][, 2] # vector of event indicator (delta)
nTime <- length(Time) # number of subject having Time
zeros <- numeric(nTime) # for zero trick in Bayesian procedure
# design matrice
mfZ <- model.frame(formSurv, data = tmp)
Z <- model.matrix(formSurv, mfZ)
# use survival::coxph function to initiated values
cat("> Initialisation of survival parameter values using 'survival' package. \n")
tmp_model <- survival::coxph(formSurv,
data = tmp,
x = TRUE)
# Complete the jags data
priorMean.alpha <- c(0, tmp_model$coefficients)
priorTau.alpha <- diag(c(1/precision, 1/(precision*diag(tmp_model$var))))
jags.data <- c(jags.data,
list(C = C,
zeros = numeric(nTime),
Time = Time,
event = event,
Z = Z,
ncZ = ncol(Z),
priorMean.alpha = priorMean.alpha,
priorTau.alpha = priorTau.alpha,
priorTau.alphaA = 1/precision)
)
# initialisation values of survival parameters
initial.values$alpha <- c(0, tmp_model$coefficients)
# if(survMod=="weibull")
# initial.values$shape <- 1
if(param=="value")
initial.values$alpha.assoc <- 0
if(param=="sharedRE")
initial.values$alpha.assoc <- rep(0, ncol(U))
#--- shared current value case
data.id <- data_long[!duplicated(id), ]
if (!timeVar %in% names(data_long))
stop("\n'timeVar' does not correspond to one of the columns in formulas")
if (param %in% c("value")) {
data.id[[timeVar]] <- pmax(Time - lag, 0)
mfX.id <- model.frame(formFixed, data = data.id)
Xtime <- model.matrix(formFixed, mfX.id)
mfU.id <- model.frame(formRandom, data = data.id)
Utime <- model.matrix(formRandom, mfU.id)
# if (one.RE)
# Utime <- cbind(Utime, rep(0, nrow(Utime)))
jags.data <- c(jags.data, list(Xtime = Xtime, Utime = Utime))
#-- approxitmation of the intergral via the Gaussian quadrature (Gauss Kronrod rule)
gaussKronrod <-
function (k = 15) {
sk <- c(-0.949107912342758524526189684047851, -0.741531185599394439863864773280788, -0.405845151377397166906606412076961, 0,
0.405845151377397166906606412076961, 0.741531185599394439863864773280788, 0.949107912342758524526189684047851, -0.991455371120812639206854697526329,
-0.864864423359769072789712788640926, -0.586087235467691130294144838258730, -0.207784955007898467600689403773245, 0.207784955007898467600689403773245,
0.586087235467691130294144838258730, 0.864864423359769072789712788640926, 0.991455371120812639206854697526329)
wk15 <- c(0.063092092629978553290700663189204, 0.140653259715525918745189590510238, 0.190350578064785409913256402421014,
0.209482141084727828012999174891714, 0.190350578064785409913256402421014, 0.140653259715525918745189590510238, 0.063092092629978553290700663189204,
0.022935322010529224963732008058970, 0.104790010322250183839876322541518, 0.169004726639267902826583426598550, 0.204432940075298892414161999234649,
0.204432940075298892414161999234649, 0.169004726639267902826583426598550, 0.104790010322250183839876322541518, 0.022935322010529224963732008058970)
wk7 <- c(0.129484966168869693270611432679082, 0.279705391489276667901467771423780, 0.381830050505118944950369775488975,
0.417959183673469387755102040816327, 0.381830050505118944950369775488975, 0.279705391489276667901467771423780, 0.129484966168869693270611432679082)
if (k == 7)
list(sk = sk[1:7], wk = wk7)
else
list(sk = sk, wk = wk15)
}
wk <- gaussKronrod()$wk
sk <- gaussKronrod()$sk
K <- length(sk)
P <- Time/2
st <- outer(P, sk + 1)
id.GK <- rep(seq_along(Time), each = K)
data.id2 <- data.id[id.GK, ]
data.id2[[timeVar]] <- c(t(st))
mfX <- model.frame(formFixed, data = data.id2)
mfU <- model.frame(formRandom, data = data.id2)
Xs <- model.matrix(formFixed, mfX)
Us <- model.matrix(formRandom, mfU)
jags.data <- c(jags.data, list(K = K, P = P, st = st, wk = wk, Xs = Xs, Us = Us))
}
#---- Model for JAGS
# model to consider
model <- switch(paste(survMod, RE_ind, param, sep = "/"),
# wishart distribution when RE are considered dependent
`weibull/FALSE/value` = jags_qrjm.weib.value,
# inverse gamma distribution when RE are considered independent
`weibull/TRUE/value` = jags_qrjm.weib.value.IG,
# wishart distribution when RE are considered dependent
`weibull/FALSE/sharedRE` = jags_qrjm.weib.sharedRE,
# inverse gamma distribution when RE are considered independent
`weibull/TRUE/sharedRE` = jags_qrjm.weib.sharedRE.IG
)
# parameters to save in the sampling step
parms_to_save <- c("alpha", "alpha.assoc", "beta", "sigma", "b", "covariance.b")
if(save_va)
parms_to_save <- c(parms_to_save, "va1")
# complement given survMod
if(survMod == "weibull"){
jags.data <- c(jags.data, list(priorA.shape = 1/precision, priorB.shape = 1/precision))
parms_to_save <- c(parms_to_save, "shape")
}
# # initial values to improve chain convergence
# initial.values <- list(gamma = priorMean.gamma,
# alpha = priorMean.alpha,
# shape = 3)
#-- write jags model in txt from R function
working.directory = getwd()
write.model.jags(model = model,
name_model = "jags_qrjm",
intitled = file.path(working.directory, "JagsModel.txt"),
Data = jags.data,
param = param)
#---- use JAGS sampler
# if (!require("rjags"))
# stop("'rjags' is required.\n")
if(n.chains==3)
inits <- list(initial.values,
initial.values,
initial.values)
if(n.chains==2)
inits <- list(initial.values,
initial.values)
if(n.chains==1)
inits <- initial.values
# using jagsUI
out_jags = jagsUI::jags(data = jags.data,
parameters.to.save = parms_to_save,
model.file = "JagsModel.txt",
inits = inits,
n.chains = n.chains,
parallel = parallel,
n.adapt = n.adapt,
n.iter = n.iter,
n.burnin = n.burnin,
n.thin = n.thin,
DIC = F)
file.remove(file.path(working.directory, "JagsModel.txt"))
#---- output building
#-- MCMClist management
#- arguments
out <- list(data = data)
out$control <- list(formFixed = formFixed,
formRandom = formRandom,
formGroup = formGroup,
formSurv = formSurv,
timeVar = timeVar,
tau = tau,
call_function = "qrjm",
I = I,
C = C,
param = param,
survMod = survMod,
n.chains = n.chains,
parallel = parallel,
n.adapt = n.adapt,
n.iter = n.iter,
n.burnin = n.burnin,
n.thin = n.thin,
RE_ind = RE_ind,
event = event,
Time = Time)
#- other outputs
# sims.list output
out$sims.list <- out_jags$sims.list
out$sims.list$b <- NULL
if(save_va)
out$sims.list$va1 <- NULL
# random effect output
out$random_effect <- list(postMeans = out_jags$mean$b,
postSd = out_jags$sd$b)
colnames(out$random_effect$postMeans) <- colnames(U)
colnames(out$random_effect$postSd) <- colnames(U)
# median : Posterior median of parameters
out$median <- out_jags$q50
out$median$b <- NULL
# mean : Posterior mean of parameters
out$mean <- out_jags$mean
out$mean$b <- NULL
# modes of parameters
out$modes <- lapply(out$sims.list, function(x) {
m <- function(x) {
d <- density(x, bw = "nrd", adjust = 3, n = 1000)
d$x[which.max(d$y)]
}
if (is.matrix(x))
as.array(apply(x, 2, m))
else{
if(is.array(x))
apply(x, c(2,3), m)
else m(x)
}
})
# standard error of parameters
out$StErr <- lapply(out$sims.list, function(x) {
f <- function(x) {
acf.x <- drop(acf(x, lag.max = 0.4 * length(x), plot = FALSE)$acf)[-1]
acf.x <- acf.x[seq_len(rle(acf.x > 0)$lengths[1])]
ess <- length(x)/(1 + 2 * sum(acf.x))
sqrt(var(x)/ess)
}
if (is.matrix(x))
as.array(apply(x, 2, f))
else{
if(is.array(x))
apply(x, c(2,3), f)
else f(x)
}
})
# standard deviation of parameters
out$StDev <- out_jags$sd
out$StDev$b <- NULL
# Rhat : Gelman & Rubin diagnostic
out$Rhat <- out_jags$Rhat
out$Rhat$b <- NULL
# clean regarding auxilary variable (information avalaible in jagsUI output)
if(save_va)
out$median$va1 <- out$mean$va1 <- out$StDev$va1 <- out$Rhat$va1 <- NULL
# names
names(out$mean$beta) <-
names(out$median$beta) <-
names(out$modes$beta) <-
names(out$StErr$beta) <-
names(out$Rhat$beta) <-
names(out$StDev$beta) <- colnames(X)
if(RE_ind){
names(out$mean$covariance.b) <-
names(out$median$covariance.b) <-
names(out$modes$covariance.b) <-
names(out$StErr$covariance.b) <-
names(out$Rhat$covariance.b) <-
names(out$StDev$covariance.b) <- colnames(U)
}else{
colnames(out$mean$covariance.b) <-
rownames(out$mean$covariance.b) <-
colnames(out$median$covariance.b) <-
rownames(out$median$covariance.b) <-
colnames(out$modes$covariance.b) <-
rownames(out$modes$covariance.b) <-
colnames(out$Rhat$covariance.b) <-
rownames(out$Rhat$covariance.b) <-
colnames(out$StErr$covariance.b) <-
rownames(out$StErr$covariance.b) <-
colnames(out$StDev$covariance.b) <-
rownames(out$StDev$covariance.b) <- colnames(U)
}
names(out$mean$alpha) <-
names(out$median$alpha) <-
names(out$modes$alpha) <-
names(out$Rhat$alpha) <-
names(out$StErr$alpha) <-
names(out$StDev$alpha) <- colnames(Z)
# credible intervalles
out$CIs$beta <- cbind(as.vector(t(out_jags$q2.5$beta)),
as.vector(t(out_jags$q97.5$beta)))
rownames(out$CIs$beta) <- colnames(X)
colnames(out$CIs$beta) <- c("2.5%", "97.5%")
out$CIs$sigma <- c(out_jags$q2.5$sigma,
out_jags$q97.5$sigma)
names(out$CIs$sigma) <- c("2.5%", "97.5%")
out$CIs$shape <- c(out_jags$q2.5$shape,
out_jags$q97.5$shape)
names(out$CIs$shape) <- c("2.5%", "97.5%")
if(param %in% c("value")){
out$CIs$alpha.assoc <- c(out_jags$q2.5$alpha.assoc,
out_jags$q97.5$alpha.assoc)
names(out$CIs$alpha.assoc) <- c("2.5%", "97.5%")
}
if(param %in% c("sharedRE")){
if(jags.data$ncU>1){
out$CIs$alpha.assoc <- cbind(as.vector(t(out_jags$q2.5$alpha.assoc)),
as.vector(t(out_jags$q97.5$alpha.assoc)))
rownames(out$CIs$alpha.assoc) <- colnames(U)
colnames(out$CIs$alpha.assoc) <- c("2.5%", "97.5%")
}else{
out$CIs$alpha.assoc <- c(out_jags$q2.5$alpha.assoc,
out_jags$q97.5$alpha.assoc)
names(out$CIs$alpha.assoc) <- c("2.5%", "97.5%")
}
}
out$CIs$alpha <- cbind(as.vector(t(out_jags$q2.5$alpha)),
as.vector(t(out_jags$q97.5$alpha)))
rownames(out$CIs$alpha) <- colnames(Z)
colnames(out$CIs$alpha) <- c("2.5%", "97.5%")
# only for diagonal elements of covariance matrix of random effects
out$CIs$variances.b <- cbind(as.vector(diag(out_jags$q2.5$covariance.b)),
as.vector(diag(out_jags$q97.5$covariance.b)))
rownames(out$CIs$variances.b) <- colnames(U)
colnames(out$CIs$variances.b) <- c("2.5%", "97.5%")
# save jags output if requires
if(save_jagsUI)
out$out_jagsUI <- out_jags
#---- End of the function defining the class and retruning the output
class(out) <- "BQt"
out
}
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