/
main-aids-normal.R
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main-aids-normal.R
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rm(list=ls(all=TRUE))
# Required sources
library(rstan)
library(rstanarm)
library(statmod)
library(JMbayes)
# Function for mode estimation
mode2 <- function(x){
lim.inf <- min(x)-1
lim.sup <- max(x)+1
s <- density(x,from=lim.inf,to=lim.sup,bw=0.2)
n <- length(s$y)
v1 <- s$y[1:(n-2)]
v2 <- s$y[2:(n-1)]
v3 <- s$y[3:n]
ix <- 1+which((v1<v2)&(v2>v3))
md <- s$x[which(s$y==max(s$y))]
return(md)
}
# Gauss-Legendre quadrature (15 points)
glq <- gauss.quad(15, kind = "legendre")
xk <- glq$nodes # nodes
wk <- glq$weights # weights
K <- length(xk) # K-points
# Number of patients
n <- nrow(aids.id)
# Number of longitudinal observations per patient
M <- as.numeric(table(aids$patient))
###############################################
# Joint specification (JS) approach #
###############################################
# Setting initial values
init_fun1 <- function(...){
list(beta=c(0,0,0), gamma=c(0,0), alpha=0, phi=1, sigma_e=1, Sigma=diag(c(1,1)), bi=matrix(0,nrow=n,ncol=2))
}
start_time1 <- Sys.time()
fitJS <- stan(file = "stan/JS_normal.stan",
data = list(N=nrow(aids), n=n, y=aids$CD4, times=aids$obstime,
Time=aids.id$Time, status=aids.id$death,
x=as.numeric(aids.id$drug)-1, ID=rep(1:n,M),
K=K, xk=xk, wk=wk),
init = init_fun1,
warmup = 1000,
iter = 2000,
chains = 1,
seed = 1)
end_time1 <- Sys.time()
end_time1 - start_time1
print(fitJS)
###############################################
###############################################
# Standard Two-Stage (STS) approach #
###############################################
# Stage 1 - Longitudinal submodel
# Setting initial values
init_fun21 <- function(...){
list(beta=c(0,0,0), sigma_e=1, Sigma=diag(c(1,1)), bi=matrix(0,nrow=n,ncol=2))
}
start_time21 <- Sys.time()
fitL <- stan(file = "stan/LongTS_normal.stan",
data = list(N=nrow(aids), n=n, y=aids$CD4, times=aids$obstime,
x=as.numeric(aids.id$drug)-1, ID=rep(1:n,M)),
init = init_fun21,
warmup = 1000,
iter = 2000,
chains = 1,
seed = 1)
end_time21 <- Sys.time()
# Extracting random-effects
bi <- extract(fitL)$bi
bimode <- apply(bi,c(2,3),mode2)
# Extracting fixed-effects
beta1 <- unlist(extract(fitL, par="beta[1]"))
beta2 <- unlist(extract(fitL, par="beta[2]"))
beta3 <- unlist(extract(fitL, par="beta[3]"))
betamode <- c(mode2(beta1),mode2(beta2),mode2(beta3))
# Stage 2 - Survival submodel
# Setting initial values
init_fun22 <- function(...){
list(gamma=c(0,0), alpha=0, phi=1)
}
start_time22 <- Sys.time()
fitSTS <- stan(file = "stan/STS_normal.stan",
data = list(n=n, Time=aids.id$Time, status=aids.id$death,
x=as.numeric(aids.id$drug)-1,
beta=betamode, bi=bimode,
K=K, xk=xk, wk=wk),
init = init_fun22,
warmup = 500,
iter = 1000,
chains = 1,
seed = 1)
end_time22 <- Sys.time()
end_time22 - start_time21
print(fitSTS)
###############################################
###############################################
# Novel Two-Stage (NTS) approach #
###############################################
# Extracting random-effects variance-covariance matrix
sigma2b1 <- mode2(unlist(extract(fitL, par="Sigma[1,1]")))
sigma2b2 <- mode2(unlist(extract(fitL, par="Sigma[2,2]")))
sigma2b12 <- mode2(unlist(extract(fitL, par="Sigma[1,2]")))
Sigmamode <- matrix(c(sigma2b1,sigma2b12,sigma2b12,sigma2b2),2,2)
# Extracting error standard deviation
sigma_emode <- mode2(extract(fitL, "sigma_e")$sigma_e)
# Stage 2 - Survival submodel
# Setting initial values
init_fun3 <- function(...){
list(gamma=c(0,0), alpha=0, phi=1, bi=matrix(0,nrow=n,ncol=2))
}
start_time3 <- Sys.time()
fitNTS <- stan(file = "stan/NTS_normal.stan",
data = list(N=nrow(aids), n=n, y=aids$CD4, times=aids$obstime,
Time=aids.id$Time, status=aids.id$death,
x=as.numeric(aids.id$drug)-1, ID=rep(1:n,M),
beta=betamode, sigma_e=sigma_emode, Sigma=Sigmamode,
K=K, xk=xk, wk=wk),
init = init_fun3,
warmup = 500,
iter = 1000,
chains = 1,
seed = 1)
end_time3 <- Sys.time()
end_time3 - start_time3 + end_time21 - start_time21
print(fitNTS)
###############################################