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rizopoulos2012.R
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rizopoulos2012.R
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##*********************************************************
## Data
##*********************************************************
library(joineR)
library(nlme)
library(JM)
epileptic <- read.table("epileptic.txt", header = TRUE)
head(epileptic)
epileptic$time <- epileptic$time / 365.25
epileptic$with.time <- epileptic$with.time / 365.25
epileptic$treat <- as.numeric(epileptic$treat == "LTG")
# Time-to-event data (one row per subject)
survdat <- epileptic
survdat <- survdat[!duplicated(survdat$id), ]
survdat$status <- rep("alive", nrow(survdat))
survdat$status[survdat$with.status.uae == 1] <- "UAE"
survdat$status[survdat$with.status.isc == 1] <- "ISC"
survdat <- survdat[ , c(1, 4, 8, 12)]
survdat.CR <- crLong(survdat, statusVar = "status",
censLevel = "alive", nameStrata = "CR")
##*********************************************************
## Custom summary function
##*********************************************************
# JM uses contrasts, therefore we need to extract cov-var terms
# in order to get the SEs and effects we are interested in
jm.summary <- function(model.in, D = 0) {
out <- confint(model.in)
vcv <- solve(model.in$Hessian)[6:11, 6:11] # take up to 11 just in case extra alphas
SE.beta <- sqrt(vcv[1,1] + vcv[2,2] + 2*vcv[1,2])
SE.alpha <- sqrt(vcv[3,3] + vcv[4,4] + 2*vcv[3,4])
sigma <- c(NA, model.in$coefficients$sigma, NA)
Sigma11 <- c(NA, model.in$coefficients$D[1, 1], NA)
Sigma22 <- c(NA, model.in$coefficients$D[2, 2], NA)
Sigma12 <- c(NA, model.in$coefficients$D[2, 1], NA)
out[6, 2] <- sum(model.in$coefficients$gammas)
out[6, 1] <- out[6, 2] - qnorm(0.975)*SE.beta
out[6, 3] <- out[6, 2] + qnorm(0.975)*SE.beta
if (D == 0 | D == 2) {
out[8, 2] <- sum(model.in$coefficients$alpha)
}
if (D == 1) {
out[8, 2] <- sum(model.in$coefficients$Dalpha)
}
out[8, 1] <- out[8, 2] - qnorm(0.975)*SE.alpha
out[8, 3] <- out[8, 2] + qnorm(0.975)*SE.alpha
if (D == 2) {
SE.alpha2 <- sqrt(vcv[5,5] + vcv[6,6] + 2*vcv[5,6])
out[10, 2] <- sum(model.in$coefficients$Dalpha)
out[10, 1] <- out[10, 2] - qnorm(0.975)*SE.alpha2
out[10, 3] <- out[10, 2] + qnorm(0.975)*SE.alpha2
}
out <- t(out)
out <- cbind(out, sigma, Sigma11, Sigma22, Sigma12)
out <- round(out, 3)
ci <- paste("(", paste(out[1, ], out[3, ], sep = ", "), ")", sep = "")
out <- rbind(out[2, ], ci)
if (ncol(out) == 14) out <- out[ , c(1, 3, 2, 4, 11:14, 5:10)]
else out <- out[ , c(1, 3, 2, 4, 9:12, 5:8)]
return(out)
}
##*********************************************************
## Fit models
##*********************************************************
## Separate models
# Longitudinal submodel
lmeFit <- lme(dose ~ treat * time,
random = ~ time | id,
data = epileptic)
summary(lmeFit)
# Time-to-event submodel
coxFit <- coxph(Surv(with.time, status2) ~ treat*CR + strata(CR),
data = survdat.CR,
x = TRUE)
summary(coxFit)
# Current value parameterization
ptm <- proc.time()
jointFit1 <- jointModel(lmeFit, coxFit,
timeVar = "time",
method = "spline-PH-aGH",
CompRisk = TRUE,
interFact = list(value = ~ CR, data = survdat.CR),
#GHk = 9,
#GKk = 15,
#iter.qN = 500,
#numeriDeriv = "cd",
verbose = FALSE)
summary(jointFit1)
proc.time() - ptm # CPU time
# Time-dependent slopes parameterization
ptm <- proc.time()
dform <- list(
fixed = ~ 1 + treat, indFixed = 3:4,
random = ~ 1, indRandom = 2)
jointFit2 <- jointModel(lmeFit, coxFit,
timeVar = "time",
method = "spline-PH-aGH",
CompRisk = TRUE,
interFact = list(value = ~ CR, slope = ~ CR,
data = survdat.CR),
#GHk = 9,
#GKk = 15,
#iter.qN = 500,
#numeriDeriv = "cd",
parameterization = "both",
derivForm = dform,
verbose = FALSE)
summary(jointFit2)
proc.time() - ptm # CPU time
anova(jointFit1, jointFit2)
# Lagged effects (6-months)
ptm <- proc.time()
jointFit3 <- update(jointFit1, lag = 0.5)
summary(jointFit3)
proc.time() - ptm # CPU time
# Cummulative effects parameterization
ptm <- proc.time()
iform <- list(
fixed = ~ -1 + time + I(treat * time) +
I(time^2 / 2) + I(treat * time^2 / 2),
indFixed = 1:4,
random = ~ -1 + time + I(time^2 / 2),
indRandom = 1:2)
jointFit4 <- jointModel(lmeFit, coxFit,
timeVar = "time",
method = "spline-PH-aGH",
CompRisk = TRUE,
interFact = list(slope = ~ CR,
data = survdat.CR),
#GHk = 9,
#GKk = 15,
#iter.qN = 500,
#numeriDeriv = "cd",
parameterization = "slope",
derivForm = iform,
verbose = FALSE)
summary(jointFit4)
proc.time() - ptm # CPU time
# Weighted-cummulative effects parameterization
ptm <- proc.time()
g <- function(u, pow = 0) {
f <- function(t) integrate(function(s) s^pow * dnorm(t - s), 0, t)$value
sapply(u, f)
}
iformW <- list(
fixed = ~ -1 + I(g(time)) + I(treat * g(time)) +
I(g(time, 1)) + I(treat * g(time, 1)),
indFixed = 1:4,
random = ~ -1 + I(g(time)) + I(g(time, 1)),
indRandom = 1:2)
jointFit5 <- jointModel(lmeFit, coxFit,
timeVar = "time",
method = "spline-PH-aGH",
CompRisk = TRUE,
interFact = list(slope = ~ CR,
data = survdat.CR),
#GHk = 9,
#GKk = 15,
#iter.qN = 500,
#numeriDeriv = "cd",
parameterization = "slope",
derivForm = iformW,
verbose = FALSE)
summary(jointFit5)
proc.time() - ptm # CPU time
# Random effects parameterization (fixed + random slopes only)
ptm <- proc.time()
dform2 <- list(
fixed = ~ 1, indFixed = 3,
random = ~ 1, indRandom = 2)
# The re-scaling by 0.45 is the SD from model without the scales
# dform2 <- list(
# fixed = ~ -1 + I(rep(1/0.45, length(treat))), indFixed = 3,
# random = ~ -1 + I(rep(1/0.45, length(treat))), indRandom = 2)
jointFit6 <- jointModel(lmeFit, coxFit,
timeVar = "time",
method = "spline-PH-aGH",
CompRisk = TRUE,
interFact = list(slope = ~ CR,
data = survdat.CR),
#GHk = 9,
#GKk = 15,
#iter.qN = 500,
#numeriDeriv = "cd",
parameterization = "slope",
derivForm = dform2,
verbose = FALSE)
summary(jointFit6)
proc.time() - ptm # CPU time
ests <- rbind(
jm.summary(jointFit1, D = 0),
jm.summary(jointFit3, D = 0),
jm.summary(jointFit4, D = 1),
jm.summary(jointFit5, D = 1),
jm.summary(jointFit6, D = 1)
)
write.csv(ests, "Riz2012_models13456.csv", row.names = FALSE)
write.csv(jm.summary(jointFit2, D = 2), "Riz2012_models2.csv", row.names = FALSE)
##*********************************************************
## Diagnostics
##*********************************************************
## Longitudinal
pdf("resid_plot_JM.pdf", width = 9, height = 5)
#png("resid_plot.png", width = 9, height = 5, units = "in", res = 300)
par(mfrow = c(1, 2))
plot(jointFit1)
dev.off()