predict.jointModel <-
function (object, newdata, type = c("Marginal", "Subject"),
interval = c("none", "confidence", "prediction"), level = 0.95, idVar = "id",
FtTimes = NULL, M = 300, returnData = FALSE, scale = 1.6, ...) {
if (!inherits(object, "jointModel"))
stop("Use only with 'jointModel' objects.\n")
if (!is.data.frame(newdata) || nrow(newdata) == 0)
stop("'newdata' must be a data.frame with more than one rows.\n")
type <- match.arg(type)
interval <- match.arg(interval)
if (type == "Marginal") {
TermsX <- delete.response(object$termsYx)
mf <- model.frame(TermsX, data = newdata)
form <- reformulate(attr(TermsX, "term.labels"))
X <- model.matrix(form, data = mf)
out <- c(X %*% object$coefficients$betas)
names(out) <- row.names(newdata)
if (interval == "prediction") {
warning("\nfor type = 'Marginal' only confidence intervals are calculated.")
interval <- "confidence"
}
if (interval == "confidence") {
V <- vcov(object)
ind <- head(grep("Y.", colnames(V), fixed = TRUE), -1)
se.fit <- sqrt(diag(X %*% tcrossprod(V[ind, ind], X)))
alpha <- 1 - level
low <- out + qnorm(alpha/2) * se.fit
up <- out + qnorm(1-alpha/2) * se.fit
names(se.fit) <- names(low) <- names(up) <- row.names(newdata)
out <- list(pred = out, se.fit = se.fit, low = low, upp = up)
}
if (returnData) {
out <- if (is.list(out))
cbind(newdata, do.call(cbind, out))
else
cbind(newdata, pred = out)
}
} else {
if (object$CompRisk)
stop("predict() with type = 'Subject' is not currently ",
"\n implemented for competing risks joint models.\n")
if (is.null(newdata[[idVar]]))
stop("'idVar' not in 'newdata.\n'")
method <- object$method
timeVar <- object$timeVar
interFact <- object$interFact
parameterization <- object$parameterization
derivForm <- object$derivForm
indFixed <- derivForm$indFixed
indRandom <- derivForm$indRandom
#id <- as.numeric(unclass(newdata[[idVar]]))
#id <- match(id, unique(id))
LongFormat <- object$LongFormat
TermsX <- object$termsYx
TermsZ <- object$termsYz
TermsX.deriv <- object$termsYx.deriv
TermsZ.deriv <- object$termsYz.deriv
mfX <- model.frame(TermsX, data = newdata)
mfZ <- model.frame(TermsZ, data = newdata)
formYx <- reformulate(attr(delete.response(TermsX), "term.labels"))
formYz <- object$formYz
na.ind <- as.vector(attr(mfX, "na.action"))
na.ind <- if (is.null(na.ind)) {
rep(TRUE, nrow(newdata))
} else {
!seq_len(nrow(newdata)) %in% na.ind
}
id <- as.numeric(unclass(newdata[[idVar]]))
id <- id. <- match(id, unique(id))
id <- id[na.ind]
y <- model.response(mfX)
X <- model.matrix(formYx, mfX)
Z <- model.matrix(formYz, mfZ)[na.ind, , drop = FALSE]
TermsT <- object$termsT
#data.id <- if (LongFormat) newdata else newdata[!duplicated(id), ]
data.id <- if (LongFormat) {
nams.ind <- all.vars(delete.response(TermsT))
ind <- !duplicated(newdata[nams.ind])
newdata[ind, ]
} else newdata[!duplicated(id), ]
idT <- data.id[[idVar]]
idT <- match(idT, unique(idT))
mfT <- model.frame(delete.response(TermsT), data = data.id)
formT <- if (!is.null(kk <- attr(TermsT, "specials")$strata)) {
strt <- eval(attr(TermsT, "variables"), data.id)[[kk]]
tt <- drop.terms(TermsT, kk - 1, keep.response = FALSE)
reformulate(attr(tt, "term.labels"))
} else if (!is.null(kk <- attr(TermsT, "specials")$cluster)) {
tt <- drop.terms(TermsT, kk - 1, keep.response = FALSE)
reformulate(attr(tt, "term.labels"))
} else {
tt <- attr(delete.response(TermsT), "term.labels")
if (length(tt)) reformulate(tt) else reformulate("1")
}
W <- model.matrix(formT, mfT)
WintF.vl <- WintF.sl <- as.matrix(rep(1, nrow(data.id)))
if (!is.null(interFact)) {
if (!is.null(interFact$value))
WintF.vl <- model.matrix(interFact$value, data = data.id)
if (!is.null(interFact$slope))
WintF.sl <- model.matrix(interFact$slope, data = data.id)
}
obs.times <- split(newdata[[timeVar]], id.)
last.time <- tapply(newdata[[timeVar]], id., tail, n = 1)
times.to.pred <- if (is.null(FtTimes)) {
lapply(last.time,
function (t) seq(t, max(object$times) +
0.1 * mad(object$times), length = 25))
} else {
if (!is.list(FtTimes) || length(FtTimes) != length(last.time))
rep(list(FtTimes), length(last.time))
else
FtTimes
}
n <- object$n
n.tp <- length(last.time)
ncx <- ncol(X)
ncz <- ncol(Z)
ncww <- ncol(W)
lag <- object$y$lag
betas <- object$coefficients[['betas']]
sigma <- object$coefficients[['sigma']]
D <- object$coefficients[['D']]
diag.D <- ncol(D) == 1 & nrow(D) > 1
D <- if (diag.D) diag(c(D)) else D
gammas <- object$coefficients[['gammas']]
alpha <- object$coefficients[['alpha']]
Dalpha <- object$coefficients[['Dalpha']]
sigma.t <- object$coefficients[['sigma.t']]
xi <- object$coefficients[['xi']]
gammas.bs <- object$coefficients[['gammas.bs']]
list.thetas <- list(betas = betas, log.sigma = log(sigma),
gammas = gammas, alpha = alpha,
Dalpha = Dalpha,
log.sigma.t = if (is.null(sigma.t)) NULL else log(sigma.t),
log.xi = if (is.null(xi)) NULL else log(xi), gammas.bs = gammas.bs,
D = if (diag.D) log(diag(D)) else chol.transf(D))
if (method %in% c("weibull-PH-GH", "weibull-AFT-GH") &&
!is.null(object$scaleWB)) {
list.thetas$log.sigma.t <- NULL
}
if (method %in% c("piecewise-PH-GH", "spline-PH-GH")) {
if (ncww == 1) {
W <- NULL
ncww <- 0
} else {
W <- W[, -1, drop = FALSE]
ncww <- ncww - 1
}
Q <- object$x$Q
}
list.thetas <- list.thetas[!sapply(list.thetas, is.null)]
if (!method %in% c("weibull-PH-GH", "weibull-AFT-GH",
"piecewise-PH-GH", "spline-PH-GH")) {
stop("\nsurvfitJM() is not yet available for this type of joint model.")
}
list.thetas <- list.thetas[!sapply(list.thetas, is.null)]
thetas <- unlist(as.relistable(list.thetas))
Var.thetas <- vcov(object)
environment(log.posterior.b) <- environment(ModelMats) <- environment()
# construct model matrices to calculate the survival functions
obs.times.surv <- split(data.id[[timeVar]], idT)
survMats.last <- vector("list", n.tp)
for (i in seq_len(n.tp)) {
survMats.last[[i]] <- ModelMats(last.time[i], ii = i,
obs.times = obs.times.surv,
survTimes = unlist(times.to.pred, use.names = FALSE))
}
data.id2 <- newdata[!duplicated(id), ]
data.id2 <- data.id2[rep(1:nrow(data.id2),
sapply(times.to.pred, length)), ]
data.id2[[timeVar]] <- unlist(times.to.pred)
mfXpred <- model.frame(TermsX, data = data.id2)
mfZpred <- model.frame(TermsZ, data = data.id2)
Xpred <- model.matrix(formYx, mfXpred)
Zpred <- model.matrix(formYz, mfZpred)
id2 <- as.numeric(unclass(data.id2[[idVar]]))
id2 <- match(id2, unique(id2))
# calculate the Empirical Bayes estimates and their (scaled) variance
modes.b <- matrix(0, n.tp, ncz)
Vars.b <- vector("list", n.tp)
for (i in seq_len(n.tp)) {
betas.new <- betas
sigma.new <- sigma
D.new <- D
gammas.new <- gammas
alpha.new <- alpha
Dalpha.new <- Dalpha
sigma.t.new <- sigma.t
xi.new <- xi
gammas.bs.new <- gammas.bs
ff <- function (b, y, tt, mm, i)
-log.posterior.b(b, y, Mats = tt, method = mm, ii = i)
opt <- try(optim(rep(0, ncz), ff, y = y, tt = survMats.last, mm = method, i = i,
method = "BFGS", hessian = TRUE), TRUE)
if (inherits(opt, "try-error")) {
gg <- function (b, y, tt, mm, i) cd(b, ff, y = y, tt = tt, mm = mm, i = i)
opt <- optim(rep(0, ncz), ff, gg, y = y, tt = survMats.last, mm = method,
i = i, method = "BFGS", hessian = TRUE)
}
modes.b[i, ] <- opt$par
Vars.b[[i]] <- scale * solve(opt$hessian)
}
res <- vector("list", M)
success.rate <- matrix(FALSE, M, n.tp)
b.old <- b.new <- modes.b
if (n.tp == 1)
dim(b.old) <- dim(b.new) <- c(1, ncz)
for (m in 1:M) {
# Step 1: simulate new parameter values
thetas.new <- mvrnorm(1, thetas, Var.thetas)
thetas.new <- relist(thetas.new, skeleton = list.thetas)
betas.new <- thetas.new$betas
sigma.new <- exp(thetas.new$log.sigma)
gammas.new <- thetas.new$gammas
alpha.new <- thetas.new$alpha
D.new <- thetas.new$D
D.new <- if (diag.D) exp(D.new) else chol.transf(D.new)
if (method == "weibull-PH-GH" || method == "weibull-AFT-GH") {
sigma.t.new <- if (is.null(object$scaleWB))
exp(thetas.new$log.sigma.t) else object$scaleWB
} else if (method == "piecewise-PH-GH") {
xi.new <- exp(thetas.new$log.xi)
} else if (method == "spline-PH-GH") {
gammas.bs.new <- thetas.new$gammas.bs
}
y.new <- vector("list", n.tp)
for (i in seq_len(n.tp)) {
# Step 2: simulate new random effects values
proposed.b <- rmvt(1, modes.b[i, ], Vars.b[[i]], 4)
dmvt.old <- dmvt(b.old[i, ], modes.b[i, ], Vars.b[[i]], 4, TRUE)
dmvt.proposed <- dmvt(proposed.b, modes.b[i, ], Vars.b[[i]], 4, TRUE)
a <- min(exp(log.posterior.b(proposed.b, y, survMats.last, method, ii = i) + dmvt.old -
log.posterior.b(b.old[i, ], y, survMats.last, method, ii = i) - dmvt.proposed), 1)
ind <- runif(1) <= a
success.rate[m, i] <- ind
if (!is.na(ind) && ind)
b.new[i, ] <- proposed.b
# Step 3: compute future Ys
Xpred.i <- Xpred[id2 == i, , drop = FALSE]
Zpred.i <- Zpred[id2 == i, , drop = FALSE]
mu.i <- as.vector(c(Xpred.i %*% betas.new) +
rowSums(Zpred.i * rep(b.new[i, ], each = nrow(Zpred.i))))
y.new[[i]] <- if (interval == "confidence") mu.i else
if (interval == "prediction") rnorm(length(mu.i), mu.i, sigma.new)
}
b.old <- b.new
res[[m]] <- y.new
}
oo <- vector("list", n.tp)
for (i in seq_len(n.tp)) {
oo[[i]] <- do.call(rbind, sapply(res, "[", i))
}
out <- as.vector(c(Xpred %*% betas) +
rowSums(Zpred * modes.b[id2, , drop = FALSE]))
if (interval %in% c("confidence", "prediction")) {
alpha <- 1 - level
se.fit <- lapply(oo, function (m) {
if (is.matrix(m))
apply(m, 2, sd)
else
sd(m)
})
f1 <- function (mat) apply(mat, 2, quantile, probs = alpha/2)
f2 <- function (mat) apply(mat, 2, quantile, probs = 1 - alpha/2)
low <- lapply(oo, f1)
up <- lapply(oo, f2)
out <- list(pred = out, se.fit = unlist(se.fit),
low = unlist(low), upp = unlist(up))
}
if (returnData) {
newdata$pred <- c(X %*% betas) + rowSums(Z * modes.b[id, ])
out <- if (is.list(out)) {
newdata$upp <- newdata$low <- newdata$se.fit <- NA
rbind(newdata, cbind(data.id2, do.call(cbind, out)))
} else {
rbind(newdata, cbind(data.id2, pred = out))
}
} else
attr(out, "time.to.pred") <- times.to.pred
rm(list = ".Random.seed", envir = globalenv())
}
out
}
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