survfitJM.jointModel <- function (object, newdata, idVar = "id", simulate = TRUE, survTimes = NULL,
last.time = NULL, M = 200, CI.levels = c(0.025, 0.975), scale = 1.6, ...) {
if (!inherits(object, "jointModel"))
stop("Use only with 'jointModel' objects.\n")
if (object$CompRisk)
stop("survfitJM() is not currently implemented for ",
"competing risks joint models.\n")
if (!is.data.frame(newdata) || nrow(newdata) == 0)
stop("'newdata' must be a data.frame with more than one rows.\n")
if (is.null(newdata[[idVar]]))
stop("'idVar' not in 'newdata.\n'")
if (is.null(survTimes) || !is.numeric(survTimes))
survTimes <- seq(min(exp(object$y$logT)),
max(exp(object$y$logT)) + 0.1, length.out = 35)
method <- object$method
timeVar <- object$timeVar
interFact <- object$interFact
parameterization <- object$parameterization
derivForm <- object$derivForm
indFixed <- derivForm$indFixed
indRandom <- derivForm$indRandom
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$termsT
data.id <- if (LongFormat) {
nams.ind <- all.vars(delete.response(TermsT))
ind <- !duplicated(newdata[nams.ind])
newdata[ind, ]
} else newdata[tapply(row.names(newdata), id, tail, n = 1L),]
idT <- data.id[[idVar]]
idT <- match(idT, unique(idT))
mfT <- model.frame(delete.response(TermsT), data = data.id)
formT <- if (!is.null(kk <- attr(TermsT, "specials")$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$slope, data = data.id)
}
obs.times <- split(newdata[[timeVar]][na.ind], id)
last.time <- if (is.null(last.time)) {
tapply(newdata[[timeVar]], id., tail, n = 1)
} else if (is.character(last.time) && length(last.time) == 1) {
tapply(newdata[[last.time]], id., tail, n = 1)
} else if (is.numeric(last.time) && length(last.time) == nrow(data.id)) {
last.time
} else {
stop("\nnot appropriate value for 'last.time' argument.")
}
times.to.pred <- lapply(last.time, function (t) survTimes[survTimes > t])
n <- object$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$Q
}
list.thetas <- list.thetas[!sapply(list.thetas, is.null)]
if (!method %in% c("weibull-PH-GH", "weibull-AFT-GH", "piecewise-PH-GH", "spline-PH-GH")) {
stop("\nsurvfitJM() is not yet available for this type of joint model.")
}
list.thetas <- list.thetas[!sapply(list.thetas, is.null)]
thetas <- unlist(as.relistable(list.thetas))
Var.thetas <- vcov(object)
environment(log.posterior.b) <- environment(S.b) <- environment(ModelMats) <- environment()
# construct model matrices to calculate the survival functions
obs.times.surv <- split(data.id[[timeVar]], idT)
survMats <- survMats.last <- vector("list", n.tp)
for (i in seq_len(n.tp)) {
survMats[[i]] <- lapply(times.to.pred[[i]], ModelMats, ii = i,
obs.times = obs.times.surv, survTimes = survTimes)
survMats.last[[i]] <- ModelMats(last.time[i], ii = i,
obs.times = obs.times.surv, survTimes = survTimes)
}
# calculate the Empirical Bayes estimates and their (scaled) variance
modes.b <- matrix(0, n.tp, ncz)
Vars.b <- vector("list", n.tp)
for (i in seq_len(n.tp)) {
betas.new <- betas
sigma.new <- sigma
D.new <- D
gammas.new <- gammas
alpha.new <- alpha
Dalpha.new <- Dalpha
sigma.t.new <- sigma.t
xi.new <- xi
gammas.bs.new <- gammas.bs
ff <- function (b, y, tt, mm, i) -log.posterior.b(b, y, Mats = tt, method = mm, ii = i)
opt <- try(optim(rep(0, ncz), ff, y = y, tt = survMats.last, mm = method, i = i,
method = "BFGS", hessian = TRUE), TRUE)
if (inherits(opt, "try-error")) {
gg <- function (b, y, tt, mm, i) cd(b, ff, y = y, tt = tt, mm = mm, i = i)
opt <- optim(rep(0, ncz), ff, gg, y = y, tt = survMats.last, mm = method,
i = i, method = "BFGS", hessian = TRUE)
}
modes.b[i, ] <- opt$par
Vars.b[[i]] <- scale * solve(opt$hessian)
}
if (!simulate) {
res <- vector("list", n.tp)
for (i in seq_len(n.tp)) {
S.last <- S.b(last.time[i], modes.b[i, ], i, survMats.last[[i]])
S.pred <- numeric(length(times.to.pred[[i]]))
for (l in seq_along(S.pred))
S.pred[l] <- S.b(times.to.pred[[i]][l], modes.b[i, ], i, survMats[[i]][[l]])
res[[i]] <- cbind(times = times.to.pred[[i]], predSurv = S.pred / S.last)
rownames(res[[i]]) <- seq_along(S.pred)
}
} else {
out <- vector("list", M)
success.rate <- matrix(FALSE, M, n.tp)
b.old <- b.new <- modes.b
if (n.tp == 1)
dim(b.old) <- dim(b.new) <- c(1, ncz)
for (m in 1:M) {
# Step 1: simulate new parameter values
thetas.new <- mvrnorm(1, thetas, Var.thetas)
thetas.new <- relist(thetas.new, skeleton = list.thetas)
betas.new <- thetas.new$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
}
SS <- 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 Pr(T > t_k | T > t_{k - 1}; theta.new, b.new)
S.last <- S.b(last.time[i], b.new[i, ], i, survMats.last[[i]])
S.pred <- numeric(length(times.to.pred[[i]]))
for (l in seq_along(S.pred))
S.pred[l] <- S.b(times.to.pred[[i]][l], b.new[i, ], i, survMats[[i]][[l]])
SS[[i]] <- S.pred / S.last
}
b.old <- b.new
out[[m]] <- SS
}
res <- vector("list", n.tp)
for (i in seq_len(n.tp)) {
rr <- sapply(out, "[[", i)
if (!is.matrix(rr))
rr <- rbind(rr)
res[[i]] <- cbind(
times = times.to.pred[[i]],
"Mean" = rowMeans(rr, na.rm = TRUE),
"Median" = apply(rr, 1, median, na.rm = TRUE),
"Lower" = apply(rr, 1, quantile, probs = CI.levels[1], na.rm = TRUE),
"Upper" = apply(rr, 1, quantile, probs = CI.levels[2], na.rm = TRUE)
)
rownames(res[[i]]) <- as.character(seq_len(NROW(res[[i]])))
}
}
y <- split(y, id)
newdata. <- do.call(rbind, mapply(function (d, t) {
d. <- rbind(d, d[nrow(d), ])
d.[[timeVar]][nrow(d.)] <- t
d.
}, split(newdata, id.), last.time, SIMPLIFY = FALSE))
id. <- as.numeric(unclass(newdata.[[idVar]]))
id. <- match(id., unique(id.))
mfX. <- model.frame(delete.response(TermsX), data = newdata.)
mfZ. <- model.frame(TermsZ, data = newdata.)
X. <- model.matrix(formYx, mfX.)
Z. <- model.matrix(formYz, mfZ.)
fitted.y <- split(c(X. %*% betas) + rowSums(Z. * modes.b[id., , drop = FALSE]), id.)
names(res) <- names(y) <- names(last.time) <- names(obs.times) <- unique(unclass(newdata[[idVar]]))
res <- list(summaries = res, survTimes = survTimes, last.time = last.time,
obs.times = obs.times, y = y,
fitted.times = split(newdata.[[timeVar]], factor(newdata.[[idVar]])),
fitted.y = fitted.y, ry = range(object$y$y, na.rm = TRUE))
if (simulate) {
res$full.results <- out
res$success.rate <- success.rate
rm(list = ".Random.seed", envir = globalenv())
}
class(res) <- "survfitJM"
res
}
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