#' Long term survival predictions
#'
#' Function for computing survival estimates using a relative survival model and the
#' expected general population survival.
#'
#' @param fit Fitted model to do predictions from. Possible classes are \code{gfcm}, \code{stpm2},
#' \code{pstpm2}, and \code{cm}.
#' @param type Prediction type (see details). The default is \code{surv}.
#' @param newdata Data frame from which to compute predictions. If empty, predictions are made on the the data which
#' the model was fitted on.
#' @param time Optional time points at which to compute predictions. If empty, a grid of 100 time points between 0
#' and the maximum follow-up time is selected.
#' @param var.type Character. Possible values are "\code{ci}" (default) for confidence intervals,
#' "\code{se}" for standard errors, and "\code{n}" for neither.
#' @param ratetable Object of class \code{ratetable} used to compute the general population survival.
#' Default is \code{survexp.dk}.
#' @param exp.fun Object of class \code{list} containing functions for the expected survival
#' of each row in \code{newdata}. If not specified, the function computes the expected
#' survival based on \code{newdata} using the \code{survival::survexp} function. If \code{newdata} is not provided,
#' the expected survival is based on the data which the model was fitted on.
#' @param rmap List to be passed to \code{survexp} from the \code{survival} package if \code{exp.fun = NULL}.
#' Detailed documentation on this argument can be found by \code{?survexp}.
#' @param scale Numeric. Passed to the \code{survival::survexp} function and defaults to 365.24.
#' That is, the time scale is assumed to be in years.
#' @param smooth.exp Logical. If \code{TRUE}, the general population survival function is smoothed by the function
#' \code{smooth.spline} using the the argument \code{all.knots = TRUE}.
#' @param link Character, indicating the link function for the variance calculations.
#' Possible values are "\code{log}", "\code{cloglog}" for \eqn{log(-log(x))} , "\code{mlog}" for -log(x),
#' and "\code{I}" for the indentity.
#' @param mean Logical. If \code{TRUE}, the function outputs the average estimate across the
#' rows in \code{newdata}. If \code{newdata = NULL}, the argument is not used. The default is \code{FALSE}.
#' @return An object of class \code{lts} containing the predictions of each individual in \code{newdata}.
#' @details
#' Possible values for argument \code{type} are:\cr
#' \code{surv}: Survival function computed by \eqn{S(t) = R(t)S^*(t)}\cr
#' \code{hazard}: Hazard function computed by \eqn{h(t) = \lambda(t) + h^*(t)}\cr
#' \code{cumhaz}: The cumulative hazard function computed by \eqn{H(t) = \Lambda(t) + H^*(t)}\cr
#' \code{loghazard}: The log-hazard function computed by \eqn{\log(\lambda(t) + h^*(t))}\cr
#' \code{fail}: The distribution function computed by \eqn{1 - R(t)S^*(t)}
#' @export
#' @example inst/predict.lts.ex.R
lts <- function(fit, type = c("surv", "hazard", "cumhaz", "loghaz", "fail"),
newdata = NULL, time = NULL, var.type = c("ci", "se", "n"),
exp.fun = NULL, ratetable = cuRe::survexp.dk, rmap, scale = 365.24,
smooth.exp = FALSE, link = NULL, mean = FALSE){
var.type <- match.arg(var.type)
type <- match.arg(type)
if(is.null(time)){
if(any(class(fit) %in% c("stpm2", "pstpm2"))){
time <- seq(1e-05, max(fit@data[[fit@timeVar]]), length.out = 100)
} else {
time <- seq(1e-05, max(fit$time), length.out = 100)
}
}
is_null_newdata <- is.null(newdata)
if(is_null_newdata){
if(any(class(fit) %in% c("stpm2", "pstpm2"))){
data <- fit@data
newdata <- data.frame(arbritary_var = 0)
}else{
data <- fit$data
}
}
if(is_null_newdata) mean <- FALSE
if(mean) var.type <- "n"
if(is.null(exp.fun)){
#The time points for the expected survival
times <- seq(0, max(time) + 1, by = 0.1)
#Extract expected survival function
if(is_null_newdata){
expected <- list(do.call("survexp",
list(formula = ~ 1, rmap = substitute(rmap),
data = data, ratetable = ratetable,
scale = scale, times = times * scale)))
}else{
expected <- vector("list", nrow(newdata))
for(i in 1:length(expected)){
expected[[i]] <- do.call("survexp",
list(formula = ~ 1, rmap = substitute(rmap),
data = newdata[i, ], ratetable = ratetable,
scale = scale, times = times * scale))
}
}
if(smooth.exp){
exp.fun <- lapply(1:length(expected), function(i){
smooth.obj <- smooth.spline(x = expected[[i]]$time, y = expected[[i]]$surv, all.knots = T)
function(time) predict(smooth.obj, x = time)$y
})
} else {
exp.fun <- lapply(1:length(expected), function(i){
function(time){
s <- summary(expected[[i]], time)
names(s$surv) <- s$time
survs <- s$surv[as.character(time)]
names(survs) <- NULL
survs
}
})
}
}
if(any(class(fit) %in% c("stpm2", "pstpm2"))){
if(inherits(fit, "stpm2")){
response_name <- all.vars(fit@call.formula)[1]
}else{
response_name <- all.vars(fit@fullformula)[1]
}
fit_tmp <- fit
rel_surv <- lapply(1:length(exp.fun), function(i){
function(t, pars){
#res <- rep(NA, length(t))
fit_tmp@fullcoef <- pars
#wh <- which(t != 0)
suppressWarnings(newdata_tmp <- cbind(newdata[i,,drop = F], t))
names(newdata_tmp)[ncol(newdata_tmp)] <- response_name
#res[wh] <-
as.numeric(predict(fit_tmp, newdata = newdata_tmp, type = "surv"))
#res[-wh] <- 1
#res
}
})
excess_haz <- lapply(1:length(exp.fun), function(i){
function(t, pars){
fit_tmp@fullcoef <- pars
suppressWarnings(newdata_tmp <- cbind(newdata[i,,drop = F], t))
names(newdata_tmp)[ncol(newdata_tmp)] <- response_name
as.numeric(predict(fit_tmp, newdata = newdata_tmp, type = "hazard"))
}
})
model.params <- fit@fullcoef
cov <- fit@vcov
}else{
if ("cuRe" %in% class(fit)) {
rel_surv <- lapply(1:length(exp.fun), function(i){
function(t, pars) predict(fit, newdata = newdata[i,, drop = F],
time = t, pars = pars, var.type = "n")[[1]]$Estimate
})
excess_haz <- lapply(1:length(exp.fun), function(i){
function(t, pars) predict(fit, newdata = newdata[i,, drop = F],
time = t, pars = pars, type = "hazard",
var.type = "n")[[1]]$Estimate
})
}
model.params <- c(unlist(fit$coefs), fit$coefs.spline)
cov <- fit$covariance
}
expected_haz <- lapply(1:length(exp.fun), function(i){
cum_haz_smooth <- function(t) -log(exp.fun[[i]](t))
function(t, pars) numDeriv::grad(func = cum_haz_smooth, t)
})
#Set default link functions based on the type of predictions
if(is.null(link)){
link <- switch(type, surv = "cloglog", hazard = "log", cumhaz = "log", loghazard = "I", fail = "mlog")
}
#Define link functions and their inverse based on the link argument
var.link <- switch(link, I = function(x) x, log = function(x) log(x),
cloglog = function(x) log(-log(x)), mlog = function(x) -log(x))
var.link.inv <- switch(link, I = function(x) x, log = function(x) exp(x),
cloglog = function(x) exp(-exp(x)), mlog = function(x) exp(-x))
res <- vector("list", length(exp.fun))
for(i in 1:length(exp.fun)){
est <- lts.local(exp.fun = exp.fun[[i]], rel_surv = rel_surv[[i]], excess_haz = excess_haz[[i]],
expected_haz = expected_haz[[i]], time = time,
model.params = model.params, var.link = var.link, type = type)
D <- data.frame(Estimate = est)
if(var.type != "n"){
gr <- numDeriv::jacobian(lts.local, x = model.params, time = time, exp.fun = exp.fun[[i]],
rel_surv = rel_surv[[i]], excess_haz = excess_haz[[i]],
expected_haz = expected_haz[[i]], var.link = var.link, type = type)
D$SE <- sqrt(apply(gr, 1, function(x) x %*% cov %*% x))
if(var.type == "ci"){
lower <- var.link.inv(D$Estimate - D$SE * qnorm(0.975))
upper <- var.link.inv(D$Estimate + D$SE * qnorm(0.975))
D$lower <- pmin(lower, upper)
D$upper <- pmax(lower, upper)
D <- subset(D, select = -SE)
}
}
D$Estimate <- var.link.inv(D$Estimate)
res[[i]] <- D
}
#Compute mean estimates
if(mean){
res <- rowMeans(do.call(cbind, res))
}
#Add attributes to the results
attributes(res) <- list(time = time, type = type, var.type = var.type)
class(res) <- "lts"
res
}
lts.local <- function(exp.fun, rel_surv, excess_haz, expected_haz, time, model.params, var.link, type){
Est <- if(type == "surv"){
exp.fun(time) * rel_surv(time, model.params)
} else if(type == "hazard"){
expected_haz(time) + excess_haz(time, model.params)
} else if(type == "cumhaz"){
-log(exp.fun(time) * rel_surv(time, model.params))
} else if(type == "loghazard"){
log(expected_haz(time) + excess_haz(time, model.params))
} else if(type == "fail"){
1 - (exp.fun(time) * rel_surv(time, model.params))
}
return(var.link(Est))
}
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