Nothing
R/emfrail.R
In frailtyEM: Fitting Frailty Models with the EM Algorithm
Defines functions
emfrail
Documented in
emfrail
#' Fitting semi-parametric shared frailty models with the EM algorithm
#'
#' @importFrom survival Surv coxph cox.zph
#' @importFrom stats approx coef model.frame model.matrix pchisq printCoefmat nlm uniroot cor optimize
#' @importFrom magrittr "%>%"
#' @importFrom Rcpp evalCpp
#' @importFrom Matrix bdiag
#' @importFrom numDeriv hessian
#' @useDynLib frailtyEM, .registration=TRUE
#' @include em_fit.R
#' @include emfrail_aux.R
#'
#' @param formula A formula that contains on the left hand side an object of the type \code{Surv}
#' and on the right hand side a \code{+cluster(id)} statement. Two special statments may also be used:
#' \code{+strata()} for specifying a grouping column that will represent different strata and
#' \code{+terminal()}
#' @param data A \code{data.frame} in which the formula argument can be evaluated
#' @param distribution An object as created by \code{\link{emfrail_dist}}
#' @param control An object as created by \code{\link{emfrail_control}}
#' @param model Logical. Should the model frame be returned?
#' @param model.matrix Logical. Should the model matrix be returned?
#' @param ... Other arguments, currently used to warn about deprecated argument names
#' @export
#'
#' @details The \code{emfrail} function fits shared frailty models for processes which have intensity
#' \deqn{\lambda(t) = z \lambda_0(t) \exp(\beta' \mathbf{x})}
#' with a non-parametric (Breslow) baseline intensity \eqn{\lambda_0(t)}. The outcome
#' (left hand side of the \code{formula}) must be a \code{Surv} object.
#'
#' If the object is \code{Surv(tstop, status)} then the usual failure time data is represented.
#' Gap-times between recurrent events are represented in the same way.
#' If the left hand side of the formula is created as \code{Surv(tstart, tstop, status)}, this may represent a number of things:
#' (a) recurrent events episodes in calendar time where a recurrent event episode starts at \code{tstart} and ends at \code{tstop}
#' (b) failure time data with time-dependent covariates where \code{tstop} is the time of a change in covariates or censoring
#' (\code{status = 0}) or an event time (\code{status = 1}) or (c) clustered failure time with left truncation, where
#' \code{tstart} is the individual's left truncation time. Unlike regular Cox models, a major distinction is that in case (c) the
#' distribution of the frailty must be considered conditional on survival up to the left truncation time.
#'
#' The \code{+cluster()} statement specified the column that determines the grouping (the observations that share the same frailty).
#' The \code{+strata()} statement specifies a column that determines different strata, for which different baseline hazards are calculated.
#' The \code{+terminal} specifies a column that contains an indicator for dependent censoring, and then performs a score test
#'
#' The \code{distribution} argument must be generated by a call to \code{\link{emfrail_dist}}. This determines the
#' frailty distribution, which may be one of gamma, positive stable or PVF (power-variance-function), and the starting
#' value for the maximum likelihood estimation. The PVF family
#' also includes a tuning parameter that differentiates between inverse Gaussian and compound Poisson distributions.
#' Note that, with univariate data (at most one event per individual, no clusters), only distributions with finite expectation
#' are identifiable. This means that the positive stable distribution should have a maximum likelihood on the edge of the parameter
#' space (\eqn{theta = +\inf}, corresponding to a Cox model for independent observations).
#'
#' The \code{control} argument must be generated by a call to \code{\link{emfrail_control}}. Several parameters
#' may be adjusted that control the precision of the convergenge criteria or supress the calculation of different
#' quantities.
#'
#' @return An object of class \code{emfrail} that contains the following fields:
#' \item{coefficients}{A named vector of the estimated regression coefficients}
#' \item{hazard}{The breslow estimate of the baseline hazard at each event time point, in chronological order}
#' \item{var}{The variance-covariance matrix corresponding to the coefficients and hazard, assuming \eqn{\theta} constant}
#' \item{var_adj}{The variance-covariance matrx corresponding to the
#' coefficients and hazard, adjusted for the estimation of theta}
#' \item{logtheta}{The logarithm of the point estimate of \eqn{\theta}. For the gamma and
#' PVF family of distributions, this is the inverse of the estimated frailty variance.}
#' \item{var_logtheta}{The variance of the estimated logarithm of \eqn{\theta}}
#' \item{ci_logtheta}{The likelihood-based 95\% confidence interval for the logarithm of \eqn{\theta}}
#' \item{frail}{The posterior (empirical Bayes) estimates of the frailty for each cluster}
#' \item{residuals}{A list with two elements, cluster which is a vector that the sum of the
#' cumulative hazards from each cluster for a frailty value of 1, and
#' individual, which is a vector that contains the cumulative hazard corresponding to each row of the data,
#' multiplied by the corresponding frailty estimate}
#' \item{tev}{The time points of the events in the data set, this is the same length as hazard}
#' \item{nevents_id}{The number of events for each cluster}
#' \item{loglik}{A vector of length two with the log-likelihood of the starting Cox model
#' and the maximized log-likelihood}
#' \item{ca_test}{The results of the Commenges-Andersen test for heterogeneity}
#' \item{cens_test}{The results of the test for dependence between a recurrent event and a terminal event,
#' if the \code{+terminal()} statement is specified and the frailty distribution is gamma}
#' \item{zph}{The result of \code{cox.zph} called on a model with the estimated log-frailties as offset}
#' \item{formula, distribution, control}{The original arguments}
#' \item{nobs, fitted}{Number of observations and fitted values (i.e. \eqn{z \exp(\beta^T x)})}
#' \item{mf}{The \code{model.frame}, if \code{model = TRUE}}
#' \item{mm}{The \code{model.matrix}, if \code{model.matrix = TRUE}}
#'
#' @md
#' @note Several options in the \code{control} arguemnt shorten the running time for \code{emfrail} significantly.
#' These are disabling the adjustemnt of the standard errors (\code{se_adj = FALSE}), disabling the likelihood-based confidence intervals (\code{lik_ci = FALSE}) or
#' disabling the score test for heterogeneity (\code{ca_test = FALSE}).
#'
#' The algorithm is detailed in the package vignette. For the gamma frailty,
#' the results should be identical with those from \code{coxph} with \code{ties = "breslow"}.
#'
#' @seealso \code{\link{plot.emfrail}} and \code{\link{autoplot.emfrail}} for plot functions directly available, \code{\link{emfrail_pll}} for calculating \eqn{\widehat{L}(\theta)} at specific values of \eqn{\theta},
#' \code{\link{summary.emfrail}} for transforming the \code{emfrail} object into a more human-readable format and for
#' visualizing the frailty (empirical Bayes) estimates,
#' \code{\link{predict.emfrail}} for calculating and visalizing conditional and marginal survival and cumulative
#' hazard curves. \code{\link{residuals.emfrail}} for extracting martingale residuals and \code{\link{logLik.emfrail}} for extracting
#' the log-likelihood of the fitted model.
#'
#' @examples
#'
#' m_gamma <- emfrail(formula = Surv(time, status) ~ rx + sex + cluster(litter),
#' data = rats)
#'
#' # Inverse Gaussian distribution
#' m_ig <- emfrail(formula = Surv(time, status) ~ rx + sex + cluster(litter),
#' data = rats,
#' distribution = emfrail_dist(dist = "pvf"))
#'
#' # for the PVF distribution with m = 0.75
#' m_pvf <- emfrail(formula = Surv(time, status) ~ rx + sex + cluster(litter),
#' data = rats,
#' distribution = emfrail_dist(dist = "pvf", pvfm = 0.75))
#'
#' # for the positive stable distribution
#' m_ps <- emfrail(formula = Surv(time, status) ~ rx + sex + cluster(litter),
#' data = rats,
#' distribution = emfrail_dist(dist = "stable"))
#' \dontrun{
#' # Compare marginal log-likelihoods
#' models <- list(m_gamma, m_ig, m_pvf, m_ps)
#'
#' models
#' logliks <- lapply(models, logLik)
#'
#' names(logliks) <- lapply(models,
#' function(x) with(x$distribution,
#' ifelse(dist == "pvf",
#' paste(dist, "/", pvfm),
#' dist))
#' )
#'
#' logliks
#' }
#'
#' # Stratified analysis
#' \dontrun{
#' m_strat <- emfrail(formula = Surv(time, status) ~ rx + strata(sex) + cluster(litter),
#' data = rats)
#' }
#'
#'
#' # Test for conditional proportional hazards (log-frailty as offset)
#' \dontrun{
#' m_gamma <- emfrail(formula = Surv(time, status) ~ rx + sex + cluster(litter),
#' data = rats, control = emfrail_control(zph = TRUE))
#' par(mfrow = c(1,2))
#' plot(m_gamma$zph)
#' }
#'
#' # Draw the profile log-likelihood
#' \dontrun{
#' fr_var <- seq(from = 0.01, to = 1.4, length.out = 20)
#'
#' # For gamma the variance is 1/theta (see parametrizations)
#' pll_gamma <- emfrail_pll(formula = Surv(time, status) ~ rx + sex + cluster(litter),
#' data = rats,
#' values = 1/fr_var )
#' plot(fr_var, pll_gamma,
#' type = "l",
#' xlab = "Frailty variance",
#' ylab = "Profile log-likelihood")
#'
#'
#' # Recurrent events
#' mod_rec <- emfrail(Surv(start, stop, status) ~ treatment + cluster(id), bladder1)
#' # The warnings appear from the Surv object, they also appear in coxph.
#'
#' plot(mod_rec, type = "hist")
#' }
#'
#' # Left truncation
#' \dontrun{
#' # We simulate some data with truncation times
#' set.seed(2018)
#' nclus <- 300
#' nind <- 5
#' x <- sample(c(0,1), nind * nclus, TRUE)
#' u <- rep(rgamma(nclus,1,1), each = 3)
#'
#' stime <- rexp(nind * nclus, rate = u * exp(0.5 * x))
#'
#' status <- ifelse(stime > 5, 0, 1)
#' stime[status == 0] <- 5
#'
#' # truncate uniform between 0 and 2
#' ltime <- runif(nind * nclus, min = 0, max = 2)
#'
#' d <- data.frame(id = rep(1:nclus, each = nind),
#' x = x,
#' stime = stime,
#' u = u,
#' ltime = ltime,
#' status = status)
#' d_left <- d[d$stime > d$ltime,]
#'
#' mod <- emfrail(Surv(stime, status)~ x + cluster(id), d)
#' # This model ignores the left truncation, 0.378 frailty variance:
#' mod_1 <- emfrail(Surv(stime, status)~ x + cluster(id), d_left)
#'
#' # This model takes left truncation into account,
#' # but it considers the distribution of the frailty unconditional on the truncation
#' mod_2 <- emfrail(Surv(ltime, stime, status)~ x + cluster(id), d_left)
#'
#' # This is identical with:
#' mod_cox <- coxph(Surv(ltime, stime, status)~ x + frailty(id), data = d_left)
#'
#'
#' # The correct thing is to consider the distribution of the frailty given the truncation
#' mod_3 <- emfrail(Surv(ltime, stime, status)~ x + cluster(id), d_left,
#' distribution = emfrail_dist(left_truncation = TRUE))
#'
#' summary(mod_1)
#' summary(mod_2)
#' summary(mod_3)
#' }
#' @author Theodor Balan \email{hello@@tbalan.com}
#' @references Balan TA, Putter H (2019) "frailtyEM: An R Package for Estimating Semiparametric Shared Frailty Models", \emph{Journal of Statistical Software} \strong{90}(7) 1-29. doi:10.18637/jss.v090.i07
emfrail <- function(formula,
data,
distribution = emfrail_dist(),
control = emfrail_control(),
model = FALSE, model.matrix = FALSE,
...) {
# browser()
# This part is because the update breaks old code
extraargs <- list(...)
if(!inherits(formula, "formula")) {
if(inherits(formula, "data.frame")) warning("You gave a data.frame instead of a formula.
Argument order has changed; now it's emfrail(formula, data, etc..).")
stop("formula is not an object of type formula")
}
if(!inherits(data, "data.frame")) {
if(inherits(data, "formula")) warning("You gave a formula instead of a data.frame.
Argument order has changed; now it's emfrail(formula, data, etc..).")
stop("data is not an object of type data.frame")
}
if(!inherits(distribution, "emfrail_dist"))
stop("distribution argument misspecified; see ?emfrail_dist()")
if(!inherits(control, "emfrail_control"))
stop("control argument misspecified; see ?emfrail_control()")
if(isTRUE(control$em_control$fast_fit)) {
if(!(distribution$dist %in% c("gamma", "pvf"))) {
#message("fast_fit option only available for gamma and pvf with m=-1/2 distributions")
control$em_control$fast_fit <- FALSE
}
# version 0.5.6, the IG fast fit gets super sensitive at small frailty variance...
if(distribution$dist == "pvf")
control$em_control$fast_fit <- FALSE
}
Call <- match.call()
if(missing(formula) | missing(data)) stop("Missing arguments")
cluster <- function(x) x
terminal <- function(x) x
strata <- function(x) x
mf <- model.frame(formula, data)
# Identify the cluster and the ID column
pos_cluster <- grep("cluster", names(mf))
if(length(pos_cluster) != 1) stop("misspecified or non-specified cluster")
id <- mf[[pos_cluster]]
pos_terminal <- grep("terminal", names(mf))
if(length(pos_terminal) > 1) stop("misspecified terminal()")
pos_strata <- grep("strata", names(mf))
if(length(pos_strata) > 0) {
if(length(pos_strata) > 1) stop("only one strata() variable allowed")
strats <- as.numeric(mf[[pos_strata]])
label_strats <- levels(mf[[pos_strata]])
} else {
# else, everyone is in the same strata
strats <- NULL
label_strats <- "1"
}
Y <- mf[[1]]
if(!inherits(Y, "Surv")) stop("left hand side not a survival object")
if(ncol(Y) != 3) {
# making it all in (tstart, tstop) format
Y <- Surv(rep(0, nrow(Y)), Y[,1], Y[,2])
}
X1 <- model.matrix(formula, data)
pos_cluster_X1 <- grep("cluster", colnames(X1))
pos_terminal_X1 <- grep("terminal", colnames(X1))
pos_strata_X1 <- grep("strata", colnames(X1))
X <- X1[,-c(1, pos_cluster_X1, pos_terminal_X1, pos_strata_X1), drop=FALSE]
# note: X has no attributes, in coxph it does.
# mcox also works with empty matrices, but also with NULL as x.
mcox <- survival::agreg.fit(x = X, y = Y, strata = strats, offset = NULL, init = NULL,
control = survival::coxph.control(),
weights = NULL, method = "breslow", rownames = NULL)
# order(strat, -Y[,2])
# the "baseline" case // this will stay constant
if(length(X) == 0) {
newrisk <- 1
exp_g_x <- matrix(rep(1, length(mcox$linear.predictors)), nrow = 1)
g <- 0
g_x <- t(matrix(rep(0, length(mcox$linear.predictors)), nrow = 1))
} else {
x2 <- matrix(rep(0, ncol(X)), nrow = 1, dimnames = list(123, dimnames(X)[[2]]))
x2 <- scale(x2, center = mcox$means, scale = FALSE)
newrisk <- exp(c(x2 %*% mcox$coefficients) + 0)
exp_g_x <- exp(mcox$coefficients %*% t(X))
g <- mcox$coefficients
g_x <- t(mcox$coefficients %*% t(X))
}
explp <- exp(mcox$linear.predictors) # these are with centered covariates
# now thing is that maybe this is not very necessary,
# but it keeps track of which row belongs to which cluster
# and then we don't have to keep on doing this
order_id <- match(id, unique(id))
nev_id <- as.numeric(rowsum(Y[,3], order_id, reorder = FALSE)) # nevent per cluster
names(nev_id) <- unique(id)
# nrisk has the sum with every tstop and the sum of elp at risk at that tstop
# esum has the sum of elp who enter at every tstart
# indx groups which esum is right after each nrisk;
# the difference between the two is the sum of elp really at risk at that time point.
if(!is.null(strats)) {
explp_str <- split(explp, strats)
tstop_str <- split(Y[,2], strats)
tstart_str <- split(Y[,1], strats)
ord_tstop_str <- lapply(tstop_str, function(x) match(x, sort(unique(x))))
ord_tstart_str <- lapply(tstart_str, function(x) match(x, sort(unique(x))))
nrisk <- mapply(FUN = function(explp, y) rowsum_vec(explp, y, max(y)),
explp_str,
ord_tstop_str,
SIMPLIFY = FALSE)
# nrisk <- mapply(FUN = function(explp, y) rev(cumsum(rev(rowsum(explp, y[,2])))),
# split(explp, strats),
# split.data.frame(Y, strats),
# SIMPLIFY = FALSE)
esum <- mapply(FUN = function(explp, y) rowsum_vec(explp, y, max(y)),
explp_str,
ord_tstart_str,
SIMPLIFY = FALSE)
# esum <- mapply(FUN = function(explp, y) rev(cumsum(rev(rowsum(explp, y[,1])))),
# split(explp, strats),
# split.data.frame(Y, strats),
# SIMPLIFY = FALSE)
death <- lapply(
X = split.default(Y[,3], strats),
FUN = function(y) (y == 1)
)
nevent <- mapply(
FUN = function(y, d)
as.vector(rowsum(1 * d, y)),
tstop_str,
death,
SIMPLIFY = FALSE
)
time_str <- lapply(
X = tstop_str,
FUN = function(y) sort(unique(y))
)
delta <- min(diff(sort(unique(Y[,2]))))/2
time <- sort(unique(Y[,2])) # unique tstops
etime <- lapply(
X = tstart_str,
FUN = function(y) c(0, sort(unique(y)), max(y) + delta)
)
indx <-
mapply(FUN = function(time, etime) findInterval(time, etime, left.open = TRUE),
time_str,
etime,
SIMPLIFY = FALSE
)
indx2 <-
mapply(FUN = function(y, time) findInterval(y, time),
tstart_str,
time_str,
SIMPLIFY = FALSE
)
time_to_stop <-
mapply(FUN = function(y, time) match(y, time),
tstop_str,
time_str,
SIMPLIFY = FALSE
)
positions_strata <- do.call(c,split(1:nrow(Y), strats))
atrisk <- list(death = death, nevent = nevent, nev_id = nev_id,
order_id = order_id, time = time, indx = indx, indx2 = indx2,
time_to_stop = time_to_stop,
ord_tstart_str = ord_tstart_str,
ord_tstop_str = ord_tstop_str,
positions_strata = positions_strata,
strats = strats)
nrisk <- mapply(FUN = function(nrisk, esum, indx) nrisk - c(esum, 0,0)[indx],
nrisk,
esum,
indx,
SIMPLIFY = FALSE)
if(newrisk == 0) warning("Hazard ratio very extreme; please check (and/or rescale) your data")
haz <- mapply(FUN = function(nevent, nrisk) nevent/nrisk * newrisk,
nevent,
nrisk,
SIMPLIFY = FALSE)
basehaz_line <- mapply(FUN = function(haz, time_to_stop) haz[time_to_stop],
haz,
time_to_stop,
SIMPLIFY = FALSE)
cumhaz <- lapply(haz, cumsum)
cumhaz_0_line <- mapply(FUN = function(cumhaz, time_to_stop) cumhaz[time_to_stop],
cumhaz,
time_to_stop,
SIMPLIFY = FALSE)
cumhaz_tstart <- mapply(FUN = function(cumhaz, indx2) c(0, cumhaz)[indx2 + 1],
cumhaz,
indx2,
SIMPLIFY = FALSE)
cumhaz_line <- mapply(FUN = function(cumhaz_0_line, cumhaz_tstart, explp)
(cumhaz_0_line - cumhaz_tstart) * explp / newrisk,
cumhaz_0_line,
cumhaz_tstart,
split(explp, strats),
SIMPLIFY = FALSE)
cumhaz_line <- do.call(c, cumhaz_line)[order(positions_strata)]
} else {
ord_tstop <- match(Y[,2], sort(unique(Y[,2])))
ord_tstart <- match(Y[,1], sort(unique(Y[,1])))
nrisk <- rowsum_vec(explp, ord_tstop, max(ord_tstop))
# nrisk <- rev(cumsum(rev(rowsum(explp, Y[, ncol(Y) - 1]))))
esum <- rowsum_vec(explp, ord_tstart, max(ord_tstart))
# esum <- rev(cumsum(rev(rowsum(explp, Y[, 1]))))
death <- (Y[, 3] == 1)
nevent <- as.vector(rowsum(1 * death, Y[, ncol(Y) - 1])) # per time point
time <- sort(unique(Y[,2])) # unique tstops
etime <- c(0, sort(unique(Y[, 1])), max(Y[, 1]) + min(diff(time))/2)
indx <- findInterval(time, etime, left.open = TRUE) # left.open = TRUE is very important
# this gives for every tstart (line variable), after which event time did it come
indx2 <- findInterval(Y[,1], time)
time_to_stop <- match(Y[,2], time)
atrisk <- list(death = death, nevent = nevent, nev_id = nev_id,
order_id = order_id,
time = time, indx = indx, indx2 = indx2,
time_to_stop = time_to_stop,
ord_tstart = ord_tstart, ord_tstop = ord_tstop,
strats = NULL)
nrisk <- nrisk - c(esum, 0,0)[indx]
if(newrisk == 0) warning("Hazard ratio very extreme; please check (and/or rescale) your data")
haz <- nevent/nrisk * newrisk
basehaz_line <- haz[atrisk$time_to_stop]
cumhaz <- cumsum(haz)
cumhaz_0_line <- cumhaz[atrisk$time_to_stop]
cumhaz_tstart <- c(0, cumhaz)[atrisk$indx2 + 1]
cumhaz_line <- (cumhaz[atrisk$time_to_stop] - c(0, cumhaz)[atrisk$indx2 + 1]) * explp / newrisk
}
Cvec <- rowsum(cumhaz_line, order_id, reorder = FALSE)
# browser()
# this part under construction!
# if(distribution$basehaz != "breslow") {
# if(any(Y[,1] != 0))
# stop("(tstart, tstop) not supported for parametric models")
#
# dlist <- survival::survreg.distributions[[distribution$basehaz]]
#
# # this stuff is more or less copied from survreg
#
# logcorrect <- 0 #correction to the loglik due to transformations
# Ysave <- Y # for use in the y component
# if (!is.null(dlist$trans)) {
# tranfun <- dlist$trans
# exactsurv <- Y[, ncol(Y)] == 1
# if (any(exactsurv)) {
# logcorrect <- sum(log(dlist$dtrans(Y[exactsurv, 1])))
# }
# if (!all(is.finite(Y)))
# stop("Invalid survival times for this distribution")
#
# }
#
# if (!is.null(dlist$scale)) {
# if (!missing(scale))
# warning(paste(dlist$name, "has a fixed scale, user specified value ignored"))
# scale <- dlist$scale
# } else scale <- 0
#
# if (!is.null(dlist$dist))
# if (is.atomic(dlist$dist))
# dlist <- survreg.distributions[[dlist$dist]] else dlist <- dlist$dist
#
# if (any(scale < 0))
# stop("Invalid scale value")
# # Now we convert this to a format that survreg.fit likes
#
# fit <- survreg.fit(cbind(1, X), cbind(tranfun(Y[,2]), Y[,3]),
# weights = NULL,
# offset = NULL,
# init = NULL,
# controlvals = survreg.control() ,
# dist = dlist, scale = scale, nstrat = 1, strata = 0, parms= NULL)
#
#
# }
#
#
#
# srg1 <- survreg_simple(formula = Surv(time, status) ~ rx + sex, data = rats, dist = "weibull")
#
# srg1$coefficients
# fit$coefficients
#
# fit <- survreg.fit(X, Y, weights = NULL, offset = NULL, init = NULL,
# controlvals = survreg.control(), dist = dlist, scale = 0)
#
# distribution
# dlist <- survival::survreg.distributions[[distribution$]]
# ca_test <- NULL
# ca_test_fit does not know strata ?!?
if(isTRUE(control$ca_test)) {
if(!is.null(strats)) ca_test <- NULL else
ca_test <- ca_test_fit(mcox, X, atrisk, exp_g_x, cumhaz)
}
if(isTRUE(distribution$left_truncation)) {
if(!is.null(strats))
cumhaz_tstart <- do.call(c, cumhaz_tstart)[order(atrisk$positions_strata)]
Cvec_lt <- rowsum(cumhaz_tstart, atrisk$order_id, reorder = FALSE)
} else Cvec_lt <- 0 * Cvec
# a fit just for the log-likelihood;
if(!isTRUE(control$opt_fit)) {
return(
em_fit(logfrailtypar = log(distribution$theta),
dist = distribution$dist, pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk,
basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control)
)
}
# browser()
if(distribution$dist == "stable") {
# thing is: with stable small values of theta mean high dependence
# I have yet to see a very high dependence there; furthermore,
# the likelihood is pretty flat there.
# therefore I would rather drag this towards "no dependence".
distribution$theta <- distribution$theta + 1
}
outer_m <- do.call(nlm, args = c(list(f = em_fit,
p = log(distribution$theta),
hessian = TRUE,
dist = distribution$dist,
pvfm = distribution$pvfm,
Y = Y, Xmat = X,
atrisk = atrisk,
basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec,
lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control), control$nlm_control))
# control$lik_interval_stable
if(outer_m$hessian < 1) {
outer_m_opt <- do.call(optimize,
args = c(list(f = em_fit,
dist = distribution$dist,
pvfm = distribution$pvfm,
Y = Y, Xmat = X,
atrisk = atrisk,
basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec,
lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control), lower = log(control$lik_interval)[1],
upper = log(control$lik_interval)[2]))
if(outer_m_opt$objective < outer_m$minimum) {
hess <- numDeriv::hessian(func = em_fit, x = outer_m_opt$minimum,
dist = distribution$dist,
pvfm = distribution$pvfm,
Y = Y, Xmat = X,
atrisk = atrisk,
basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec,
lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control)
outer_m <- list(minimum = outer_m_opt$objective,
estimate = outer_m_opt$minimum,
hessian = hess)
}
}
if(outer_m$hessian == 0) warning("Hessian virtually 0; frailty variance might be at the edge of the parameter space.")
if(outer_m$hessian <= 0) hessian <- NA else hessian <- outer_m$hessian
# likelihood-based confidence intervals
theta_low <- theta_high <- NULL
if(isTRUE(control$lik_ci)) {
# With the stable distribution, a problem pops up for small values, i.e. very large association (tau large)
# So there I use another interval for this
if(distribution$dist == "stable") {
control$lik_interval <- control$lik_interval_stable
}
skip_ci <- FALSE
lower_llik <- try(em_fit(log(control$lik_interval[1]),
dist = distribution$dist,
pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk, basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control), silent = TRUE)
if(class(lower_llik) == "try-error") {
warning("likelihood-based CI could not be calcuated; disable or change lik_interval[1] in emfrail_control")
lower_llik <- NA
log_theta_low <- log_theta_high <- NA
skip_ci <- TRUE
}
upper_llik <- try(em_fit(log(control$lik_interval[2]),
dist = distribution$dist,
pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk, basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control), silent = TRUE)
if(class(upper_llik) == "try-error") {
warning("likelihood-based CI could not be calcuated; disable or lik_interval[2] in emfrail_control")
upper_llik <- NA
log_theta_low <- log_theta_high <- NA
skip_ci <- TRUE
}
if(!isTRUE(skip_ci)) {
if(lower_llik - outer_m$minimum < 1.92) {
log_theta_low <- log(control$lik_interval[1])
warning("Likelihood-based confidence interval lower limit reached, probably 0;
You can try a lower value for control$lik_interval[1].")
} else
log_theta_low <- uniroot(function(x, ...) outer_m$minimum - em_fit(x, ...) + 1.92,
interval = c(log(control$lik_interval[1]), outer_m$estimate),
f.lower = outer_m$minimum - lower_llik + 1.92, f.upper = 1.92,
tol = .Machine$double.eps^0.1,
dist = distribution$dist,
pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk, basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control,
maxiter = 100)$root
# this says that if I can't get a significant difference on the right side, then it's infinity
if(upper_llik - outer_m$minimum < 1.92) log_theta_high <- Inf else
log_theta_high <- uniroot(function(x, ...) outer_m$minimum - em_fit(x, ...) + 1.92,
interval = c(outer_m$estimate, log(control$lik_interval[2])),
f.lower = 1.92, f.upper = outer_m$minimum - upper_llik + 1.92,
extendInt = c("downX"),
dist = distribution$dist,
pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk, basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control)$root
}
} else
log_theta_low <- log_theta_high <- NA
if(isTRUE(control$se)) {
inner_m <- em_fit(logfrailtypar = outer_m$estimate,
dist = distribution$dist, pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk, basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = TRUE,
em_control = control$em_control,
return_loglik = FALSE)
} else
inner_m <- em_fit(logfrailtypar = outer_m$estimate,
dist = distribution$dist, pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk, basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control,
return_loglik = FALSE)
# Cox.ZPH stuff
if(isTRUE(control$zph)) {
# Here just fit a Cox model with the log-frailty as offset
# note: the cox.zph function in the new version of the survival package has a terms = TRUE argument.
# This part here is added so that emfrail continues to work with both versions.
# do.call is needed because otherwise R CMD check returns a warning when ran on a system with the
# old version of cox.zph
if("terms" %in% names(formals(cox.zph))) {
if(!is.null(strats)) {
zph <- do.call(cox.zph, args = list(fit = coxph(Y ~ X + strata(strats) + offset(inner_m$logz), ties = "breslow"),
transform = control$zph_transform,
terms = FALSE))
# zph <- cox.zph(coxph(Y ~ X + strata(strats) + offset(inner_m$logz), ties = "breslow"),
# transform = control$zph_transform, terms = FALSE)
} else {
zph <- do.call(cox.zph, args = list(fit = coxph(Y ~ X + offset(inner_m$logz), ties = "breslow"),
transform = control$zph_transform,
terms = FALSE))
# zph <- cox.zph(coxph(Y ~ X + offset(inner_m$logz), ties = "breslow"),
# transform = control$zph_transform, terms = FALSE)
}
} else {
if(!is.null(strats)) {
zph <- do.call(cox.zph, args = list(fit = coxph(Y ~ X + strata(strats) + offset(inner_m$logz), ties = "breslow"),
transform = control$zph_transform))
} else
zph <- do.call(cox.zph, args = list(fit = coxph(Y ~ X + offset(inner_m$logz), ties = "breslow"),
transform = control$zph_transform))
}
# fix the names for nice output
# if there is only one covariate there is not "GLOBAL" test
attr(zph$table, "dimnames")[[1]][1:length(inner_m$coef)] <- names(inner_m$coef)
attr(zph$y, "dimnames")[[2]] <- names(mcox$coef)
} else zph <- NULL
# adjusted standard error
if(isTRUE(control$se) & isTRUE(attr(inner_m$Vcov, "class") == "try-error")) {
inner_m$Vcov <- matrix(NA, length(inner_m$coef) + length(inner_m$haz))
warning("Information matrix is singular")
}
# adjusted SE: only go on if requested and if Vcov was calculated
if(isTRUE(control$se) &
isTRUE(control$se_adj) &
!all(is.na(inner_m$Vcov))) {
# absolute value should be redundant. but sometimes the "hessian" might be 0.
# in that case it might appear negative; this happened only on Linux...
# h <- as.numeric(sqrt(abs(1/(attr(outer_m, "details")[[3]])))/2)
h<- as.numeric(sqrt(abs(1/hessian))/2)
lfp_minus <- max(outer_m$estimate - h , outer_m$estimate - 5, na.rm = TRUE)
lfp_plus <- min(outer_m$estimate + h , outer_m$estimate + 5, na.rm = TRUE)
final_fit_minus <- em_fit(logfrailtypar = lfp_minus,
dist = distribution$dist, pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk, basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control,
return_loglik = FALSE)
final_fit_plus <- em_fit(logfrailtypar = lfp_plus,
dist = distribution$dist, pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk, basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control, return_loglik = FALSE)
# instructional: this should be more or less equal to the
# -(final_fit_plus$loglik + final_fit_minus$loglik - 2 * inner_m$loglik)/h^2
# se_logtheta^2 / (2 * (final_fit$loglik -final_fit_plus$loglik ))
if(!is.null(atrisk$strats))
deta_dtheta <- (c(final_fit_plus$coef, do.call(c, final_fit_plus$haz)) -
c(final_fit_minus$coef, do.call(c, final_fit_minus$haz))) / (2*h) else
deta_dtheta <- (c(final_fit_plus$coef, final_fit_plus$haz) -
c(final_fit_minus$coef, final_fit_minus$haz)) / (2*h)
#adj_se <- sqrt(diag(deta_dtheta %*% (1/(attr(opt_object, "details")[[3]])) %*% t(deta_dtheta)))
# vcov_adj = inner_m$Vcov + deta_dtheta %*% (1/(attr(outer_m, "details")[[3]])) %*% t(deta_dtheta)
vcov_adj = inner_m$Vcov + deta_dtheta %*% (1/outer_m$hessian) %*% t(deta_dtheta)
} else
if(all(is.na(inner_m$Vcov)))
vcov_adj <- inner_m$Vcov else
vcov_adj = matrix(NA, nrow(inner_m$Vcov), nrow(inner_m$Vcov))
if(length(pos_terminal_X1) > 0 & distribution$dist == "gamma") {
Y[,3] <- X1[,pos_terminal_X1]
Mres <- survival::agreg.fit(x = X, y = Y, strata = atrisk$strats, offset = NULL, init = NULL,
control = survival::coxph.control(),
weights = NULL, method = "breslow", rownames = NULL)$residuals
Mres_id <- rowsum(Mres, atrisk$order_id, reorder = FALSE)
theta <- exp(outer_m$estimate)
fr <- with(inner_m, estep[,1] / estep[,2])
numerator <- theta + inner_m$nev_id
denominator <- numerator / fr
lfr <- digamma(numerator) - log(denominator)
lfr2 <- (digamma(numerator))^2 + trigamma(numerator) - (log(denominator))^2 - 2 * log(denominator) * lfr
r <- cor(lfr, Mres_id)
tr <- r* sqrt((length(fr) - 2) / (1 - r^2))
p.cor <- pchisq(tr^2, df = 1, lower.tail = F)
cens_test = c(tstat = tr, pval = p.cor)
} else cens_test = NULL
# Prepare some things for the output object
if(!isTRUE(model)) model_frame <- NULL else
model_frame <- mf
if(!isTRUE(model.matrix)) X <- NULL
frail <- inner_m$frail
names(frail) <- unique(id)
residuals <- list(group = as.numeric(inner_m$Cvec),
individual = as.numeric(inner_m$cumhaz_line * inner_m$fitted))
names(residuals$group) <- unique(id)
haz <- inner_m$haz
tev <- inner_m$tev
if(!is.null(atrisk$strats)) {
names(haz) <- label_strats
names(tev) <- label_strats
}
res <- list(coefficients = inner_m$coef, #
hazard = haz,
var = inner_m$Vcov,
var_adj = vcov_adj,
logtheta = outer_m$estimate,
var_logtheta = 1/hessian,
ci_logtheta = c(log_theta_low, log_theta_high),
frail = frail,
residuals = residuals,
tev = tev,
nevents_id = inner_m$nev_id,
loglik = c(mcox$loglik[length(mcox$loglik)], -outer_m$minimum),
ca_test = ca_test,
cens_test = cens_test,
zph = zph,
formula = formula,
distribution = distribution,
control = control,
nobs = nrow(mf),
fitted = as.numeric(inner_m$fitted),
mf = model_frame,
mm = X)
# these are things that make the predict work and other methods
terms_2 <- delete.response(attr(mf, "terms"))
pos_cluster_2 <- grep("cluster", attr(terms_2, "term.labels"))
if(!is.null(mcox$coefficients)) {
terms <- drop.terms(terms_2, pos_cluster_2)
myxlev <- .getXlevels(terms, mf)
attr(res, "metadata") <- list(terms, myxlev)
}
attr(res, "call") <- Call
attr(res, "class") <- "emfrail"
res
}
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Defines functions emfrail
Documented in emfrail
#' Fitting semi-parametric shared frailty models with the EM algorithm
#'
#' @importFrom survival Surv coxph cox.zph
#' @importFrom stats approx coef model.frame model.matrix pchisq printCoefmat nlm uniroot cor optimize
#' @importFrom magrittr "%>%"
#' @importFrom Rcpp evalCpp
#' @importFrom Matrix bdiag
#' @importFrom numDeriv hessian
#' @useDynLib frailtyEM, .registration=TRUE
#' @include em_fit.R
#' @include emfrail_aux.R
#'
#' @param formula A formula that contains on the left hand side an object of the type \code{Surv}
#' and on the right hand side a \code{+cluster(id)} statement. Two special statments may also be used:
#' \code{+strata()} for specifying a grouping column that will represent different strata and
#' \code{+terminal()}
#' @param data A \code{data.frame} in which the formula argument can be evaluated
#' @param distribution An object as created by \code{\link{emfrail_dist}}
#' @param control An object as created by \code{\link{emfrail_control}}
#' @param model Logical. Should the model frame be returned?
#' @param model.matrix Logical. Should the model matrix be returned?
#' @param ... Other arguments, currently used to warn about deprecated argument names
#' @export
#'
#' @details The \code{emfrail} function fits shared frailty models for processes which have intensity
#' \deqn{\lambda(t) = z \lambda_0(t) \exp(\beta' \mathbf{x})}
#' with a non-parametric (Breslow) baseline intensity \eqn{\lambda_0(t)}. The outcome
#' (left hand side of the \code{formula}) must be a \code{Surv} object.
#'
#' If the object is \code{Surv(tstop, status)} then the usual failure time data is represented.
#' Gap-times between recurrent events are represented in the same way.
#' If the left hand side of the formula is created as \code{Surv(tstart, tstop, status)}, this may represent a number of things:
#' (a) recurrent events episodes in calendar time where a recurrent event episode starts at \code{tstart} and ends at \code{tstop}
#' (b) failure time data with time-dependent covariates where \code{tstop} is the time of a change in covariates or censoring
#' (\code{status = 0}) or an event time (\code{status = 1}) or (c) clustered failure time with left truncation, where
#' \code{tstart} is the individual's left truncation time. Unlike regular Cox models, a major distinction is that in case (c) the
#' distribution of the frailty must be considered conditional on survival up to the left truncation time.
#'
#' The \code{+cluster()} statement specified the column that determines the grouping (the observations that share the same frailty).
#' The \code{+strata()} statement specifies a column that determines different strata, for which different baseline hazards are calculated.
#' The \code{+terminal} specifies a column that contains an indicator for dependent censoring, and then performs a score test
#'
#' The \code{distribution} argument must be generated by a call to \code{\link{emfrail_dist}}. This determines the
#' frailty distribution, which may be one of gamma, positive stable or PVF (power-variance-function), and the starting
#' value for the maximum likelihood estimation. The PVF family
#' also includes a tuning parameter that differentiates between inverse Gaussian and compound Poisson distributions.
#' Note that, with univariate data (at most one event per individual, no clusters), only distributions with finite expectation
#' are identifiable. This means that the positive stable distribution should have a maximum likelihood on the edge of the parameter
#' space (\eqn{theta = +\inf}, corresponding to a Cox model for independent observations).
#'
#' The \code{control} argument must be generated by a call to \code{\link{emfrail_control}}. Several parameters
#' may be adjusted that control the precision of the convergenge criteria or supress the calculation of different
#' quantities.
#'
#' @return An object of class \code{emfrail} that contains the following fields:
#' \item{coefficients}{A named vector of the estimated regression coefficients}
#' \item{hazard}{The breslow estimate of the baseline hazard at each event time point, in chronological order}
#' \item{var}{The variance-covariance matrix corresponding to the coefficients and hazard, assuming \eqn{\theta} constant}
#' \item{var_adj}{The variance-covariance matrx corresponding to the
#' coefficients and hazard, adjusted for the estimation of theta}
#' \item{logtheta}{The logarithm of the point estimate of \eqn{\theta}. For the gamma and
#' PVF family of distributions, this is the inverse of the estimated frailty variance.}
#' \item{var_logtheta}{The variance of the estimated logarithm of \eqn{\theta}}
#' \item{ci_logtheta}{The likelihood-based 95\% confidence interval for the logarithm of \eqn{\theta}}
#' \item{frail}{The posterior (empirical Bayes) estimates of the frailty for each cluster}
#' \item{residuals}{A list with two elements, cluster which is a vector that the sum of the
#' cumulative hazards from each cluster for a frailty value of 1, and
#' individual, which is a vector that contains the cumulative hazard corresponding to each row of the data,
#' multiplied by the corresponding frailty estimate}
#' \item{tev}{The time points of the events in the data set, this is the same length as hazard}
#' \item{nevents_id}{The number of events for each cluster}
#' \item{loglik}{A vector of length two with the log-likelihood of the starting Cox model
#' and the maximized log-likelihood}
#' \item{ca_test}{The results of the Commenges-Andersen test for heterogeneity}
#' \item{cens_test}{The results of the test for dependence between a recurrent event and a terminal event,
#' if the \code{+terminal()} statement is specified and the frailty distribution is gamma}
#' \item{zph}{The result of \code{cox.zph} called on a model with the estimated log-frailties as offset}
#' \item{formula, distribution, control}{The original arguments}
#' \item{nobs, fitted}{Number of observations and fitted values (i.e. \eqn{z \exp(\beta^T x)})}
#' \item{mf}{The \code{model.frame}, if \code{model = TRUE}}
#' \item{mm}{The \code{model.matrix}, if \code{model.matrix = TRUE}}
#'
#' @md
#' @note Several options in the \code{control} arguemnt shorten the running time for \code{emfrail} significantly.
#' These are disabling the adjustemnt of the standard errors (\code{se_adj = FALSE}), disabling the likelihood-based confidence intervals (\code{lik_ci = FALSE}) or
#' disabling the score test for heterogeneity (\code{ca_test = FALSE}).
#'
#' The algorithm is detailed in the package vignette. For the gamma frailty,
#' the results should be identical with those from \code{coxph} with \code{ties = "breslow"}.
#'
#' @seealso \code{\link{plot.emfrail}} and \code{\link{autoplot.emfrail}} for plot functions directly available, \code{\link{emfrail_pll}} for calculating \eqn{\widehat{L}(\theta)} at specific values of \eqn{\theta},
#' \code{\link{summary.emfrail}} for transforming the \code{emfrail} object into a more human-readable format and for
#' visualizing the frailty (empirical Bayes) estimates,
#' \code{\link{predict.emfrail}} for calculating and visalizing conditional and marginal survival and cumulative
#' hazard curves. \code{\link{residuals.emfrail}} for extracting martingale residuals and \code{\link{logLik.emfrail}} for extracting
#' the log-likelihood of the fitted model.
#'
#' @examples
#'
#' m_gamma <- emfrail(formula = Surv(time, status) ~ rx + sex + cluster(litter),
#' data = rats)
#'
#' # Inverse Gaussian distribution
#' m_ig <- emfrail(formula = Surv(time, status) ~ rx + sex + cluster(litter),
#' data = rats,
#' distribution = emfrail_dist(dist = "pvf"))
#'
#' # for the PVF distribution with m = 0.75
#' m_pvf <- emfrail(formula = Surv(time, status) ~ rx + sex + cluster(litter),
#' data = rats,
#' distribution = emfrail_dist(dist = "pvf", pvfm = 0.75))
#'
#' # for the positive stable distribution
#' m_ps <- emfrail(formula = Surv(time, status) ~ rx + sex + cluster(litter),
#' data = rats,
#' distribution = emfrail_dist(dist = "stable"))
#' \dontrun{
#' # Compare marginal log-likelihoods
#' models <- list(m_gamma, m_ig, m_pvf, m_ps)
#'
#' models
#' logliks <- lapply(models, logLik)
#'
#' names(logliks) <- lapply(models,
#' function(x) with(x$distribution,
#' ifelse(dist == "pvf",
#' paste(dist, "/", pvfm),
#' dist))
#' )
#'
#' logliks
#' }
#'
#' # Stratified analysis
#' \dontrun{
#' m_strat <- emfrail(formula = Surv(time, status) ~ rx + strata(sex) + cluster(litter),
#' data = rats)
#' }
#'
#'
#' # Test for conditional proportional hazards (log-frailty as offset)
#' \dontrun{
#' m_gamma <- emfrail(formula = Surv(time, status) ~ rx + sex + cluster(litter),
#' data = rats, control = emfrail_control(zph = TRUE))
#' par(mfrow = c(1,2))
#' plot(m_gamma$zph)
#' }
#'
#' # Draw the profile log-likelihood
#' \dontrun{
#' fr_var <- seq(from = 0.01, to = 1.4, length.out = 20)
#'
#' # For gamma the variance is 1/theta (see parametrizations)
#' pll_gamma <- emfrail_pll(formula = Surv(time, status) ~ rx + sex + cluster(litter),
#' data = rats,
#' values = 1/fr_var )
#' plot(fr_var, pll_gamma,
#' type = "l",
#' xlab = "Frailty variance",
#' ylab = "Profile log-likelihood")
#'
#'
#' # Recurrent events
#' mod_rec <- emfrail(Surv(start, stop, status) ~ treatment + cluster(id), bladder1)
#' # The warnings appear from the Surv object, they also appear in coxph.
#'
#' plot(mod_rec, type = "hist")
#' }
#'
#' # Left truncation
#' \dontrun{
#' # We simulate some data with truncation times
#' set.seed(2018)
#' nclus <- 300
#' nind <- 5
#' x <- sample(c(0,1), nind * nclus, TRUE)
#' u <- rep(rgamma(nclus,1,1), each = 3)
#'
#' stime <- rexp(nind * nclus, rate = u * exp(0.5 * x))
#'
#' status <- ifelse(stime > 5, 0, 1)
#' stime[status == 0] <- 5
#'
#' # truncate uniform between 0 and 2
#' ltime <- runif(nind * nclus, min = 0, max = 2)
#'
#' d <- data.frame(id = rep(1:nclus, each = nind),
#' x = x,
#' stime = stime,
#' u = u,
#' ltime = ltime,
#' status = status)
#' d_left <- d[d$stime > d$ltime,]
#'
#' mod <- emfrail(Surv(stime, status)~ x + cluster(id), d)
#' # This model ignores the left truncation, 0.378 frailty variance:
#' mod_1 <- emfrail(Surv(stime, status)~ x + cluster(id), d_left)
#'
#' # This model takes left truncation into account,
#' # but it considers the distribution of the frailty unconditional on the truncation
#' mod_2 <- emfrail(Surv(ltime, stime, status)~ x + cluster(id), d_left)
#'
#' # This is identical with:
#' mod_cox <- coxph(Surv(ltime, stime, status)~ x + frailty(id), data = d_left)
#'
#'
#' # The correct thing is to consider the distribution of the frailty given the truncation
#' mod_3 <- emfrail(Surv(ltime, stime, status)~ x + cluster(id), d_left,
#' distribution = emfrail_dist(left_truncation = TRUE))
#'
#' summary(mod_1)
#' summary(mod_2)
#' summary(mod_3)
#' }
#' @author Theodor Balan \email{hello@@tbalan.com}
#' @references Balan TA, Putter H (2019) "frailtyEM: An R Package for Estimating Semiparametric Shared Frailty Models", \emph{Journal of Statistical Software} \strong{90}(7) 1-29. doi:10.18637/jss.v090.i07
emfrail <- function(formula,
data,
distribution = emfrail_dist(),
control = emfrail_control(),
model = FALSE, model.matrix = FALSE,
...) {
# browser()
# This part is because the update breaks old code
extraargs <- list(...)
if(!inherits(formula, "formula")) {
if(inherits(formula, "data.frame")) warning("You gave a data.frame instead of a formula.
Argument order has changed; now it's emfrail(formula, data, etc..).")
stop("formula is not an object of type formula")
}
if(!inherits(data, "data.frame")) {
if(inherits(data, "formula")) warning("You gave a formula instead of a data.frame.
Argument order has changed; now it's emfrail(formula, data, etc..).")
stop("data is not an object of type data.frame")
}
if(!inherits(distribution, "emfrail_dist"))
stop("distribution argument misspecified; see ?emfrail_dist()")
if(!inherits(control, "emfrail_control"))
stop("control argument misspecified; see ?emfrail_control()")
if(isTRUE(control$em_control$fast_fit)) {
if(!(distribution$dist %in% c("gamma", "pvf"))) {
#message("fast_fit option only available for gamma and pvf with m=-1/2 distributions")
control$em_control$fast_fit <- FALSE
}
# version 0.5.6, the IG fast fit gets super sensitive at small frailty variance...
if(distribution$dist == "pvf")
control$em_control$fast_fit <- FALSE
}
Call <- match.call()
if(missing(formula) | missing(data)) stop("Missing arguments")
cluster <- function(x) x
terminal <- function(x) x
strata <- function(x) x
mf <- model.frame(formula, data)
# Identify the cluster and the ID column
pos_cluster <- grep("cluster", names(mf))
if(length(pos_cluster) != 1) stop("misspecified or non-specified cluster")
id <- mf[[pos_cluster]]
pos_terminal <- grep("terminal", names(mf))
if(length(pos_terminal) > 1) stop("misspecified terminal()")
pos_strata <- grep("strata", names(mf))
if(length(pos_strata) > 0) {
if(length(pos_strata) > 1) stop("only one strata() variable allowed")
strats <- as.numeric(mf[[pos_strata]])
label_strats <- levels(mf[[pos_strata]])
} else {
# else, everyone is in the same strata
strats <- NULL
label_strats <- "1"
}
Y <- mf[[1]]
if(!inherits(Y, "Surv")) stop("left hand side not a survival object")
if(ncol(Y) != 3) {
# making it all in (tstart, tstop) format
Y <- Surv(rep(0, nrow(Y)), Y[,1], Y[,2])
}
X1 <- model.matrix(formula, data)
pos_cluster_X1 <- grep("cluster", colnames(X1))
pos_terminal_X1 <- grep("terminal", colnames(X1))
pos_strata_X1 <- grep("strata", colnames(X1))
X <- X1[,-c(1, pos_cluster_X1, pos_terminal_X1, pos_strata_X1), drop=FALSE]
# note: X has no attributes, in coxph it does.
# mcox also works with empty matrices, but also with NULL as x.
mcox <- survival::agreg.fit(x = X, y = Y, strata = strats, offset = NULL, init = NULL,
control = survival::coxph.control(),
weights = NULL, method = "breslow", rownames = NULL)
# order(strat, -Y[,2])
# the "baseline" case // this will stay constant
if(length(X) == 0) {
newrisk <- 1
exp_g_x <- matrix(rep(1, length(mcox$linear.predictors)), nrow = 1)
g <- 0
g_x <- t(matrix(rep(0, length(mcox$linear.predictors)), nrow = 1))
} else {
x2 <- matrix(rep(0, ncol(X)), nrow = 1, dimnames = list(123, dimnames(X)[[2]]))
x2 <- scale(x2, center = mcox$means, scale = FALSE)
newrisk <- exp(c(x2 %*% mcox$coefficients) + 0)
exp_g_x <- exp(mcox$coefficients %*% t(X))
g <- mcox$coefficients
g_x <- t(mcox$coefficients %*% t(X))
}
explp <- exp(mcox$linear.predictors) # these are with centered covariates
# now thing is that maybe this is not very necessary,
# but it keeps track of which row belongs to which cluster
# and then we don't have to keep on doing this
order_id <- match(id, unique(id))
nev_id <- as.numeric(rowsum(Y[,3], order_id, reorder = FALSE)) # nevent per cluster
names(nev_id) <- unique(id)
# nrisk has the sum with every tstop and the sum of elp at risk at that tstop
# esum has the sum of elp who enter at every tstart
# indx groups which esum is right after each nrisk;
# the difference between the two is the sum of elp really at risk at that time point.
if(!is.null(strats)) {
explp_str <- split(explp, strats)
tstop_str <- split(Y[,2], strats)
tstart_str <- split(Y[,1], strats)
ord_tstop_str <- lapply(tstop_str, function(x) match(x, sort(unique(x))))
ord_tstart_str <- lapply(tstart_str, function(x) match(x, sort(unique(x))))
nrisk <- mapply(FUN = function(explp, y) rowsum_vec(explp, y, max(y)),
explp_str,
ord_tstop_str,
SIMPLIFY = FALSE)
# nrisk <- mapply(FUN = function(explp, y) rev(cumsum(rev(rowsum(explp, y[,2])))),
# split(explp, strats),
# split.data.frame(Y, strats),
# SIMPLIFY = FALSE)
esum <- mapply(FUN = function(explp, y) rowsum_vec(explp, y, max(y)),
explp_str,
ord_tstart_str,
SIMPLIFY = FALSE)
# esum <- mapply(FUN = function(explp, y) rev(cumsum(rev(rowsum(explp, y[,1])))),
# split(explp, strats),
# split.data.frame(Y, strats),
# SIMPLIFY = FALSE)
death <- lapply(
X = split.default(Y[,3], strats),
FUN = function(y) (y == 1)
)
nevent <- mapply(
FUN = function(y, d)
as.vector(rowsum(1 * d, y)),
tstop_str,
death,
SIMPLIFY = FALSE
)
time_str <- lapply(
X = tstop_str,
FUN = function(y) sort(unique(y))
)
delta <- min(diff(sort(unique(Y[,2]))))/2
time <- sort(unique(Y[,2])) # unique tstops
etime <- lapply(
X = tstart_str,
FUN = function(y) c(0, sort(unique(y)), max(y) + delta)
)
indx <-
mapply(FUN = function(time, etime) findInterval(time, etime, left.open = TRUE),
time_str,
etime,
SIMPLIFY = FALSE
)
indx2 <-
mapply(FUN = function(y, time) findInterval(y, time),
tstart_str,
time_str,
SIMPLIFY = FALSE
)
time_to_stop <-
mapply(FUN = function(y, time) match(y, time),
tstop_str,
time_str,
SIMPLIFY = FALSE
)
positions_strata <- do.call(c,split(1:nrow(Y), strats))
atrisk <- list(death = death, nevent = nevent, nev_id = nev_id,
order_id = order_id, time = time, indx = indx, indx2 = indx2,
time_to_stop = time_to_stop,
ord_tstart_str = ord_tstart_str,
ord_tstop_str = ord_tstop_str,
positions_strata = positions_strata,
strats = strats)
nrisk <- mapply(FUN = function(nrisk, esum, indx) nrisk - c(esum, 0,0)[indx],
nrisk,
esum,
indx,
SIMPLIFY = FALSE)
if(newrisk == 0) warning("Hazard ratio very extreme; please check (and/or rescale) your data")
haz <- mapply(FUN = function(nevent, nrisk) nevent/nrisk * newrisk,
nevent,
nrisk,
SIMPLIFY = FALSE)
basehaz_line <- mapply(FUN = function(haz, time_to_stop) haz[time_to_stop],
haz,
time_to_stop,
SIMPLIFY = FALSE)
cumhaz <- lapply(haz, cumsum)
cumhaz_0_line <- mapply(FUN = function(cumhaz, time_to_stop) cumhaz[time_to_stop],
cumhaz,
time_to_stop,
SIMPLIFY = FALSE)
cumhaz_tstart <- mapply(FUN = function(cumhaz, indx2) c(0, cumhaz)[indx2 + 1],
cumhaz,
indx2,
SIMPLIFY = FALSE)
cumhaz_line <- mapply(FUN = function(cumhaz_0_line, cumhaz_tstart, explp)
(cumhaz_0_line - cumhaz_tstart) * explp / newrisk,
cumhaz_0_line,
cumhaz_tstart,
split(explp, strats),
SIMPLIFY = FALSE)
cumhaz_line <- do.call(c, cumhaz_line)[order(positions_strata)]
} else {
ord_tstop <- match(Y[,2], sort(unique(Y[,2])))
ord_tstart <- match(Y[,1], sort(unique(Y[,1])))
nrisk <- rowsum_vec(explp, ord_tstop, max(ord_tstop))
# nrisk <- rev(cumsum(rev(rowsum(explp, Y[, ncol(Y) - 1]))))
esum <- rowsum_vec(explp, ord_tstart, max(ord_tstart))
# esum <- rev(cumsum(rev(rowsum(explp, Y[, 1]))))
death <- (Y[, 3] == 1)
nevent <- as.vector(rowsum(1 * death, Y[, ncol(Y) - 1])) # per time point
time <- sort(unique(Y[,2])) # unique tstops
etime <- c(0, sort(unique(Y[, 1])), max(Y[, 1]) + min(diff(time))/2)
indx <- findInterval(time, etime, left.open = TRUE) # left.open = TRUE is very important
# this gives for every tstart (line variable), after which event time did it come
indx2 <- findInterval(Y[,1], time)
time_to_stop <- match(Y[,2], time)
atrisk <- list(death = death, nevent = nevent, nev_id = nev_id,
order_id = order_id,
time = time, indx = indx, indx2 = indx2,
time_to_stop = time_to_stop,
ord_tstart = ord_tstart, ord_tstop = ord_tstop,
strats = NULL)
nrisk <- nrisk - c(esum, 0,0)[indx]
if(newrisk == 0) warning("Hazard ratio very extreme; please check (and/or rescale) your data")
haz <- nevent/nrisk * newrisk
basehaz_line <- haz[atrisk$time_to_stop]
cumhaz <- cumsum(haz)
cumhaz_0_line <- cumhaz[atrisk$time_to_stop]
cumhaz_tstart <- c(0, cumhaz)[atrisk$indx2 + 1]
cumhaz_line <- (cumhaz[atrisk$time_to_stop] - c(0, cumhaz)[atrisk$indx2 + 1]) * explp / newrisk
}
Cvec <- rowsum(cumhaz_line, order_id, reorder = FALSE)
# browser()
# this part under construction!
# if(distribution$basehaz != "breslow") {
# if(any(Y[,1] != 0))
# stop("(tstart, tstop) not supported for parametric models")
#
# dlist <- survival::survreg.distributions[[distribution$basehaz]]
#
# # this stuff is more or less copied from survreg
#
# logcorrect <- 0 #correction to the loglik due to transformations
# Ysave <- Y # for use in the y component
# if (!is.null(dlist$trans)) {
# tranfun <- dlist$trans
# exactsurv <- Y[, ncol(Y)] == 1
# if (any(exactsurv)) {
# logcorrect <- sum(log(dlist$dtrans(Y[exactsurv, 1])))
# }
# if (!all(is.finite(Y)))
# stop("Invalid survival times for this distribution")
#
# }
#
# if (!is.null(dlist$scale)) {
# if (!missing(scale))
# warning(paste(dlist$name, "has a fixed scale, user specified value ignored"))
# scale <- dlist$scale
# } else scale <- 0
#
# if (!is.null(dlist$dist))
# if (is.atomic(dlist$dist))
# dlist <- survreg.distributions[[dlist$dist]] else dlist <- dlist$dist
#
# if (any(scale < 0))
# stop("Invalid scale value")
# # Now we convert this to a format that survreg.fit likes
#
# fit <- survreg.fit(cbind(1, X), cbind(tranfun(Y[,2]), Y[,3]),
# weights = NULL,
# offset = NULL,
# init = NULL,
# controlvals = survreg.control() ,
# dist = dlist, scale = scale, nstrat = 1, strata = 0, parms= NULL)
#
#
# }
#
#
#
# srg1 <- survreg_simple(formula = Surv(time, status) ~ rx + sex, data = rats, dist = "weibull")
#
# srg1$coefficients
# fit$coefficients
#
# fit <- survreg.fit(X, Y, weights = NULL, offset = NULL, init = NULL,
# controlvals = survreg.control(), dist = dlist, scale = 0)
#
# distribution
# dlist <- survival::survreg.distributions[[distribution$]]
# ca_test <- NULL
# ca_test_fit does not know strata ?!?
if(isTRUE(control$ca_test)) {
if(!is.null(strats)) ca_test <- NULL else
ca_test <- ca_test_fit(mcox, X, atrisk, exp_g_x, cumhaz)
}
if(isTRUE(distribution$left_truncation)) {
if(!is.null(strats))
cumhaz_tstart <- do.call(c, cumhaz_tstart)[order(atrisk$positions_strata)]
Cvec_lt <- rowsum(cumhaz_tstart, atrisk$order_id, reorder = FALSE)
} else Cvec_lt <- 0 * Cvec
# a fit just for the log-likelihood;
if(!isTRUE(control$opt_fit)) {
return(
em_fit(logfrailtypar = log(distribution$theta),
dist = distribution$dist, pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk,
basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control)
)
}
# browser()
if(distribution$dist == "stable") {
# thing is: with stable small values of theta mean high dependence
# I have yet to see a very high dependence there; furthermore,
# the likelihood is pretty flat there.
# therefore I would rather drag this towards "no dependence".
distribution$theta <- distribution$theta + 1
}
outer_m <- do.call(nlm, args = c(list(f = em_fit,
p = log(distribution$theta),
hessian = TRUE,
dist = distribution$dist,
pvfm = distribution$pvfm,
Y = Y, Xmat = X,
atrisk = atrisk,
basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec,
lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control), control$nlm_control))
# control$lik_interval_stable
if(outer_m$hessian < 1) {
outer_m_opt <- do.call(optimize,
args = c(list(f = em_fit,
dist = distribution$dist,
pvfm = distribution$pvfm,
Y = Y, Xmat = X,
atrisk = atrisk,
basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec,
lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control), lower = log(control$lik_interval)[1],
upper = log(control$lik_interval)[2]))
if(outer_m_opt$objective < outer_m$minimum) {
hess <- numDeriv::hessian(func = em_fit, x = outer_m_opt$minimum,
dist = distribution$dist,
pvfm = distribution$pvfm,
Y = Y, Xmat = X,
atrisk = atrisk,
basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec,
lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control)
outer_m <- list(minimum = outer_m_opt$objective,
estimate = outer_m_opt$minimum,
hessian = hess)
}
}
if(outer_m$hessian == 0) warning("Hessian virtually 0; frailty variance might be at the edge of the parameter space.")
if(outer_m$hessian <= 0) hessian <- NA else hessian <- outer_m$hessian
# likelihood-based confidence intervals
theta_low <- theta_high <- NULL
if(isTRUE(control$lik_ci)) {
# With the stable distribution, a problem pops up for small values, i.e. very large association (tau large)
# So there I use another interval for this
if(distribution$dist == "stable") {
control$lik_interval <- control$lik_interval_stable
}
skip_ci <- FALSE
lower_llik <- try(em_fit(log(control$lik_interval[1]),
dist = distribution$dist,
pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk, basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control), silent = TRUE)
if(class(lower_llik) == "try-error") {
warning("likelihood-based CI could not be calcuated; disable or change lik_interval[1] in emfrail_control")
lower_llik <- NA
log_theta_low <- log_theta_high <- NA
skip_ci <- TRUE
}
upper_llik <- try(em_fit(log(control$lik_interval[2]),
dist = distribution$dist,
pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk, basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control), silent = TRUE)
if(class(upper_llik) == "try-error") {
warning("likelihood-based CI could not be calcuated; disable or lik_interval[2] in emfrail_control")
upper_llik <- NA
log_theta_low <- log_theta_high <- NA
skip_ci <- TRUE
}
if(!isTRUE(skip_ci)) {
if(lower_llik - outer_m$minimum < 1.92) {
log_theta_low <- log(control$lik_interval[1])
warning("Likelihood-based confidence interval lower limit reached, probably 0;
You can try a lower value for control$lik_interval[1].")
} else
log_theta_low <- uniroot(function(x, ...) outer_m$minimum - em_fit(x, ...) + 1.92,
interval = c(log(control$lik_interval[1]), outer_m$estimate),
f.lower = outer_m$minimum - lower_llik + 1.92, f.upper = 1.92,
tol = .Machine$double.eps^0.1,
dist = distribution$dist,
pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk, basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control,
maxiter = 100)$root
# this says that if I can't get a significant difference on the right side, then it's infinity
if(upper_llik - outer_m$minimum < 1.92) log_theta_high <- Inf else
log_theta_high <- uniroot(function(x, ...) outer_m$minimum - em_fit(x, ...) + 1.92,
interval = c(outer_m$estimate, log(control$lik_interval[2])),
f.lower = 1.92, f.upper = outer_m$minimum - upper_llik + 1.92,
extendInt = c("downX"),
dist = distribution$dist,
pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk, basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control)$root
}
} else
log_theta_low <- log_theta_high <- NA
if(isTRUE(control$se)) {
inner_m <- em_fit(logfrailtypar = outer_m$estimate,
dist = distribution$dist, pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk, basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = TRUE,
em_control = control$em_control,
return_loglik = FALSE)
} else
inner_m <- em_fit(logfrailtypar = outer_m$estimate,
dist = distribution$dist, pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk, basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control,
return_loglik = FALSE)
# Cox.ZPH stuff
if(isTRUE(control$zph)) {
# Here just fit a Cox model with the log-frailty as offset
# note: the cox.zph function in the new version of the survival package has a terms = TRUE argument.
# This part here is added so that emfrail continues to work with both versions.
# do.call is needed because otherwise R CMD check returns a warning when ran on a system with the
# old version of cox.zph
if("terms" %in% names(formals(cox.zph))) {
if(!is.null(strats)) {
zph <- do.call(cox.zph, args = list(fit = coxph(Y ~ X + strata(strats) + offset(inner_m$logz), ties = "breslow"),
transform = control$zph_transform,
terms = FALSE))
# zph <- cox.zph(coxph(Y ~ X + strata(strats) + offset(inner_m$logz), ties = "breslow"),
# transform = control$zph_transform, terms = FALSE)
} else {
zph <- do.call(cox.zph, args = list(fit = coxph(Y ~ X + offset(inner_m$logz), ties = "breslow"),
transform = control$zph_transform,
terms = FALSE))
# zph <- cox.zph(coxph(Y ~ X + offset(inner_m$logz), ties = "breslow"),
# transform = control$zph_transform, terms = FALSE)
}
} else {
if(!is.null(strats)) {
zph <- do.call(cox.zph, args = list(fit = coxph(Y ~ X + strata(strats) + offset(inner_m$logz), ties = "breslow"),
transform = control$zph_transform))
} else
zph <- do.call(cox.zph, args = list(fit = coxph(Y ~ X + offset(inner_m$logz), ties = "breslow"),
transform = control$zph_transform))
}
# fix the names for nice output
# if there is only one covariate there is not "GLOBAL" test
attr(zph$table, "dimnames")[[1]][1:length(inner_m$coef)] <- names(inner_m$coef)
attr(zph$y, "dimnames")[[2]] <- names(mcox$coef)
} else zph <- NULL
# adjusted standard error
if(isTRUE(control$se) & isTRUE(attr(inner_m$Vcov, "class") == "try-error")) {
inner_m$Vcov <- matrix(NA, length(inner_m$coef) + length(inner_m$haz))
warning("Information matrix is singular")
}
# adjusted SE: only go on if requested and if Vcov was calculated
if(isTRUE(control$se) &
isTRUE(control$se_adj) &
!all(is.na(inner_m$Vcov))) {
# absolute value should be redundant. but sometimes the "hessian" might be 0.
# in that case it might appear negative; this happened only on Linux...
# h <- as.numeric(sqrt(abs(1/(attr(outer_m, "details")[[3]])))/2)
h<- as.numeric(sqrt(abs(1/hessian))/2)
lfp_minus <- max(outer_m$estimate - h , outer_m$estimate - 5, na.rm = TRUE)
lfp_plus <- min(outer_m$estimate + h , outer_m$estimate + 5, na.rm = TRUE)
final_fit_minus <- em_fit(logfrailtypar = lfp_minus,
dist = distribution$dist, pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk, basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control,
return_loglik = FALSE)
final_fit_plus <- em_fit(logfrailtypar = lfp_plus,
dist = distribution$dist, pvfm = distribution$pvfm,
Y = Y, Xmat = X, atrisk = atrisk, basehaz_line = basehaz_line,
mcox = list(coefficients = g, loglik = mcox$loglik), # a "fake" cox model
Cvec = Cvec, lt = distribution$left_truncation,
Cvec_lt = Cvec_lt, se = FALSE,
em_control = control$em_control, return_loglik = FALSE)
# instructional: this should be more or less equal to the
# -(final_fit_plus$loglik + final_fit_minus$loglik - 2 * inner_m$loglik)/h^2
# se_logtheta^2 / (2 * (final_fit$loglik -final_fit_plus$loglik ))
if(!is.null(atrisk$strats))
deta_dtheta <- (c(final_fit_plus$coef, do.call(c, final_fit_plus$haz)) -
c(final_fit_minus$coef, do.call(c, final_fit_minus$haz))) / (2*h) else
deta_dtheta <- (c(final_fit_plus$coef, final_fit_plus$haz) -
c(final_fit_minus$coef, final_fit_minus$haz)) / (2*h)
#adj_se <- sqrt(diag(deta_dtheta %*% (1/(attr(opt_object, "details")[[3]])) %*% t(deta_dtheta)))
# vcov_adj = inner_m$Vcov + deta_dtheta %*% (1/(attr(outer_m, "details")[[3]])) %*% t(deta_dtheta)
vcov_adj = inner_m$Vcov + deta_dtheta %*% (1/outer_m$hessian) %*% t(deta_dtheta)
} else
if(all(is.na(inner_m$Vcov)))
vcov_adj <- inner_m$Vcov else
vcov_adj = matrix(NA, nrow(inner_m$Vcov), nrow(inner_m$Vcov))
if(length(pos_terminal_X1) > 0 & distribution$dist == "gamma") {
Y[,3] <- X1[,pos_terminal_X1]
Mres <- survival::agreg.fit(x = X, y = Y, strata = atrisk$strats, offset = NULL, init = NULL,
control = survival::coxph.control(),
weights = NULL, method = "breslow", rownames = NULL)$residuals
Mres_id <- rowsum(Mres, atrisk$order_id, reorder = FALSE)
theta <- exp(outer_m$estimate)
fr <- with(inner_m, estep[,1] / estep[,2])
numerator <- theta + inner_m$nev_id
denominator <- numerator / fr
lfr <- digamma(numerator) - log(denominator)
lfr2 <- (digamma(numerator))^2 + trigamma(numerator) - (log(denominator))^2 - 2 * log(denominator) * lfr
r <- cor(lfr, Mres_id)
tr <- r* sqrt((length(fr) - 2) / (1 - r^2))
p.cor <- pchisq(tr^2, df = 1, lower.tail = F)
cens_test = c(tstat = tr, pval = p.cor)
} else cens_test = NULL
# Prepare some things for the output object
if(!isTRUE(model)) model_frame <- NULL else
model_frame <- mf
if(!isTRUE(model.matrix)) X <- NULL
frail <- inner_m$frail
names(frail) <- unique(id)
residuals <- list(group = as.numeric(inner_m$Cvec),
individual = as.numeric(inner_m$cumhaz_line * inner_m$fitted))
names(residuals$group) <- unique(id)
haz <- inner_m$haz
tev <- inner_m$tev
if(!is.null(atrisk$strats)) {
names(haz) <- label_strats
names(tev) <- label_strats
}
res <- list(coefficients = inner_m$coef, #
hazard = haz,
var = inner_m$Vcov,
var_adj = vcov_adj,
logtheta = outer_m$estimate,
var_logtheta = 1/hessian,
ci_logtheta = c(log_theta_low, log_theta_high),
frail = frail,
residuals = residuals,
tev = tev,
nevents_id = inner_m$nev_id,
loglik = c(mcox$loglik[length(mcox$loglik)], -outer_m$minimum),
ca_test = ca_test,
cens_test = cens_test,
zph = zph,
formula = formula,
distribution = distribution,
control = control,
nobs = nrow(mf),
fitted = as.numeric(inner_m$fitted),
mf = model_frame,
mm = X)
# these are things that make the predict work and other methods
terms_2 <- delete.response(attr(mf, "terms"))
pos_cluster_2 <- grep("cluster", attr(terms_2, "term.labels"))
if(!is.null(mcox$coefficients)) {
terms <- drop.terms(terms_2, pos_cluster_2)
myxlev <- .getXlevels(terms, mf)
attr(res, "metadata") <- list(terms, myxlev)
}
attr(res, "call") <- Call
attr(res, "class") <- "emfrail"
res
}
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