Nothing
R/probtrans.R
In mstate: Data Preparation, Estimation and Prediction in Multi-State Models
Defines functions
`probtrans`
#' Compute subject-specific or overall transition probabilities with standard
#' errors
#'
#' This function computes subject-specific or overall transition probabilities
#' in multi-state models. If requested, also standard errors are calculated.
#'
#' For details refer to de Wreede, Fiocco & Putter (2010).
#'
#' @param object \link{msfit} object containing estimated cumulative hazards
#' for each of the transitions in the multi-state model and, if standard errors
#' are requested, (co)variances of these cumulative hazards for each pair of
#' transitions
#' @param predt A positive number indicating the prediction time. This is
#' either the time at which the prediction is made (if \code{direction}=
#' \code{"forward"}) or the time for which the prediction is to be made (if
#' \code{direction}=\code{"fixedhorizon"})
#' @param direction One of \code{"forward"} (default) or \code{"fixedhorizon"},
#' indicating whether prediction is forward or for a fixed horizon
#' @param method A character string specifying the type of variances to be
#' computed (so only needed if either \code{variance} or \code{covariance} is
#' \code{TRUE}). Possible values are \code{"aalen"} or \code{"greenwood"}
#' @param variance Logical value indicating whether standard errors are to be
#' calculated (default is \code{TRUE})
#' @param covariance Logical value indicating whether covariances of transition
#' probabilities for different states are to be calculated (default is
#' \code{FALSE})
#' @return An object of class \code{"probtrans"}, which is a list of which item
#' [[s]] contains a data frame with the estimated transition probabilities (and
#' standard errors if \code{variance}=\code{TRUE}) from state s. If
#' \code{covariance}=\code{TRUE}, item \code{varMatrix} contains an array of
#' dimension K^2 x K^2 x (nt+1) (with K the number of states and nt the
#' distinct transition time points); the time points correspond to those in the
#' data frames with the estimated transition probabilities. Finally, there are
#' items \code{trans}, \code{method}, \code{predt}, \code{direction}, recording
#' the transition matrix, and the method, predt and direction arguments used in
#' the call to probtrans. Plot and summary methods have been defined for
#' \code{"probtrans"} objects.
#' @author Liesbeth de Wreede and Hein Putter \email{H.Putter@@lumc.nl}
#' @references Andersen PK, Borgan O, Gill RD, Keiding N (1993).
#' \emph{Statistical Models Based on Counting Processes}. Springer, New York.
#'
#' Putter H, Fiocco M, Geskus RB (2007). Tutorial in biostatistics: Competing
#' risks and multi-state models. \emph{Statistics in Medicine} \bold{26},
#' 2389--2430.
#'
#' Therneau TM, Grambsch PM (2000). \emph{Modeling Survival Data: Extending the
#' Cox Model}. Springer, New York.
#'
#' de Wreede LC, Fiocco M, and Putter H (2010). The mstate package for
#' estimation and prediction in non- and semi-parametric multi-state and
#' competing risks models. \emph{Computer Methods and Programs in Biomedicine}
#' \bold{99}, 261--274.
#'
#' de Wreede LC, Fiocco M, and Putter H (2011). mstate: An R Package for the
#' Analysis of Competing Risks and Multi-State Models. \emph{Journal of
#' Statistical Software}, Volume 38, Issue 7.
#' @keywords survival
#' @examples
#'
#' # transition matrix for illness-death model
#' tmat <- trans.illdeath()
#' # data in wide format, for transition 1 this is dataset E1 of
#' # Therneau & Grambsch (2000)
#' tg <- data.frame(illt=c(1,1,6,6,8,9),ills=c(1,0,1,1,0,1),
#' dt=c(5,1,9,7,8,12),ds=c(1,1,1,1,1,1),
#' x1=c(1,1,1,0,0,0),x2=c(6:1))
#' # data in long format using msprep
#' tglong <- msprep(time=c(NA,"illt","dt"),status=c(NA,"ills","ds"),
#' data=tg,keep=c("x1","x2"),trans=tmat)
#' # events
#' events(tglong)
#' table(tglong$status,tglong$to,tglong$from)
#' # expanded covariates
#' tglong <- expand.covs(tglong,c("x1","x2"))
#' # Cox model with different covariate
#' cx <- coxph(Surv(Tstart,Tstop,status)~x1.1+x2.2+strata(trans),
#' data=tglong,method="breslow")
#' summary(cx)
#' # new data, to check whether results are the same for transition 1 as
#' # those in appendix E.1 of Therneau & Grambsch (2000)
#' newdata <- data.frame(trans=1:3,x1.1=c(0,0,0),x2.2=c(0,1,0),strata=1:3)
#' HvH <- msfit(cx,newdata,trans=tmat)
#' # probtrans
#' pt <- probtrans(HvH,predt=0)
#' # predictions from state 1
#' pt[[1]]
#'
#' @export
`probtrans` <- function(object,predt,direction=c("forward","fixedhorizon"),
method=c("aalen","greenwood"),variance=TRUE,covariance=FALSE)
{
if (!inherits(object, "msfit"))
stop("'object' must be a 'msfit' object")
method <- match.arg(method)
direction <- match.arg(direction)
trans <- object$trans
transit <- to.trans2(trans)
numtrans <- nrow(transit)
variance_boot <- FALSE
# Check if bootstrap replications are in the object:
if("Haz.boot" %in% names(object)){
# We don't want to calculate (co)variances with the usual methods:
covariance <- FALSE
if(variance){
variance <- FALSE
variance_boot <- TRUE # we want to calculate bootstrapped variances
}
}
stackhaz <- object$Haz
stackvarhaz <- object$varHaz
for (i in 1:numtrans)
stackhaz$dhaz[stackhaz$trans==i] <- diff(c(0,stackhaz$Haz[stackhaz$trans==i]))
if (direction=="forward")
stackhaz <- stackhaz[stackhaz$time > predt,]
else stackhaz <- stackhaz[stackhaz$time <= predt,]
untimes <- sort(unique(stackhaz$time))
TT <- length(untimes)
S <- nrow(trans)
if (covariance) variance <- TRUE # if covariance=TRUE and variance=FALSE, variance is overruled
if (direction=="forward") {
if (variance==TRUE) res <- array(0,c(TT+1,2*S+1,S)) # 2*S+1 for time, probs (S), se (S)
else res <- array(0,c(TT+1,S+1,S)) # S+1 for time, probs (S)
# first line (in case of forward) contains values for t=predt
res[1,1,] <- predt
for (j in 1:S) res[1, 1+j,] <- rep(c(0,1,0), c(j-1,1,S-j))
if (variance) res[1,(S+2):(2*S+1),] <- 0
}
else {
# situation for backward is different from forward,
# depends on whether predt is an event time
if (predt %in% untimes) {
if (variance) res <- array(0,c(TT+1,2*S+1,S)) # t=0 and all event times
else res <- array(0,c(TT+1,S+1,S))
res[TT+1,1,] <- predt
for (j in 1:S) res[TT+1, 1+j,] <- rep(c(0,1,0), c(j-1,1,S-j))
if (variance) res[TT+1,(S+2):(2*S+1),] <- 0
}
else {
if (variance) res <- array(0,c(TT+2,2*S+1,S)) # t=0, event times, t=predt
else res <- array(0,c(TT+2,S+1,S))
res[TT+1,1,] <- max(untimes)
for (j in 1:S) res[TT+1, 1+j,] <- rep(c(0,1,0), c(j-1,1,S-j))
if (variance) res[TT+1,(S+2):(2*S+1),] <- 0
res[TT+2,1,] <- predt
for (j in 1:S) res[TT+2, 1+j,] <- rep(c(0,1,0), c(j-1,1,S-j))
if (variance) res[TT+2,(S+2):(2*S+1),] <- 0
}
}
P <- diag(S)
if (covariance) {
varParr <- array(0,c(S^2,S^2,TT+1))
if ((direction=="fixedhorizon") & !(predt %in% untimes))
varParr <- array(0,c(S^2,S^2,TT+2))
ffrom <- rep(1:S, S)
tto <- rep(1:S, rep(S,S))
fromto <- paste("from",ffrom,"to",tto,sep="")
if (direction=="forward")
dimnames(varParr) <- list(fromto,fromto,c(predt,untimes))
else {
if (predt %in% untimes) dimnames(varParr) <- list(fromto,fromto,c(0,untimes))
else dimnames(varParr) <- list(fromto,fromto,c(0,untimes,predt))
}
}
if (variance) {
varP <- matrix(0,S^2,S^2)
if (direction=="forward") {
varAnew <- array(0,c(S,S,S,S))
if (predt !=0) {
tmin <- max(stackvarhaz$time[stackvarhaz$time <=predt])
varHaz <- stackvarhaz[stackvarhaz$time==tmin,]
lHaz <- nrow(varHaz)
for (j in 1:lHaz)
{
from1 <- transit$from[transit$transno==varHaz$trans1[j]]
to1 <- transit$to[transit$transno==varHaz$trans1[j]]
from2 <- transit$from[transit$transno==varHaz$trans2[j]]
to2 <- transit$to[transit$transno==varHaz$trans2[j]]
varAnew[from1, to1, from2, to2] <-
varAnew[from2, to2, from1, to1] <- varHaz$varHaz[j]
}
}
}
else {
# varA on last event time (only those elements borrowed
# directly from object, rest is calculated later)
varA <- array(0,c(S,S,S,S))
varHaz <- stackvarhaz[stackvarhaz$time==untimes[TT],]
lHaz <- nrow(varHaz)
for (j in 1:lHaz)
{
from1 <- transit$from[transit$transno==varHaz$trans1[j]]
to1 <- transit$to[transit$transno==varHaz$trans1[j]]
from2 <- transit$from[transit$transno==varHaz$trans2[j]]
to2 <- transit$to[transit$transno==varHaz$trans2[j]]
varA[from1, to1, from2, to2] <-
varA[from2, to2, from1, to1] <- varHaz$varHaz[j]
}
}
}
for (i in 1:TT)
{
idx <- ifelse(direction=="forward",i,TT+1-i)
tt <- untimes[idx]
Haztt <- stackhaz[stackhaz$time==tt,]
lHaztt <- nrow(Haztt)
# build S x S matrix IplusdA
IplusdA <- diag(S)
for (j in 1:lHaztt)
{
from <- transit$from[transit$transno==Haztt$trans[j]]
to <- transit$to[transit$transno==Haztt$trans[j]]
IplusdA[from, to] <- Haztt$dhaz[j]
IplusdA[from, from] <- IplusdA[from, from] - Haztt$dhaz[j]
}
if (any(diag(IplusdA)<0))
warning("Warning! Negative diagonal elements of (I+dA); the estimate may not be meaningful. \n")
if (variance) {
if (direction=="forward"){
varA <- varAnew
varAnew <- array(0,c(S,S,S,S))
varHaztt <- stackvarhaz[stackvarhaz$time==tt,]
lHaztt <- nrow(varHaztt)
for (j in 1:lHaztt)
{
from1 <- transit$from[transit$transno==varHaztt$trans1[j]]
to1 <- transit$to[transit$transno==varHaztt$trans1[j]]
from2 <- transit$from[transit$transno==varHaztt$trans2[j]]
to2 <- transit$to[transit$transno==varHaztt$trans2[j]]
varAnew[from1, to1, from2, to2] <-
varAnew[from2, to2, from1, to1] <- varHaztt$varHaz[j]
}
vardA <- varAnew - varA
}
else {
varAttmin <- array(0,c(S,S,S,S))
varHazttmin <- stackvarhaz[stackvarhaz$time==untimes[idx-1],]
lHazttmin <- nrow(varHazttmin)
for (j in 1:lHazttmin)
{
from1 <- transit$from[transit$transno==varHazttmin$trans1[j]]
to1 <- transit$to[transit$transno==varHazttmin$trans1[j]]
from2 <- transit$from[transit$transno==varHazttmin$trans2[j]]
to2 <- transit$to[transit$transno==varHazttmin$trans2[j]]
varAttmin[from1, to1, from2, to2] <-
varAttmin[from2, to2, from1, to1] <- varHazttmin$varHaz[j]
}
vardA <- varA - varAttmin
varA <- varAttmin # ready for the next round
}
for (from in 1:S)
{
for (from2 in 1:S)
{
for (to2 in 1:S)
{
if (to2!=from2)
vardA[from, from, from2, to2] <-
vardA[from2, to2, from, from] <-
-sum(vardA[from,-from,from2,to2])
}
}
}
for (from in 1:S)
{
for (from2 in 1:S)
vardA[from,from,from2,from2] <-
vardA[from2,from2,from,from] <-
-sum(vardA[from,from,from2,-from2])
}
vardA <- matrix(vardA,S^2,S^2)
}
if (method=="aalen")
{
if (direction=="forward")
{
P <- P %*% IplusdA
if (variance) {
tmp1 <- kronecker(t(IplusdA),diag(S)) %*% varP %*% kronecker(IplusdA,diag(S))
tmp2 <- kronecker(diag(S),P) %*% vardA %*% kronecker(diag(S),t(P))
varP <- tmp1 + tmp2
}
}
else {
if (variance) {
tmp1 <- kronecker(diag(S), IplusdA) %*% varP %*% kronecker(diag(S), t(IplusdA))
tmp2 <- kronecker(t(P), IplusdA) %*% vardA %*% kronecker(P,t(IplusdA))
varP <- tmp1+tmp2
}
P <- IplusdA %*% P
}
}
if (method=="greenwood")
{
if (direction=="forward")
{
if (variance) {
tmp1 <- kronecker(t(IplusdA),diag(S)) %*% varP %*% kronecker(IplusdA,diag(S))
tmp2 <- kronecker(diag(S),P) %*% vardA %*% kronecker(diag(S),t(P))
varP <- tmp1 + tmp2
}
P <- P %*% IplusdA
}
else {
if (variance) {
tmp1 <- kronecker(diag(S), IplusdA) %*% varP %*% kronecker(diag(S), t(IplusdA))
tmp2 <- kronecker(t(P), diag(S)) %*% vardA %*% kronecker(P, diag(S))
varP <- tmp1+tmp2
}
P <- IplusdA %*% P
}
}
if (variance) {
seP <- sqrt(diag(varP))
seP <- matrix(seP,S,S)
}
if (covariance) {
if (direction=="forward") varParr[,,i+1] <- varP
else {
varParr[,,idx+1] <- varP
}
}
if (direction=="forward") {
res[idx+1,1,] <- tt
res[idx+1,2:(S+1),] <- t(P)
if (variance) res[idx+1,(S+2):(2*S+1),] <- t(seP)
}
else {
res[idx,1,] <- ifelse(i==TT,0,untimes[TT-i])
res[idx,2:(S+1),] <- t(P)
if (variance) res[idx,(S+2):(2*S+1),] <- t(seP)
}
}
if (covariance & (direction=="fixedhorizon"))
varParr[,,1] <- varParr[,,2]
### res[,,s] contains prediction from state s, convert to list of dataframes
res2 <- vector("list", S)
for (s in 1:S) {
tmp <- as.data.frame(res[,,s])
if (min(dim(tmp))==1) tmp <- res[,,s]
if (variance) names(tmp) <- c("time",paste("pstate",1:S,sep=""),paste("se",1:S,sep=""))
else names(tmp) <- c("time",paste("pstate",1:S,sep=""))
res2[[s]] <- tmp
}
if (covariance) res2$varMatrix <- varParr
# Calculate bootstrap se's for probtrans:
if(variance_boot){
# Find absorbing states:
is_absorbing <- rowSums(!is.na(trans))==0
absorbing_true <- which(is_absorbing==TRUE)
absorbing_false <- which(is_absorbing==FALSE)
# We make two steps (based on whether we deal with an absorbing or transient state):
# 1. For transprobs starting from an absorbing state put se = 0:
# Define empty SE data frames:
se_df <- as.data.frame(matrix(0, nrow=1, ncol=S))
names(se_df) <- paste("se", 1:S, sep="")
# Add zero SE's in probtrans for absorbing states:
for(s in absorbing_true){
res2[[s]] <- cbind(res2[[s]], se_df)
}
# 2. For transprobs starting from a transient state calculate bootstrap se's:
B <- length(object$Haz.boot) # find B
pt_list <- vector("list", S)
# Initialize objects:
for(s in absorbing_false){
pt_list[[s]] <- vector("list", B)
# pt_list[[s]] <- as.data.frame(matrix(NA, nrow = no_rows*B, ncol=S+1))
# names(pt_list[[s]]) <- c("time", paste("pstate",1:S,sep=""))
}
# Do the bootstrap:
for(i in 1:B){
# Prepare boot msfit object:
haz_tmp <- object$Haz.boot[[i]]
haz_tmp$b <- NULL
msfit_tmp <- list(Haz=haz_tmp, trans=trans)
class(msfit_tmp) <- "msfit"
# save bootstrapped probtrans:
pt_tmp <- suppressWarnings(probtrans(msfit_tmp, predt=predt, direction=direction, variance = FALSE, covariance = FALSE))
for(s in absorbing_false){
pt_list[[s]][[i]] <- pt_tmp[[s]]
# pt_list[[s]][((i-1)*no_rows+1):(i*no_rows),] <- pt_tmp[[s]]
# pt_list[[s]] <- rbind(pt_list[[s]], pt_tmp[[s]])
}
}
pt_list_save <- pt_list
# Add the bootstrapped se's in the probtrans object:
for(s in absorbing_false){
# Calculate SEs:
# pt_list[[s]] <- na.omit(pt_list[[s]])
pt_list[[s]] <- do.call(rbind.data.frame, pt_list[[s]])
pt_list[[s]] <- aggregate(.~time, data=pt_list[[s]], FUN = stats::sd)
# Check times:
unneeded_times <- which(!(pt_list[[s]]$time %in% res2[[s]]$time))
if(length(unneeded_times)>0) pt_list[[s]] <- pt_list[[s]][-unneeded_times,]
# Save object:
pt_list[[s]] <- pt_list[[s]][,2:ncol(pt_list[[s]])]
names(pt_list[[s]]) <- gsub("pstate", "se", names(pt_list[[s]]))
res2[[s]] <- cbind(res2[[s]], pt_list[[s]])
}
res2$pt.boot <- pt_list_save # save bootstrapped trans. probabilities
}
res2$trans <- trans
res2$method <- method
res2$predt <- predt
res2$direction <- direction
class(res2) <- "probtrans"
return(res2)
}
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Defines functions `probtrans`
#' Compute subject-specific or overall transition probabilities with standard
#' errors
#'
#' This function computes subject-specific or overall transition probabilities
#' in multi-state models. If requested, also standard errors are calculated.
#'
#' For details refer to de Wreede, Fiocco & Putter (2010).
#'
#' @param object \link{msfit} object containing estimated cumulative hazards
#' for each of the transitions in the multi-state model and, if standard errors
#' are requested, (co)variances of these cumulative hazards for each pair of
#' transitions
#' @param predt A positive number indicating the prediction time. This is
#' either the time at which the prediction is made (if \code{direction}=
#' \code{"forward"}) or the time for which the prediction is to be made (if
#' \code{direction}=\code{"fixedhorizon"})
#' @param direction One of \code{"forward"} (default) or \code{"fixedhorizon"},
#' indicating whether prediction is forward or for a fixed horizon
#' @param method A character string specifying the type of variances to be
#' computed (so only needed if either \code{variance} or \code{covariance} is
#' \code{TRUE}). Possible values are \code{"aalen"} or \code{"greenwood"}
#' @param variance Logical value indicating whether standard errors are to be
#' calculated (default is \code{TRUE})
#' @param covariance Logical value indicating whether covariances of transition
#' probabilities for different states are to be calculated (default is
#' \code{FALSE})
#' @return An object of class \code{"probtrans"}, which is a list of which item
#' [[s]] contains a data frame with the estimated transition probabilities (and
#' standard errors if \code{variance}=\code{TRUE}) from state s. If
#' \code{covariance}=\code{TRUE}, item \code{varMatrix} contains an array of
#' dimension K^2 x K^2 x (nt+1) (with K the number of states and nt the
#' distinct transition time points); the time points correspond to those in the
#' data frames with the estimated transition probabilities. Finally, there are
#' items \code{trans}, \code{method}, \code{predt}, \code{direction}, recording
#' the transition matrix, and the method, predt and direction arguments used in
#' the call to probtrans. Plot and summary methods have been defined for
#' \code{"probtrans"} objects.
#' @author Liesbeth de Wreede and Hein Putter \email{H.Putter@@lumc.nl}
#' @references Andersen PK, Borgan O, Gill RD, Keiding N (1993).
#' \emph{Statistical Models Based on Counting Processes}. Springer, New York.
#'
#' Putter H, Fiocco M, Geskus RB (2007). Tutorial in biostatistics: Competing
#' risks and multi-state models. \emph{Statistics in Medicine} \bold{26},
#' 2389--2430.
#'
#' Therneau TM, Grambsch PM (2000). \emph{Modeling Survival Data: Extending the
#' Cox Model}. Springer, New York.
#'
#' de Wreede LC, Fiocco M, and Putter H (2010). The mstate package for
#' estimation and prediction in non- and semi-parametric multi-state and
#' competing risks models. \emph{Computer Methods and Programs in Biomedicine}
#' \bold{99}, 261--274.
#'
#' de Wreede LC, Fiocco M, and Putter H (2011). mstate: An R Package for the
#' Analysis of Competing Risks and Multi-State Models. \emph{Journal of
#' Statistical Software}, Volume 38, Issue 7.
#' @keywords survival
#' @examples
#'
#' # transition matrix for illness-death model
#' tmat <- trans.illdeath()
#' # data in wide format, for transition 1 this is dataset E1 of
#' # Therneau & Grambsch (2000)
#' tg <- data.frame(illt=c(1,1,6,6,8,9),ills=c(1,0,1,1,0,1),
#' dt=c(5,1,9,7,8,12),ds=c(1,1,1,1,1,1),
#' x1=c(1,1,1,0,0,0),x2=c(6:1))
#' # data in long format using msprep
#' tglong <- msprep(time=c(NA,"illt","dt"),status=c(NA,"ills","ds"),
#' data=tg,keep=c("x1","x2"),trans=tmat)
#' # events
#' events(tglong)
#' table(tglong$status,tglong$to,tglong$from)
#' # expanded covariates
#' tglong <- expand.covs(tglong,c("x1","x2"))
#' # Cox model with different covariate
#' cx <- coxph(Surv(Tstart,Tstop,status)~x1.1+x2.2+strata(trans),
#' data=tglong,method="breslow")
#' summary(cx)
#' # new data, to check whether results are the same for transition 1 as
#' # those in appendix E.1 of Therneau & Grambsch (2000)
#' newdata <- data.frame(trans=1:3,x1.1=c(0,0,0),x2.2=c(0,1,0),strata=1:3)
#' HvH <- msfit(cx,newdata,trans=tmat)
#' # probtrans
#' pt <- probtrans(HvH,predt=0)
#' # predictions from state 1
#' pt[[1]]
#'
#' @export
`probtrans` <- function(object,predt,direction=c("forward","fixedhorizon"),
method=c("aalen","greenwood"),variance=TRUE,covariance=FALSE)
{
if (!inherits(object, "msfit"))
stop("'object' must be a 'msfit' object")
method <- match.arg(method)
direction <- match.arg(direction)
trans <- object$trans
transit <- to.trans2(trans)
numtrans <- nrow(transit)
variance_boot <- FALSE
# Check if bootstrap replications are in the object:
if("Haz.boot" %in% names(object)){
# We don't want to calculate (co)variances with the usual methods:
covariance <- FALSE
if(variance){
variance <- FALSE
variance_boot <- TRUE # we want to calculate bootstrapped variances
}
}
stackhaz <- object$Haz
stackvarhaz <- object$varHaz
for (i in 1:numtrans)
stackhaz$dhaz[stackhaz$trans==i] <- diff(c(0,stackhaz$Haz[stackhaz$trans==i]))
if (direction=="forward")
stackhaz <- stackhaz[stackhaz$time > predt,]
else stackhaz <- stackhaz[stackhaz$time <= predt,]
untimes <- sort(unique(stackhaz$time))
TT <- length(untimes)
S <- nrow(trans)
if (covariance) variance <- TRUE # if covariance=TRUE and variance=FALSE, variance is overruled
if (direction=="forward") {
if (variance==TRUE) res <- array(0,c(TT+1,2*S+1,S)) # 2*S+1 for time, probs (S), se (S)
else res <- array(0,c(TT+1,S+1,S)) # S+1 for time, probs (S)
# first line (in case of forward) contains values for t=predt
res[1,1,] <- predt
for (j in 1:S) res[1, 1+j,] <- rep(c(0,1,0), c(j-1,1,S-j))
if (variance) res[1,(S+2):(2*S+1),] <- 0
}
else {
# situation for backward is different from forward,
# depends on whether predt is an event time
if (predt %in% untimes) {
if (variance) res <- array(0,c(TT+1,2*S+1,S)) # t=0 and all event times
else res <- array(0,c(TT+1,S+1,S))
res[TT+1,1,] <- predt
for (j in 1:S) res[TT+1, 1+j,] <- rep(c(0,1,0), c(j-1,1,S-j))
if (variance) res[TT+1,(S+2):(2*S+1),] <- 0
}
else {
if (variance) res <- array(0,c(TT+2,2*S+1,S)) # t=0, event times, t=predt
else res <- array(0,c(TT+2,S+1,S))
res[TT+1,1,] <- max(untimes)
for (j in 1:S) res[TT+1, 1+j,] <- rep(c(0,1,0), c(j-1,1,S-j))
if (variance) res[TT+1,(S+2):(2*S+1),] <- 0
res[TT+2,1,] <- predt
for (j in 1:S) res[TT+2, 1+j,] <- rep(c(0,1,0), c(j-1,1,S-j))
if (variance) res[TT+2,(S+2):(2*S+1),] <- 0
}
}
P <- diag(S)
if (covariance) {
varParr <- array(0,c(S^2,S^2,TT+1))
if ((direction=="fixedhorizon") & !(predt %in% untimes))
varParr <- array(0,c(S^2,S^2,TT+2))
ffrom <- rep(1:S, S)
tto <- rep(1:S, rep(S,S))
fromto <- paste("from",ffrom,"to",tto,sep="")
if (direction=="forward")
dimnames(varParr) <- list(fromto,fromto,c(predt,untimes))
else {
if (predt %in% untimes) dimnames(varParr) <- list(fromto,fromto,c(0,untimes))
else dimnames(varParr) <- list(fromto,fromto,c(0,untimes,predt))
}
}
if (variance) {
varP <- matrix(0,S^2,S^2)
if (direction=="forward") {
varAnew <- array(0,c(S,S,S,S))
if (predt !=0) {
tmin <- max(stackvarhaz$time[stackvarhaz$time <=predt])
varHaz <- stackvarhaz[stackvarhaz$time==tmin,]
lHaz <- nrow(varHaz)
for (j in 1:lHaz)
{
from1 <- transit$from[transit$transno==varHaz$trans1[j]]
to1 <- transit$to[transit$transno==varHaz$trans1[j]]
from2 <- transit$from[transit$transno==varHaz$trans2[j]]
to2 <- transit$to[transit$transno==varHaz$trans2[j]]
varAnew[from1, to1, from2, to2] <-
varAnew[from2, to2, from1, to1] <- varHaz$varHaz[j]
}
}
}
else {
# varA on last event time (only those elements borrowed
# directly from object, rest is calculated later)
varA <- array(0,c(S,S,S,S))
varHaz <- stackvarhaz[stackvarhaz$time==untimes[TT],]
lHaz <- nrow(varHaz)
for (j in 1:lHaz)
{
from1 <- transit$from[transit$transno==varHaz$trans1[j]]
to1 <- transit$to[transit$transno==varHaz$trans1[j]]
from2 <- transit$from[transit$transno==varHaz$trans2[j]]
to2 <- transit$to[transit$transno==varHaz$trans2[j]]
varA[from1, to1, from2, to2] <-
varA[from2, to2, from1, to1] <- varHaz$varHaz[j]
}
}
}
for (i in 1:TT)
{
idx <- ifelse(direction=="forward",i,TT+1-i)
tt <- untimes[idx]
Haztt <- stackhaz[stackhaz$time==tt,]
lHaztt <- nrow(Haztt)
# build S x S matrix IplusdA
IplusdA <- diag(S)
for (j in 1:lHaztt)
{
from <- transit$from[transit$transno==Haztt$trans[j]]
to <- transit$to[transit$transno==Haztt$trans[j]]
IplusdA[from, to] <- Haztt$dhaz[j]
IplusdA[from, from] <- IplusdA[from, from] - Haztt$dhaz[j]
}
if (any(diag(IplusdA)<0))
warning("Warning! Negative diagonal elements of (I+dA); the estimate may not be meaningful. \n")
if (variance) {
if (direction=="forward"){
varA <- varAnew
varAnew <- array(0,c(S,S,S,S))
varHaztt <- stackvarhaz[stackvarhaz$time==tt,]
lHaztt <- nrow(varHaztt)
for (j in 1:lHaztt)
{
from1 <- transit$from[transit$transno==varHaztt$trans1[j]]
to1 <- transit$to[transit$transno==varHaztt$trans1[j]]
from2 <- transit$from[transit$transno==varHaztt$trans2[j]]
to2 <- transit$to[transit$transno==varHaztt$trans2[j]]
varAnew[from1, to1, from2, to2] <-
varAnew[from2, to2, from1, to1] <- varHaztt$varHaz[j]
}
vardA <- varAnew - varA
}
else {
varAttmin <- array(0,c(S,S,S,S))
varHazttmin <- stackvarhaz[stackvarhaz$time==untimes[idx-1],]
lHazttmin <- nrow(varHazttmin)
for (j in 1:lHazttmin)
{
from1 <- transit$from[transit$transno==varHazttmin$trans1[j]]
to1 <- transit$to[transit$transno==varHazttmin$trans1[j]]
from2 <- transit$from[transit$transno==varHazttmin$trans2[j]]
to2 <- transit$to[transit$transno==varHazttmin$trans2[j]]
varAttmin[from1, to1, from2, to2] <-
varAttmin[from2, to2, from1, to1] <- varHazttmin$varHaz[j]
}
vardA <- varA - varAttmin
varA <- varAttmin # ready for the next round
}
for (from in 1:S)
{
for (from2 in 1:S)
{
for (to2 in 1:S)
{
if (to2!=from2)
vardA[from, from, from2, to2] <-
vardA[from2, to2, from, from] <-
-sum(vardA[from,-from,from2,to2])
}
}
}
for (from in 1:S)
{
for (from2 in 1:S)
vardA[from,from,from2,from2] <-
vardA[from2,from2,from,from] <-
-sum(vardA[from,from,from2,-from2])
}
vardA <- matrix(vardA,S^2,S^2)
}
if (method=="aalen")
{
if (direction=="forward")
{
P <- P %*% IplusdA
if (variance) {
tmp1 <- kronecker(t(IplusdA),diag(S)) %*% varP %*% kronecker(IplusdA,diag(S))
tmp2 <- kronecker(diag(S),P) %*% vardA %*% kronecker(diag(S),t(P))
varP <- tmp1 + tmp2
}
}
else {
if (variance) {
tmp1 <- kronecker(diag(S), IplusdA) %*% varP %*% kronecker(diag(S), t(IplusdA))
tmp2 <- kronecker(t(P), IplusdA) %*% vardA %*% kronecker(P,t(IplusdA))
varP <- tmp1+tmp2
}
P <- IplusdA %*% P
}
}
if (method=="greenwood")
{
if (direction=="forward")
{
if (variance) {
tmp1 <- kronecker(t(IplusdA),diag(S)) %*% varP %*% kronecker(IplusdA,diag(S))
tmp2 <- kronecker(diag(S),P) %*% vardA %*% kronecker(diag(S),t(P))
varP <- tmp1 + tmp2
}
P <- P %*% IplusdA
}
else {
if (variance) {
tmp1 <- kronecker(diag(S), IplusdA) %*% varP %*% kronecker(diag(S), t(IplusdA))
tmp2 <- kronecker(t(P), diag(S)) %*% vardA %*% kronecker(P, diag(S))
varP <- tmp1+tmp2
}
P <- IplusdA %*% P
}
}
if (variance) {
seP <- sqrt(diag(varP))
seP <- matrix(seP,S,S)
}
if (covariance) {
if (direction=="forward") varParr[,,i+1] <- varP
else {
varParr[,,idx+1] <- varP
}
}
if (direction=="forward") {
res[idx+1,1,] <- tt
res[idx+1,2:(S+1),] <- t(P)
if (variance) res[idx+1,(S+2):(2*S+1),] <- t(seP)
}
else {
res[idx,1,] <- ifelse(i==TT,0,untimes[TT-i])
res[idx,2:(S+1),] <- t(P)
if (variance) res[idx,(S+2):(2*S+1),] <- t(seP)
}
}
if (covariance & (direction=="fixedhorizon"))
varParr[,,1] <- varParr[,,2]
### res[,,s] contains prediction from state s, convert to list of dataframes
res2 <- vector("list", S)
for (s in 1:S) {
tmp <- as.data.frame(res[,,s])
if (min(dim(tmp))==1) tmp <- res[,,s]
if (variance) names(tmp) <- c("time",paste("pstate",1:S,sep=""),paste("se",1:S,sep=""))
else names(tmp) <- c("time",paste("pstate",1:S,sep=""))
res2[[s]] <- tmp
}
if (covariance) res2$varMatrix <- varParr
# Calculate bootstrap se's for probtrans:
if(variance_boot){
# Find absorbing states:
is_absorbing <- rowSums(!is.na(trans))==0
absorbing_true <- which(is_absorbing==TRUE)
absorbing_false <- which(is_absorbing==FALSE)
# We make two steps (based on whether we deal with an absorbing or transient state):
# 1. For transprobs starting from an absorbing state put se = 0:
# Define empty SE data frames:
se_df <- as.data.frame(matrix(0, nrow=1, ncol=S))
names(se_df) <- paste("se", 1:S, sep="")
# Add zero SE's in probtrans for absorbing states:
for(s in absorbing_true){
res2[[s]] <- cbind(res2[[s]], se_df)
}
# 2. For transprobs starting from a transient state calculate bootstrap se's:
B <- length(object$Haz.boot) # find B
pt_list <- vector("list", S)
# Initialize objects:
for(s in absorbing_false){
pt_list[[s]] <- vector("list", B)
# pt_list[[s]] <- as.data.frame(matrix(NA, nrow = no_rows*B, ncol=S+1))
# names(pt_list[[s]]) <- c("time", paste("pstate",1:S,sep=""))
}
# Do the bootstrap:
for(i in 1:B){
# Prepare boot msfit object:
haz_tmp <- object$Haz.boot[[i]]
haz_tmp$b <- NULL
msfit_tmp <- list(Haz=haz_tmp, trans=trans)
class(msfit_tmp) <- "msfit"
# save bootstrapped probtrans:
pt_tmp <- suppressWarnings(probtrans(msfit_tmp, predt=predt, direction=direction, variance = FALSE, covariance = FALSE))
for(s in absorbing_false){
pt_list[[s]][[i]] <- pt_tmp[[s]]
# pt_list[[s]][((i-1)*no_rows+1):(i*no_rows),] <- pt_tmp[[s]]
# pt_list[[s]] <- rbind(pt_list[[s]], pt_tmp[[s]])
}
}
pt_list_save <- pt_list
# Add the bootstrapped se's in the probtrans object:
for(s in absorbing_false){
# Calculate SEs:
# pt_list[[s]] <- na.omit(pt_list[[s]])
pt_list[[s]] <- do.call(rbind.data.frame, pt_list[[s]])
pt_list[[s]] <- aggregate(.~time, data=pt_list[[s]], FUN = stats::sd)
# Check times:
unneeded_times <- which(!(pt_list[[s]]$time %in% res2[[s]]$time))
if(length(unneeded_times)>0) pt_list[[s]] <- pt_list[[s]][-unneeded_times,]
# Save object:
pt_list[[s]] <- pt_list[[s]][,2:ncol(pt_list[[s]])]
names(pt_list[[s]]) <- gsub("pstate", "se", names(pt_list[[s]]))
res2[[s]] <- cbind(res2[[s]], pt_list[[s]])
}
res2$pt.boot <- pt_list_save # save bootstrapped trans. probabilities
}
res2$trans <- trans
res2$method <- method
res2$predt <- predt
res2$direction <- direction
class(res2) <- "probtrans"
return(res2)
}
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