Nothing
R/LDTFPsurvival.R
In DPpackage: Bayesian Nonparametric Modeling in R
### LDTFPsurvival.R
### Fit a linear dependent TF process for survival data.
###
### Copyright: Alejandro Jara, 2011-2012.
### Last modification: 11-11-2011.
###
### This program is free software; you can redistribute it and/or modify
### it under the terms of the GNU General Public License as published by
### the Free Software Foundation; either version 2 of the License, or (at
### your option) any later version.
###
### This program is distributed in the hope that it will be useful, but
### WITHOUT ANY WARRANTY; without even the implied warranty of
### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
### General Public License for more details.
###
### You should have received a copy of the GNU General Public License
### along with this program; if not, write to the Free Software
### Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
###
### The authors' contact information:
###
### Alejandro Jara
### Department of Statistics
### Facultad de Matematicas
### Pontificia Universidad Catolica de Chile
### Casilla 306, Correo 22
### Santiago
### Chile
### Voice: +56-2-3544506 URL : http://www.mat.puc.cl/~ajara
### Fax : +56-2-3547729 Email: atjara@uc.cl
###
"LDTFPsurvival" <-
function(y,x,xtf,prediction,prior,mcmc,state,status,grid=seq(0.01,60,len=100),compute.band=FALSE,type.band="PD",
data=sys.frame(sys.parent()),na.action=na.fail,work.dir=NULL)
UseMethod("LDTFPsurvival")
"LDTFPsurvival.default" <-
function(y,
x,
xtf,
prediction,
prior,
mcmc,
state,
status,
grid=seq(0.01,60,len=100),
compute.band=FALSE,
type.band="PD",
data=sys.frame(sys.parent()),
na.action=na.fail,
work.dir=NULL)
{
#########################################################################################
# call parameters
#########################################################################################
m <- mcall <- cl <- match.call()
#########################################################################################
# data structure
#########################################################################################
nrec <- length(y[,1])
xce <- x
pce <- ncol(xce)
ptf <- ncol(xtf)
type <- rep(2,nrec)
type[y[,1]==-999] <- 1
type[y[,2]==-999] <- 3
type[y[,1]==y[,2]] <- 4
#########################################################################################
# change working directory (if requested..)
#########################################################################################
if(!is.null(work.dir))
{
cat("\n Changing working directory to ",work.dir,"\n")
old.dir <- getwd() # by default work in current working directory
setwd(work.dir)
}
#########################################################################################
# prediction
#########################################################################################
ngrid <- length(grid)
xcepred <- prediction$xdenpred
xtfpred <- prediction$xtfdenpred
npredden <- nrow(xcepred)
xcepredm <- prediction$xmedpred
xtfpredm <- prediction$xtfmedpred
npredmed <- nrow(xcepredm)
quans <- prediction$quans
if(is.null(quans)) quans <- c(0.03,0.50,0.97)
cband <- 0
if(compute.band)
{
cband <- 1
}
tband <- 0
if(type.band=="HPD")
{
tband <- 1
}
#########################################################################################
# MLE analysis
#########################################################################################
ymat2 <- y
ymat2[ymat2[,1]==-999,1] <- 0
ymat2[ymat2[,2]==-999,2] <- 10^10
ll <- ymat2[,1]
rr <- ymat2[,2]
#library(survival)
fit0 <- survreg(formula = Surv(time=ll,time2=rr,type="interval2") ~ xce-1, dist = "lognormal")
betace <- coefficients(fit0)
cgkvar <- vcov(fit0)[1:pce,1:pce]
sigma2 <- fit0$scale
#########################################################################################
# Prior information
#########################################################################################
maxm <- prior$maxm
ntprob <- 0
ntlr <- 0
for(i in 1:maxm)
{
ntprob <- ntprob + 2**i
ntlr <- ntlr +2**(i-1)
}
if(is.null(prior$a0))
{
a0b0 <- c(-1,-1)
alpha <- prior$alpha
}
else
{
a0b0 <- c(prior$a0,prior$b0)
alpha <- 1
}
betacepm <- prior$mub
precce <- solve(prior$Sb)
if(is.null(prior$tau1))
{
tau <- c(-1,-1)
}
else
{
tau <- c(prior$tau1,prior$tau2)
}
tfprior <- prior$tfprior
if(is.null(tfprior))tfprior <- 1
if(tfprior==1)
{
gprior <- 2*nrec*solve(t(xtf)%*%xtf)
}
if(tfprior==2)
{
gprior <- 2*(1/nrec)*t(xtf)%*%xtf
}
if(tfprior==3)
{
gprior <- diag(1000,ptf)
}
#########################################################################################
# mcmc specification
#########################################################################################
mcmcvec <- c(mcmc$nburn,mcmc$nskip,mcmc$ndisplay,cband,tband)
nsave <- mcmc$nsave
#########################################################################################
# output
#########################################################################################
cpo <- matrix(0,nrow=nrec,ncol=2)
densm <- matrix(0,nrow=npredden,ncol=ngrid)
densl <- matrix(0,nrow=npredden,ncol=ngrid)
densu <- matrix(0,nrow=npredden,ncol=ngrid)
survmm <- matrix(0,nrow=npredden,ncol=ngrid)
survml <- matrix(0,nrow=npredden,ncol=ngrid)
survmu <- matrix(0,nrow=npredden,ncol=ngrid)
qmm <- matrix(0,nrow=npredmed,3)
qml <- matrix(0,nrow=npredmed,3)
qmu <- matrix(0,nrow=npredmed,3)
thetasave <- matrix(0, nrow=nsave, ncol=(pce+2))
randsave <- matrix(0, nrow=nsave, ncol=((ntlr-1)*ptf))
#########################################################################################
# parameters depending on status
#########################################################################################
if(status)
{
z <- rep(0,nrec)
for(i in 1:nrec)
{
if(type[i]==1) z[i] <- log(y[i,2]/2)
if(type[i]==2) z[i] <- log((y[i,1]+y[i,2])/2)
if(type[i]==3) z[i] <- log(y[i,1]+1)
if(type[i]==4) z[i] <- log(y[i,1])
}
betatf <- matrix(0,nrow=ntlr,ncol=ptf)
}
else
{
z <- state$z
alpha <- state$alpha
betace <- state$betace
sigma2 <- state$sigma2
betatf <- state$betatf
}
#########################################################################################
# working space
#########################################################################################
seed <- c(sample(1:29000,1),sample(1:29000,1))
iflag <- rep(0,pce)
iflagtf <- rep(0,ptf)
nobsbc <- rep(0,ntprob)
obsbc <- matrix(0,nrow=ntprob,ncol=nrec)
c0 <- matrix(0,nrow=ptf,ncol=ptf)
workm1 <- matrix(0,nrow=pce,ncol=pce)
workvh1 <- rep(0,(pce*(pce+1)/2))
workv1 <- rep(0,pce)
worksam <- rep(0,nsave)
worksam2 <- matrix(0,nrow=nsave,ncol=ngrid)
worksam3 <- matrix(0,nrow=nsave,ncol=npredmed)
fs <- rep(0,ngrid)
workm2 <- matrix(0,nrow=ptf,ncol=ptf)
workvh2 <- rep(0,(ptf*(ptf+1)/2))
workv2 <- rep(0,ptf)
workv3 <- rep(0,ptf)
workv4 <- rep(0,ptf)
k <- rep(0,maxm)
prob <- rep(0,2**maxm)
probc <- rep(0,2**maxm)
#########################################################################################
# calling the fortran code
#########################################################################################
foo <- .Fortran("ldtfpsurvival",
nrec = as.integer(nrec),
ptf = as.integer(ptf),
pce = as.integer(pce),
interind = as.integer(type),
xtf = as.double(xtf),
xce = as.double(xce),
y = as.double(y),
ngrid = as.integer(ngrid),
npredden = as.integer(npredden),
npredmed = as.integer(npredmed),
grid = as.double(grid),
xtfpred = as.double(xtfpred),
xcepred = as.double(xcepred),
xtfpredm = as.double(xtfpredm),
xcepredm = as.double(xcepredm),
quans = as.double(quans),
maxm = as.integer(maxm),
ntprob = as.integer(ntprob),
ntlr = as.integer(ntlr),
a0b0 = as.double(a0b0),
betacepm = as.double(betacepm),
gprior = as.double(gprior),
precce = as.double(precce),
tau = as.double(tau),
alpha = as.double(alpha),
betace = as.double(betace),
betatf = as.double(betatf),
sigma2 = as.double(sigma2),
z = as.double(z),
mcmc = as.integer(mcmcvec),
nsave = as.integer(nsave),
seed = as.integer(seed),
cpo = as.double(cpo),
densm = as.double(densm),
densl = as.double(densl),
densu = as.double(densu),
qmm = as.double(qmm),
qml = as.double(qml),
qmu = as.double(qmu),
survmm = as.double(survmm),
survml = as.double(survml),
survmu = as.double(survmu),
thetasave = as.double(thetasave),
randsave = as.double(randsave),
iflag = as.integer(iflag),
iflagtf = as.integer(iflagtf),
nobsbc = as.integer(nobsbc),
obsbc = as.integer(obsbc),
c0 = as.double(c0),
workm1 = as.double(workm1),
workvh1 = as.double(workvh1),
workv1 = as.double(workv1),
worksam = as.double(worksam),
worksam2 = as.double(worksam2),
worksam3 = as.double(worksam3),
fs = as.double(fs),
workm2 = as.double(workm2),
workvh2 = as.double(workvh2),
workv2 = as.double(workv2),
workv3 = as.double(workv3),
workv4 = as.double(workv4),
k = as.integer(k),
prob = as.double(prob),
probc = as.double(probc),
PACKAGE = "DPpackage")
#########################################################################################
# save state
#########################################################################################
if(!is.null(work.dir))
{
cat("\n\n Changing working directory back to ",old.dir,"\n")
setwd(old.dir)
}
model.name <- "Linear dependent TF process model for time-to-event data"
cpom <- matrix(foo$cpo,nrow=nrec,ncol=2)
cpo <- cpom[,1]
fso <- cpom[,2]
densm <- matrix(foo$densm,nrow=npredden,ncol=ngrid)
densl <- NULL
densu <- NULL
qmm <- matrix(foo$qmm,nrow=npredmed,3)
qml <- NULL
qmu <- NULL
survmm <- matrix(foo$survmm,nrow=npredden,ncol=ngrid)
survml <- NULL
survmu <- NULL
if(compute.band)
{
densl <- matrix(foo$densl,nrow=npredden,ncol=ngrid)
densu <- matrix(foo$densu,nrow=npredden,ncol=ngrid)
qml <- matrix(foo$qml,nrow=npredmed,3)
qmu <- matrix(foo$qmu,nrow=npredmed,3)
survml <- matrix(foo$survml,nrow=npredden,ncol=ngrid)
survmu <- matrix(foo$survmu,nrow=npredden,ncol=ngrid)
}
thetasave <- matrix(foo$thetasave,nrow=mcmc$nsave, ncol=(pce+2))
randsave <- matrix(foo$randsave,nrow=mcmc$nsave, ncol=((ntlr-1)*ptf))
colnames(thetasave) <- c(colnames(xce),"sigma2","alpha")
coeff <- apply(thetasave,2,mean)
colnames(randsave) <- rep(colnames(xtf),(ntlr-1))
state <- list(alpha=foo$alpha,
betace=foo$betace,
sigma2=foo$sigma2,
betatf=matrix(foo$betatf,nrow=ntlr,ncol=ptf),
z=foo$z,
nobsbc=foo$nobsbc,
obsbc=matrix(foo$obsbc,nrow=ntprob,ncol=nrec))
save.state <- list(thetasave=thetasave,
randsave=randsave)
z <- list(modelname=model.name,
coefficients=coeff,
call=cl,
compute.band=compute.band,
cpo=cpo,
fso=fso,
prior=prior,
mcmc=mcmc,
state=state,
save.state=save.state,
nrec=foo$nrec,
pce=foo$pce,
ptf=foo$ptf,
y=y,
x=xce,
xtf=xtf,
ngrid=ngrid,
npredden=npredden,
npredmed=npredmed,
grid=grid,
densm=densm,
densl=densl,
densu=densu,
qmm=qmm,
qml=qml,
qmu=qmu,
survmm=survmm,
survml=survml,
survmu=survmu)
cat("\n\n")
class(z) <- c("LDTFPsurvival")
z
}
###
### Tools for LDTFPsurvival: print, summary, plot
###
### Copyright: Alejandro Jara, 2011
### Last modification: 11-11-2011.
"print.LDTFPsurvival" <- function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$modelname,"\n\nCall:\n", sep = "")
print(x$call)
cat("\n")
cat("Posterior Predictive Distributions (log):\n")
print.default(format(summary(log(x$cpo)), digits = digits), print.gap = 2,
quote = FALSE)
cat("\nPosterior Inference of Parameters:\n")
print.default(format(x$coefficients, digits = digits), print.gap = 2,
quote = FALSE)
cat("\nNumber of Observations:",x$nrec)
cat("\nNumber of Predictors for the Median:",x$pce)
cat("\nNumber of Predictors for the Tailfree Probabilities:",x$ptf,"\n")
cat("\n\n")
invisible(x)
}
"plot.LDTFPsurvival"<-function(x, hpd=TRUE, ask=TRUE, nfigr=2, nfigc=2, param=NULL, col="#bdfcc9", ...)
{
fancydensplot1<-function(x, hpd=TRUE, npts=200, xlab="", ylab="", main="",col="#bdfcc9", ...)
# Author: AJV, 2007
#
{
dens <- density(x,n=npts)
densx <- dens$x
densy <- dens$y
meanvar <- mean(x)
densx1 <- max(densx[densx<=meanvar])
densx2 <- min(densx[densx>=meanvar])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ymean <- densy1 + ((densy2-densy1)/(densx2-densx1))*(meanvar-densx1)
if(hpd==TRUE)
{
alpha<-0.05
alow<-rep(0,2)
aupp<-rep(0,2)
n<-length(x)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(x),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
xlinf<-a$alow[1]
xlsup<-a$aupp[1]
}
else
{
xlinf <- quantile(x,0.025)
xlsup <- quantile(x,0.975)
}
densx1 <- max(densx[densx<=xlinf])
densx2 <- min(densx[densx>=xlinf])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylinf <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlinf-densx1)
densx1 <- max(densx[densx<=xlsup])
densx2 <- min(densx[densx>=xlsup])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylsup <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlsup-densx1)
plot(0.,0.,xlim = c(min(densx), max(densx)), ylim = c(min(densy), max(densy)),
axes = F,type = "n" , xlab=xlab, ylab=ylab, main=main, cex=1.2)
xpol<-c(xlinf,xlinf,densx[densx>=xlinf & densx <=xlsup],xlsup,xlsup)
ypol<-c(0,ylinf,densy[densx>=xlinf & densx <=xlsup] ,ylsup,0)
polygon(xpol, ypol, border = FALSE,col=col)
lines(c(min(densx), max(densx)),c(0,0),lwd=1.2)
segments(min(densx),0, min(densx),max(densy),lwd=1.2)
lines(densx,densy,lwd=1.2)
segments(meanvar, 0, meanvar, ymean,lwd=1.2)
segments(xlinf, 0, xlinf, ylinf,lwd=1.2)
segments(xlsup, 0, xlsup, ylsup,lwd=1.2)
axis(1., at = round(c(xlinf, meanvar,xlsup), 2.), labels = T,pos = 0.)
axis(1., at = round(seq(min(densx),max(densx),length=15), 2.), labels = F,pos = 0.)
axis(2., at = round(seq(0,max(densy),length=5), 2.), labels = T,pos =min(densx))
}
if(is(x, "LDTFPsurvival"))
{
if(is.null(param))
{
coef.p <- x$coefficients
n <- length(coef.p)
pnames <- names(coef.p)
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr , ncol=nfigc ,byrow=TRUE))
for(i in 1:length(coef.p))
{
title1 <- paste("Trace of",pnames[i],sep=" ")
title2 <- paste("Density of",pnames[i],sep=" ")
plot(ts(x$save.state$thetasave[,i]),main=title1,xlab="MCMC scan",ylab=" ")
fancydensplot1(x$save.state$thetasave[,i],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
for(i in 1:x$npredden)
{
if(x$compute.band)
{
title1 <- paste("Survival Prediction #",i,sep=" ")
plot(x$grid,x$survmu[i,],main=title1,lty=2,type='l',lwd=2,xlab="time",ylab="survival",ylim=c(0,1))
lines(x$grid,x$survml[i,],lty=2,lwd=2)
lines(x$grid,x$survmm[i,],lty=1,lwd=3)
}
else
{
title1 <- paste("Survival Prediction #",i,sep=" ")
plot(x$grid,x$survmm[i,],main=title1,lty=1,type='l',lwd=2,xlab="time",ylab="survival",ylim=c(0,1))
}
}
}
else
{
coef.p <- x$coefficients
n <- length(coef.p)
pnames <- names(coef.p)
poss <- 0
for(i in 1:n)
{
if(pnames[i]==param)poss=i
}
if(poss==0 && param !="predictive")
{
stop("This parameter is not present in the original model.\n")
}
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr, ncol=nfigc, byrow = TRUE))
if(param !="predictive")
{
title1 <- paste("Trace of",pnames[poss],sep=" ")
title2 <- paste("Density of",pnames[poss],sep=" ")
plot(ts(x$save.state$thetasave[,poss]),main=title1,xlab="MCMC scan",ylab=" ")
fancydensplot1(x$save.state$thetasave[,poss],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
else
{
for(i in 1:x$npredden)
{
if(x$compute.band)
{
title1 <- paste("Survival Prediction #",i,sep=" ")
plot(x$grid,x$survmu[i,],main=title1,lty=2,type='l',lwd=2,xlab="time",ylab="survival",ylim=c(0,1))
lines(x$grid,x$survml[i,],lty=2,lwd=2)
lines(x$grid,x$survmm[i,],lty=1,lwd=3)
}
else
{
title1 <- paste("Survival Prediction #",i,sep=" ")
plot(x$grid,x$survmm[i,],main=title1,lty=1,type='l',lwd=2,xlab="time",ylab="survival",ylim=c(0,1))
}
}
}
}
}
}
"summary.LDTFPsurvival" <- function(object, hpd=TRUE, ...)
{
stde<-function(x)
{
n<-length(x)
return(sd(x)/sqrt(n))
}
hpdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[1],a$aupp[1]))
}
pdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[2],a$aupp[2]))
}
thetasave <- object$save.state$thetasave
ans <- c(object[c("call", "modelname")])
### CPO
ans$cpo <- object$cpo
### Median information
dimen1 <- object$pce
if(dimen1==1)
{
mat <- matrix(thetasave[,1],ncol=1)
}
else
{
mat <- thetasave[,1:dimen1]
}
coef.p <- object$coefficients[1:dimen1]
coef.m <- apply(mat, 2, median)
coef.sd <- apply(mat, 2, sd)
coef.se <- apply(mat, 2, stde)
if(hpd){
limm <- apply(mat, 2, hpdf)
coef.l <- limm[1,]
coef.u <- limm[2,]
}
else
{
limm <- apply(mat, 2, pdf)
coef.l <- limm[1,]
coef.u <- limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$coeff <- coef.table
### Baseline Information
mat <- matrix(thetasave[,(dimen1+1)],ncol=1)
coef.p <- object$coefficients[(dimen1+1)]
coef.m <- apply(mat, 2, median)
coef.sd <- apply(mat, 2, sd)
coef.se <- apply(mat, 2, stde)
if(hpd){
limm <- apply(mat, 2, hpdf)
coef.l <- limm[1,]
coef.u <- limm[2,]
}
else
{
limm <- apply(mat, 2, pdf)
coef.l <- limm[1,]
coef.u <- limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$base <- coef.table
### Precision parameter
if(is.null(object$prior$a0))
{
ans$prec <- NULL
}
else
{
mat <- matrix(thetasave[,(dimen1+2)],ncol=1)
coef.p <- object$coefficients[(dimen1+2)]
coef.m <- apply(mat, 2, median)
coef.sd <- apply(mat, 2, sd)
coef.se <- apply(mat, 2, stde)
if(hpd){
limm <- apply(mat, 2, hpdf)
coef.l <- limm[1,]
coef.u <- limm[2,]
}
else
{
limm <- apply(mat, 2, pdf)
coef.l <- limm[1,]
coef.u <- limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$prec <- coef.table
}
ans$nrec <- object$nrec
ans$pce <- object$pce
ans$ptf <- object$ptf
class(ans) <- "summaryLDTFPsurvival"
return(ans)
}
"print.summaryLDTFPsurvival"<-function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$modelname,"\n\nCall:\n", sep = "")
print(x$call)
cat("\n")
cat("Posterior Predictive Distributions (log):\n")
print.default(format(summary(log(as.vector(x$cpo))), digits = digits), print.gap = 2,
quote = FALSE)
cat("\nPosterior Inference of Median Regression Parameters:\n")
print.default(format(x$coeff, digits = digits), print.gap = 2,
quote = FALSE)
cat("\nPosterior Inference of Baseline Variance:\n")
print.default(format(x$base, digits = digits), print.gap = 2,
quote = FALSE)
if (length(x$prec)) {
cat("\nPrecision parameter:\n")
print.default(format(x$prec, digits = digits), print.gap = 2,
quote = FALSE)
}
cat("\nNumber of Observations:",x$nrec)
cat("\nNumber of Predictors for the Median:",x$pce)
cat("\nNumber of Predictors for the Tailfree Probabilities:",x$pce,"\n")
cat("\n\n")
invisible(x)
}
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### LDTFPsurvival.R
### Fit a linear dependent TF process for survival data.
###
### Copyright: Alejandro Jara, 2011-2012.
### Last modification: 11-11-2011.
###
### This program is free software; you can redistribute it and/or modify
### it under the terms of the GNU General Public License as published by
### the Free Software Foundation; either version 2 of the License, or (at
### your option) any later version.
###
### This program is distributed in the hope that it will be useful, but
### WITHOUT ANY WARRANTY; without even the implied warranty of
### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
### General Public License for more details.
###
### You should have received a copy of the GNU General Public License
### along with this program; if not, write to the Free Software
### Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
###
### The authors' contact information:
###
### Alejandro Jara
### Department of Statistics
### Facultad de Matematicas
### Pontificia Universidad Catolica de Chile
### Casilla 306, Correo 22
### Santiago
### Chile
### Voice: +56-2-3544506 URL : http://www.mat.puc.cl/~ajara
### Fax : +56-2-3547729 Email: atjara@uc.cl
###
"LDTFPsurvival" <-
function(y,x,xtf,prediction,prior,mcmc,state,status,grid=seq(0.01,60,len=100),compute.band=FALSE,type.band="PD",
data=sys.frame(sys.parent()),na.action=na.fail,work.dir=NULL)
UseMethod("LDTFPsurvival")
"LDTFPsurvival.default" <-
function(y,
x,
xtf,
prediction,
prior,
mcmc,
state,
status,
grid=seq(0.01,60,len=100),
compute.band=FALSE,
type.band="PD",
data=sys.frame(sys.parent()),
na.action=na.fail,
work.dir=NULL)
{
#########################################################################################
# call parameters
#########################################################################################
m <- mcall <- cl <- match.call()
#########################################################################################
# data structure
#########################################################################################
nrec <- length(y[,1])
xce <- x
pce <- ncol(xce)
ptf <- ncol(xtf)
type <- rep(2,nrec)
type[y[,1]==-999] <- 1
type[y[,2]==-999] <- 3
type[y[,1]==y[,2]] <- 4
#########################################################################################
# change working directory (if requested..)
#########################################################################################
if(!is.null(work.dir))
{
cat("\n Changing working directory to ",work.dir,"\n")
old.dir <- getwd() # by default work in current working directory
setwd(work.dir)
}
#########################################################################################
# prediction
#########################################################################################
ngrid <- length(grid)
xcepred <- prediction$xdenpred
xtfpred <- prediction$xtfdenpred
npredden <- nrow(xcepred)
xcepredm <- prediction$xmedpred
xtfpredm <- prediction$xtfmedpred
npredmed <- nrow(xcepredm)
quans <- prediction$quans
if(is.null(quans)) quans <- c(0.03,0.50,0.97)
cband <- 0
if(compute.band)
{
cband <- 1
}
tband <- 0
if(type.band=="HPD")
{
tband <- 1
}
#########################################################################################
# MLE analysis
#########################################################################################
ymat2 <- y
ymat2[ymat2[,1]==-999,1] <- 0
ymat2[ymat2[,2]==-999,2] <- 10^10
ll <- ymat2[,1]
rr <- ymat2[,2]
#library(survival)
fit0 <- survreg(formula = Surv(time=ll,time2=rr,type="interval2") ~ xce-1, dist = "lognormal")
betace <- coefficients(fit0)
cgkvar <- vcov(fit0)[1:pce,1:pce]
sigma2 <- fit0$scale
#########################################################################################
# Prior information
#########################################################################################
maxm <- prior$maxm
ntprob <- 0
ntlr <- 0
for(i in 1:maxm)
{
ntprob <- ntprob + 2**i
ntlr <- ntlr +2**(i-1)
}
if(is.null(prior$a0))
{
a0b0 <- c(-1,-1)
alpha <- prior$alpha
}
else
{
a0b0 <- c(prior$a0,prior$b0)
alpha <- 1
}
betacepm <- prior$mub
precce <- solve(prior$Sb)
if(is.null(prior$tau1))
{
tau <- c(-1,-1)
}
else
{
tau <- c(prior$tau1,prior$tau2)
}
tfprior <- prior$tfprior
if(is.null(tfprior))tfprior <- 1
if(tfprior==1)
{
gprior <- 2*nrec*solve(t(xtf)%*%xtf)
}
if(tfprior==2)
{
gprior <- 2*(1/nrec)*t(xtf)%*%xtf
}
if(tfprior==3)
{
gprior <- diag(1000,ptf)
}
#########################################################################################
# mcmc specification
#########################################################################################
mcmcvec <- c(mcmc$nburn,mcmc$nskip,mcmc$ndisplay,cband,tband)
nsave <- mcmc$nsave
#########################################################################################
# output
#########################################################################################
cpo <- matrix(0,nrow=nrec,ncol=2)
densm <- matrix(0,nrow=npredden,ncol=ngrid)
densl <- matrix(0,nrow=npredden,ncol=ngrid)
densu <- matrix(0,nrow=npredden,ncol=ngrid)
survmm <- matrix(0,nrow=npredden,ncol=ngrid)
survml <- matrix(0,nrow=npredden,ncol=ngrid)
survmu <- matrix(0,nrow=npredden,ncol=ngrid)
qmm <- matrix(0,nrow=npredmed,3)
qml <- matrix(0,nrow=npredmed,3)
qmu <- matrix(0,nrow=npredmed,3)
thetasave <- matrix(0, nrow=nsave, ncol=(pce+2))
randsave <- matrix(0, nrow=nsave, ncol=((ntlr-1)*ptf))
#########################################################################################
# parameters depending on status
#########################################################################################
if(status)
{
z <- rep(0,nrec)
for(i in 1:nrec)
{
if(type[i]==1) z[i] <- log(y[i,2]/2)
if(type[i]==2) z[i] <- log((y[i,1]+y[i,2])/2)
if(type[i]==3) z[i] <- log(y[i,1]+1)
if(type[i]==4) z[i] <- log(y[i,1])
}
betatf <- matrix(0,nrow=ntlr,ncol=ptf)
}
else
{
z <- state$z
alpha <- state$alpha
betace <- state$betace
sigma2 <- state$sigma2
betatf <- state$betatf
}
#########################################################################################
# working space
#########################################################################################
seed <- c(sample(1:29000,1),sample(1:29000,1))
iflag <- rep(0,pce)
iflagtf <- rep(0,ptf)
nobsbc <- rep(0,ntprob)
obsbc <- matrix(0,nrow=ntprob,ncol=nrec)
c0 <- matrix(0,nrow=ptf,ncol=ptf)
workm1 <- matrix(0,nrow=pce,ncol=pce)
workvh1 <- rep(0,(pce*(pce+1)/2))
workv1 <- rep(0,pce)
worksam <- rep(0,nsave)
worksam2 <- matrix(0,nrow=nsave,ncol=ngrid)
worksam3 <- matrix(0,nrow=nsave,ncol=npredmed)
fs <- rep(0,ngrid)
workm2 <- matrix(0,nrow=ptf,ncol=ptf)
workvh2 <- rep(0,(ptf*(ptf+1)/2))
workv2 <- rep(0,ptf)
workv3 <- rep(0,ptf)
workv4 <- rep(0,ptf)
k <- rep(0,maxm)
prob <- rep(0,2**maxm)
probc <- rep(0,2**maxm)
#########################################################################################
# calling the fortran code
#########################################################################################
foo <- .Fortran("ldtfpsurvival",
nrec = as.integer(nrec),
ptf = as.integer(ptf),
pce = as.integer(pce),
interind = as.integer(type),
xtf = as.double(xtf),
xce = as.double(xce),
y = as.double(y),
ngrid = as.integer(ngrid),
npredden = as.integer(npredden),
npredmed = as.integer(npredmed),
grid = as.double(grid),
xtfpred = as.double(xtfpred),
xcepred = as.double(xcepred),
xtfpredm = as.double(xtfpredm),
xcepredm = as.double(xcepredm),
quans = as.double(quans),
maxm = as.integer(maxm),
ntprob = as.integer(ntprob),
ntlr = as.integer(ntlr),
a0b0 = as.double(a0b0),
betacepm = as.double(betacepm),
gprior = as.double(gprior),
precce = as.double(precce),
tau = as.double(tau),
alpha = as.double(alpha),
betace = as.double(betace),
betatf = as.double(betatf),
sigma2 = as.double(sigma2),
z = as.double(z),
mcmc = as.integer(mcmcvec),
nsave = as.integer(nsave),
seed = as.integer(seed),
cpo = as.double(cpo),
densm = as.double(densm),
densl = as.double(densl),
densu = as.double(densu),
qmm = as.double(qmm),
qml = as.double(qml),
qmu = as.double(qmu),
survmm = as.double(survmm),
survml = as.double(survml),
survmu = as.double(survmu),
thetasave = as.double(thetasave),
randsave = as.double(randsave),
iflag = as.integer(iflag),
iflagtf = as.integer(iflagtf),
nobsbc = as.integer(nobsbc),
obsbc = as.integer(obsbc),
c0 = as.double(c0),
workm1 = as.double(workm1),
workvh1 = as.double(workvh1),
workv1 = as.double(workv1),
worksam = as.double(worksam),
worksam2 = as.double(worksam2),
worksam3 = as.double(worksam3),
fs = as.double(fs),
workm2 = as.double(workm2),
workvh2 = as.double(workvh2),
workv2 = as.double(workv2),
workv3 = as.double(workv3),
workv4 = as.double(workv4),
k = as.integer(k),
prob = as.double(prob),
probc = as.double(probc),
PACKAGE = "DPpackage")
#########################################################################################
# save state
#########################################################################################
if(!is.null(work.dir))
{
cat("\n\n Changing working directory back to ",old.dir,"\n")
setwd(old.dir)
}
model.name <- "Linear dependent TF process model for time-to-event data"
cpom <- matrix(foo$cpo,nrow=nrec,ncol=2)
cpo <- cpom[,1]
fso <- cpom[,2]
densm <- matrix(foo$densm,nrow=npredden,ncol=ngrid)
densl <- NULL
densu <- NULL
qmm <- matrix(foo$qmm,nrow=npredmed,3)
qml <- NULL
qmu <- NULL
survmm <- matrix(foo$survmm,nrow=npredden,ncol=ngrid)
survml <- NULL
survmu <- NULL
if(compute.band)
{
densl <- matrix(foo$densl,nrow=npredden,ncol=ngrid)
densu <- matrix(foo$densu,nrow=npredden,ncol=ngrid)
qml <- matrix(foo$qml,nrow=npredmed,3)
qmu <- matrix(foo$qmu,nrow=npredmed,3)
survml <- matrix(foo$survml,nrow=npredden,ncol=ngrid)
survmu <- matrix(foo$survmu,nrow=npredden,ncol=ngrid)
}
thetasave <- matrix(foo$thetasave,nrow=mcmc$nsave, ncol=(pce+2))
randsave <- matrix(foo$randsave,nrow=mcmc$nsave, ncol=((ntlr-1)*ptf))
colnames(thetasave) <- c(colnames(xce),"sigma2","alpha")
coeff <- apply(thetasave,2,mean)
colnames(randsave) <- rep(colnames(xtf),(ntlr-1))
state <- list(alpha=foo$alpha,
betace=foo$betace,
sigma2=foo$sigma2,
betatf=matrix(foo$betatf,nrow=ntlr,ncol=ptf),
z=foo$z,
nobsbc=foo$nobsbc,
obsbc=matrix(foo$obsbc,nrow=ntprob,ncol=nrec))
save.state <- list(thetasave=thetasave,
randsave=randsave)
z <- list(modelname=model.name,
coefficients=coeff,
call=cl,
compute.band=compute.band,
cpo=cpo,
fso=fso,
prior=prior,
mcmc=mcmc,
state=state,
save.state=save.state,
nrec=foo$nrec,
pce=foo$pce,
ptf=foo$ptf,
y=y,
x=xce,
xtf=xtf,
ngrid=ngrid,
npredden=npredden,
npredmed=npredmed,
grid=grid,
densm=densm,
densl=densl,
densu=densu,
qmm=qmm,
qml=qml,
qmu=qmu,
survmm=survmm,
survml=survml,
survmu=survmu)
cat("\n\n")
class(z) <- c("LDTFPsurvival")
z
}
###
### Tools for LDTFPsurvival: print, summary, plot
###
### Copyright: Alejandro Jara, 2011
### Last modification: 11-11-2011.
"print.LDTFPsurvival" <- function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$modelname,"\n\nCall:\n", sep = "")
print(x$call)
cat("\n")
cat("Posterior Predictive Distributions (log):\n")
print.default(format(summary(log(x$cpo)), digits = digits), print.gap = 2,
quote = FALSE)
cat("\nPosterior Inference of Parameters:\n")
print.default(format(x$coefficients, digits = digits), print.gap = 2,
quote = FALSE)
cat("\nNumber of Observations:",x$nrec)
cat("\nNumber of Predictors for the Median:",x$pce)
cat("\nNumber of Predictors for the Tailfree Probabilities:",x$ptf,"\n")
cat("\n\n")
invisible(x)
}
"plot.LDTFPsurvival"<-function(x, hpd=TRUE, ask=TRUE, nfigr=2, nfigc=2, param=NULL, col="#bdfcc9", ...)
{
fancydensplot1<-function(x, hpd=TRUE, npts=200, xlab="", ylab="", main="",col="#bdfcc9", ...)
# Author: AJV, 2007
#
{
dens <- density(x,n=npts)
densx <- dens$x
densy <- dens$y
meanvar <- mean(x)
densx1 <- max(densx[densx<=meanvar])
densx2 <- min(densx[densx>=meanvar])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ymean <- densy1 + ((densy2-densy1)/(densx2-densx1))*(meanvar-densx1)
if(hpd==TRUE)
{
alpha<-0.05
alow<-rep(0,2)
aupp<-rep(0,2)
n<-length(x)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(x),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
xlinf<-a$alow[1]
xlsup<-a$aupp[1]
}
else
{
xlinf <- quantile(x,0.025)
xlsup <- quantile(x,0.975)
}
densx1 <- max(densx[densx<=xlinf])
densx2 <- min(densx[densx>=xlinf])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylinf <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlinf-densx1)
densx1 <- max(densx[densx<=xlsup])
densx2 <- min(densx[densx>=xlsup])
densy1 <- densy[densx==densx1]
densy2 <- densy[densx==densx2]
ylsup <- densy1 + ((densy2-densy1)/(densx2-densx1))*(xlsup-densx1)
plot(0.,0.,xlim = c(min(densx), max(densx)), ylim = c(min(densy), max(densy)),
axes = F,type = "n" , xlab=xlab, ylab=ylab, main=main, cex=1.2)
xpol<-c(xlinf,xlinf,densx[densx>=xlinf & densx <=xlsup],xlsup,xlsup)
ypol<-c(0,ylinf,densy[densx>=xlinf & densx <=xlsup] ,ylsup,0)
polygon(xpol, ypol, border = FALSE,col=col)
lines(c(min(densx), max(densx)),c(0,0),lwd=1.2)
segments(min(densx),0, min(densx),max(densy),lwd=1.2)
lines(densx,densy,lwd=1.2)
segments(meanvar, 0, meanvar, ymean,lwd=1.2)
segments(xlinf, 0, xlinf, ylinf,lwd=1.2)
segments(xlsup, 0, xlsup, ylsup,lwd=1.2)
axis(1., at = round(c(xlinf, meanvar,xlsup), 2.), labels = T,pos = 0.)
axis(1., at = round(seq(min(densx),max(densx),length=15), 2.), labels = F,pos = 0.)
axis(2., at = round(seq(0,max(densy),length=5), 2.), labels = T,pos =min(densx))
}
if(is(x, "LDTFPsurvival"))
{
if(is.null(param))
{
coef.p <- x$coefficients
n <- length(coef.p)
pnames <- names(coef.p)
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr , ncol=nfigc ,byrow=TRUE))
for(i in 1:length(coef.p))
{
title1 <- paste("Trace of",pnames[i],sep=" ")
title2 <- paste("Density of",pnames[i],sep=" ")
plot(ts(x$save.state$thetasave[,i]),main=title1,xlab="MCMC scan",ylab=" ")
fancydensplot1(x$save.state$thetasave[,i],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
for(i in 1:x$npredden)
{
if(x$compute.band)
{
title1 <- paste("Survival Prediction #",i,sep=" ")
plot(x$grid,x$survmu[i,],main=title1,lty=2,type='l',lwd=2,xlab="time",ylab="survival",ylim=c(0,1))
lines(x$grid,x$survml[i,],lty=2,lwd=2)
lines(x$grid,x$survmm[i,],lty=1,lwd=3)
}
else
{
title1 <- paste("Survival Prediction #",i,sep=" ")
plot(x$grid,x$survmm[i,],main=title1,lty=1,type='l',lwd=2,xlab="time",ylab="survival",ylim=c(0,1))
}
}
}
else
{
coef.p <- x$coefficients
n <- length(coef.p)
pnames <- names(coef.p)
poss <- 0
for(i in 1:n)
{
if(pnames[i]==param)poss=i
}
if(poss==0 && param !="predictive")
{
stop("This parameter is not present in the original model.\n")
}
par(ask = ask)
layout(matrix(seq(1,nfigr*nfigc,1), nrow=nfigr, ncol=nfigc, byrow = TRUE))
if(param !="predictive")
{
title1 <- paste("Trace of",pnames[poss],sep=" ")
title2 <- paste("Density of",pnames[poss],sep=" ")
plot(ts(x$save.state$thetasave[,poss]),main=title1,xlab="MCMC scan",ylab=" ")
fancydensplot1(x$save.state$thetasave[,poss],hpd=hpd,main=title2,xlab="values", ylab="density",col=col)
}
else
{
for(i in 1:x$npredden)
{
if(x$compute.band)
{
title1 <- paste("Survival Prediction #",i,sep=" ")
plot(x$grid,x$survmu[i,],main=title1,lty=2,type='l',lwd=2,xlab="time",ylab="survival",ylim=c(0,1))
lines(x$grid,x$survml[i,],lty=2,lwd=2)
lines(x$grid,x$survmm[i,],lty=1,lwd=3)
}
else
{
title1 <- paste("Survival Prediction #",i,sep=" ")
plot(x$grid,x$survmm[i,],main=title1,lty=1,type='l',lwd=2,xlab="time",ylab="survival",ylim=c(0,1))
}
}
}
}
}
}
"summary.LDTFPsurvival" <- function(object, hpd=TRUE, ...)
{
stde<-function(x)
{
n<-length(x)
return(sd(x)/sqrt(n))
}
hpdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[1],a$aupp[1]))
}
pdf<-function(x)
{
alpha<-0.05
vec<-x
n<-length(x)
alow<-rep(0,2)
aupp<-rep(0,2)
a<-.Fortran("hpd",n=as.integer(n),alpha=as.double(alpha),x=as.double(vec),
alow=as.double(alow),aupp=as.double(aupp),PACKAGE="DPpackage")
return(c(a$alow[2],a$aupp[2]))
}
thetasave <- object$save.state$thetasave
ans <- c(object[c("call", "modelname")])
### CPO
ans$cpo <- object$cpo
### Median information
dimen1 <- object$pce
if(dimen1==1)
{
mat <- matrix(thetasave[,1],ncol=1)
}
else
{
mat <- thetasave[,1:dimen1]
}
coef.p <- object$coefficients[1:dimen1]
coef.m <- apply(mat, 2, median)
coef.sd <- apply(mat, 2, sd)
coef.se <- apply(mat, 2, stde)
if(hpd){
limm <- apply(mat, 2, hpdf)
coef.l <- limm[1,]
coef.u <- limm[2,]
}
else
{
limm <- apply(mat, 2, pdf)
coef.l <- limm[1,]
coef.u <- limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$coeff <- coef.table
### Baseline Information
mat <- matrix(thetasave[,(dimen1+1)],ncol=1)
coef.p <- object$coefficients[(dimen1+1)]
coef.m <- apply(mat, 2, median)
coef.sd <- apply(mat, 2, sd)
coef.se <- apply(mat, 2, stde)
if(hpd){
limm <- apply(mat, 2, hpdf)
coef.l <- limm[1,]
coef.u <- limm[2,]
}
else
{
limm <- apply(mat, 2, pdf)
coef.l <- limm[1,]
coef.u <- limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$base <- coef.table
### Precision parameter
if(is.null(object$prior$a0))
{
ans$prec <- NULL
}
else
{
mat <- matrix(thetasave[,(dimen1+2)],ncol=1)
coef.p <- object$coefficients[(dimen1+2)]
coef.m <- apply(mat, 2, median)
coef.sd <- apply(mat, 2, sd)
coef.se <- apply(mat, 2, stde)
if(hpd){
limm <- apply(mat, 2, hpdf)
coef.l <- limm[1,]
coef.u <- limm[2,]
}
else
{
limm <- apply(mat, 2, pdf)
coef.l <- limm[1,]
coef.u <- limm[2,]
}
coef.table <- cbind(coef.p, coef.m, coef.sd, coef.se , coef.l , coef.u)
if(hpd)
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%HPD-Low","95%HPD-Upp"))
}
else
{
dimnames(coef.table) <- list(names(coef.p), c("Mean", "Median", "Std. Dev.", "Naive Std.Error",
"95%CI-Low","95%CI-Upp"))
}
ans$prec <- coef.table
}
ans$nrec <- object$nrec
ans$pce <- object$pce
ans$ptf <- object$ptf
class(ans) <- "summaryLDTFPsurvival"
return(ans)
}
"print.summaryLDTFPsurvival"<-function (x, digits = max(3, getOption("digits") - 3), ...)
{
cat("\n",x$modelname,"\n\nCall:\n", sep = "")
print(x$call)
cat("\n")
cat("Posterior Predictive Distributions (log):\n")
print.default(format(summary(log(as.vector(x$cpo))), digits = digits), print.gap = 2,
quote = FALSE)
cat("\nPosterior Inference of Median Regression Parameters:\n")
print.default(format(x$coeff, digits = digits), print.gap = 2,
quote = FALSE)
cat("\nPosterior Inference of Baseline Variance:\n")
print.default(format(x$base, digits = digits), print.gap = 2,
quote = FALSE)
if (length(x$prec)) {
cat("\nPrecision parameter:\n")
print.default(format(x$prec, digits = digits), print.gap = 2,
quote = FALSE)
}
cat("\nNumber of Observations:",x$nrec)
cat("\nNumber of Predictors for the Median:",x$pce)
cat("\nNumber of Predictors for the Tailfree Probabilities:",x$pce,"\n")
cat("\n\n")
invisible(x)
}
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