recurrent-events.R
In mets: Analysis of Multivariate Event Times

## ---- include = FALSE---------------------------------------------------------
knitr::opts_chunk$set(
  collapse = TRUE,
  #dev="svg",
  dpi=50,
  fig.width=7, fig.height=5.5,
  out.width="600px",
  fig.retina=1,
  comment = "#>"
)
fullVignette <- Sys.getenv("_R_FULL_VIGNETTE_") %in% c("1","TRUE")
library(mets)

## -----------------------------------------------------------------------------
library(mets)
library(timereg)
set.seed(1000) # to control output in simulatins for p-values below.

## -----------------------------------------------------------------------------
data(base1cumhaz)
data(base4cumhaz)
data(drcumhaz)
ddr <- drcumhaz
base1 <- base1cumhaz
base4 <- base4cumhaz
rr <- simRecurrent(200,base1,death.cumhaz=ddr)
rr$x <- rnorm(nrow(rr)) 
rr$strata <- floor((rr$id-0.01)/100)
dlist(rr,.~id| id %in% c(1,7,9))

## -----------------------------------------------------------------------------
#  to fit non-parametric models with just a baseline 
xr <- phreg(Surv(entry,time,status)~cluster(id),data=rr)
dr <- phreg(Surv(entry,time,death)~cluster(id),data=rr)
par(mfrow=c(1,3))
bplot(dr,se=TRUE)
title(main="death")
bplot(xr,se=TRUE)
# robust standard errors 
rxr <-   robust.phreg(xr,fixbeta=1)
bplot(rxr,se=TRUE,robust=TRUE,add=TRUE,col=4)

# marginal mean of expected number of recurrent events 
out <- recurrentMarginal(xr,dr)
bplot(out,se=TRUE,ylab="marginal mean",col=2)

## -----------------------------------------------------------------------------
summary(out,times=c(1000,2000))

## -----------------------------------------------------------------------------
xr <- phreg(Surv(entry,time,status)~strata(strata)+cluster(id),data=rr)
dr <- phreg(Surv(entry,time,death)~strata(strata)+cluster(id),data=rr)
par(mfrow=c(1,3))
bplot(dr,se=TRUE)
title(main="death")
bplot(xr,se=TRUE)
rxr <-   robust.phreg(xr,fixbeta=1)
bplot(rxr,se=TRUE,robust=TRUE,add=TRUE,col=1:2)

out <- recurrentMarginal(xr,dr)
bplot(out,se=TRUE,ylab="marginal mean",col=1:2)

## -----------------------------------------------------------------------------
# cox case
xr <- phreg(Surv(entry,time,status)~x+cluster(id),data=rr)
dr <- phreg(Surv(entry,time,death)~x+cluster(id),data=rr)
par(mfrow=c(1,3))
bplot(dr,se=TRUE)
title(main="death")
bplot(xr,se=TRUE)
rxr <- robust.phreg(xr)
bplot(rxr,se=TRUE,robust=TRUE,add=TRUE,col=1:2)

out <- recurrentMarginal(xr,dr)
bplot(out,se=TRUE,ylab="marginal mean",col=1:2)

# predictions witout se's 
outX <- recmarg(xr,dr,Xr=1,Xd=1)
bplot(outX,add=TRUE,col=3)

## -----------------------------------------------------------------------------
rr <- simRecurrentII(200,base1,base4,death.cumhaz=ddr,cens=3/5000,dependence=4,var.z=1)
rr <-  count.history(rr)

rr <- transform(rr,statusD=status)
rr <- dtransform(rr,statusD=3,death==1)
dtable(rr,~statusD+status+death,level=2,response=1)

xr <- phreg(Surv(start,stop,status==1)~cluster(id),data=rr)
dr <- phreg(Surv(start,stop,death)~cluster(id),data=rr)
# marginal mean of expected number of recurrent events 
out <- recurrentMarginal(xr,dr)

times <- 500*(1:10)
recEFF1 <- recurrentMarginalAIPCW(Event(start,stop,statusD)~cluster(id),data=rr,times=times,cens.code=0,
				   death.code=3,cause=1,augment.model=~Nt)
with( recEFF1, cbind(times,muP,semuP,muPAt,semuPAt,semuPAt/semuP))

times <- 500*(1:10)
###recEFF14 <- recurrentMarginalAIPCW(Event(start,stop,statusD)~cluster(id),data=rr,times=times,cens.code=0,
###death.code=3,cause=1,augment.model=~Nt+Nt2+expNt+NtexpNt)
###with(recEFF14,cbind(times,muP,semuP,muPAt,semuPAt,semuPAt/semuP))

recEFF14 <- recurrentMarginalAIPCW(Event(start,stop,statusD)~cluster(id),data=rr,times=times,cens.code=0,
death.code=3,cause=1,augment.model=~Nt+I(Nt^2)+I(exp(-Nt))+ I( Nt*exp(-Nt)))
with(recEFF14,cbind(times,muP,semuP,muPAt,semuPAt,semuPAt/semuP))

bplot(out,se=TRUE,ylab="marginal mean",col=2)
k <- 1
for (t in times) {
	ci1 <- c(recEFF1$muPAt[k]-1.96*recEFF1$semuPAt[k],
  	         recEFF1$muPAt[k]+1.96*recEFF1$semuPAt[k])
	ci2 <- c(recEFF1$muP[k]-1.96*recEFF1$semuP[k],
  	         recEFF1$muP[k]+1.96*recEFF1$semuP[k])
	lines(rep(t,2)-2,ci2,col=2,lty=1,lwd=2)
	lines(rep(t,2)+2,ci1,col=1,lty=1,lwd=2)
	k <- k+1
}
legend("bottomright",c("Eff-pred"),lty=1,col=c(1,3))

## -----------------------------------------------------------------------------
rr <- mets:::simMarginalMeanCox(200,cens=3/5000,Lam1=base1,LamD=ddr,beta1=c(0.3,-0.3),
				betad=c(-0.3,0.3))
dtable(rr,~statusD+status+death,level=2,response=1)

times <- seq(500,5000,by=500)
recEFF1x <- recurrentMarginalAIPCW(Event(start,stop,statusD)~cluster(id),data=rr,times=times,
				   cens.code=0,death.code=3,cause=1,augment.model=~X1+X2)
with(recEFF1x, cbind(muP,muPA,muPAt,semuP,semuPA,semuPAt,semuPAt/semuP))

xr <- phreg(Surv(start,stop,status==1)~cluster(id),data=rr)
dr <- phreg(Surv(start,stop,death)~cluster(id),data=rr)
out <- recurrentMarginal(xr,dr)
mets::summaryTimeobject(out$times,out$mu,times=times,se.mu=out$se.mu)

## -----------------------------------------------------------------------------
 rr <- mets:::simMarginalMeanCox(200,cens=3/5000,Lam1=base1,LamD=ddr,beta1=c(0.3,-0.3),betad=c(-0.3,0.3),k1=0.1)
 dtable(rr,~statusD+status+death,level=2,response=1)

 out  <- recreg(Event(start,stop,statusD)~X1+X2+cluster(id),data=rr,cause=1,death.code=3,cens.code=0)
 outs <- recreg(Event(start,stop,statusD)~X1+X2+cluster(id),data=rr,cause=1,death.code=3,cens.code=0,
		cens.model=~strata(X1,X2))
 summary(out)$coef
 summary(outs)$coef

 ## checking baseline
 par(mfrow=c(1,1))
 bplot(out)
 bplot(outs,add=TRUE,col=2)
 lines(scalecumhaz(base1,0.1),col=3,lwd=2)

## -----------------------------------------------------------------------------
 outipcw  <- recregIPCW(Event(start,stop,statusD)~X1+X2+cluster(id),data=rr,cause=1,death.code=3,
			cens.code=0,times=2000)
 outipcws <- recregIPCW(Event(start,stop,statusD)~X1+X2+cluster(id),data=rr,cause=1,death.code=3,
		    cens.code=0,times=2000,cens.model=~strata(X1,X2))
 summary(outipcw)$coef
 summary(outipcws)$coef

## -----------------------------------------------------------------------------
 out  <- recreg(Event(start,stop,statusD)~X1+X2+cluster(id),data=rr,cause=c(1,3),
		death.code=3,cens.code=0)
 summary(out)$coef

## -----------------------------------------------------------------------------
 rr$binf <- rbinom(nrow(rr),1,0.5) 
 rr$statusDC <- rr$statusD
 rr <- dtransform(rr,statusDC=4, statusD==3 & binf==0)
 rr$weight <- 1
 rr <- dtransform(rr,weight=2,statusDC==3)

 outC  <- recreg(Event(start,stop,statusDC)~X1+X2+cluster(id),data=rr,cause=c(1,3),
		 death.code=c(3,4),cens.code=0)
 summary(outC)$coef

 outCW  <- recreg(Event(start,stop,statusDC)~X1+X2+cluster(id),data=rr,cause=c(1,3),
		  death.code=c(3,4),cens.code=0,wcomp=c(1,2))
 summary(outCW)$coef

 bplot(out,ylab="Mean composite")
 bplot(outC,col=2,add=TRUE)
 bplot(outCW,col=3,add=TRUE)

## -----------------------------------------------------------------------------
out  <- recreg(Event(start,stop,statusD)~X1+X2+cluster(id),data=rr,cause=1,death.code=3,
	        cens.code=0,cox.prep=TRUE)
baseiid <- IIDbaseline.cifreg(out,time=3000)
GLprediid(baseiid,rr[1:5,])

## -----------------------------------------------------------------------------
 outi  <- recreg(Event(start,stop,statusD)~X1+X2+cluster(id),data=rr,cause=1,death.code=3,cens.code=0,
		augment.model=~Nt+X1+X2)
 summary(outi)$coef
 outA  <- recreg(Event(start,stop,statusD)~X1+X2+cluster(id),data=rr,cause=1,death.code=3,cens.code=0,
		augment.model=~Nt+X1+X2,augment=outi$lindyn.augment)
 summary(outA)$coef


## -----------------------------------------------------------------------------
###cor.mat <- corM <- rbind(c(1.0, 0.6, 0.9), c(0.6, 1.0, 0.5), c(0.9, 0.5, 1.0))
rr <- simRecurrentII(200,base1,base4,death.cumhaz=ddr,cens=3/5000,dependence=4,var.z=1)
rr <-  count.history(rr)
dtable(rr,~death+status)

oo <- prob.exceedRecurrent(rr,1)
bplot(oo)

## -----------------------------------------------------------------------------
par(mfrow=c(1,2))
with(oo,plot(time,mu,col=2,type="l"))
#
with(oo,plot(time,varN,type="l"))

## -----------------------------------------------------------------------------
 oop <- prob.exceed.recurrent(rr,1)
 bplot(oo)
 matlines(oop$times,oop$prob,type="l")
 summaryTimeobject(oop$times,oop$prob,se.mu=oop$se.prob,times=1000)

## -----------------------------------------------------------------------------
matplot(oop$times,oop$prob,type="l")
for (i in seq(ncol(oop$prob))) 
	plotConfRegion(oop$times,cbind(oop$se.lower[,i],oop$se.upper[,i]),col=i)

## -----------------------------------------------------------------------------
rr <- simRecurrentII(200,base1,cumhaz2=base4,death.cumhaz=ddr)
rr <-  count.history(rr)
dtable(rr,~death+status)

## -----------------------------------------------------------------------------
# Bivariate probability of exceeding 
oo <- prob.exceedBiRecurrent(rr,1,2,exceed1=c(1,5),exceed2=c(1,2))
with(oo, matplot(time,pe1e2,type="s"))
nc <- ncol(oo$pe1e2)
legend("topleft",legend=colnames(oo$pe1e2),lty=1:nc,col=1:nc)

## -----------------------------------------------------------------------------
rr$strata <- 1
dtable(rr,~death+status)

covrp <- covarianceRecurrent(rr,1,2,status="status",death="death",
                        start="entry",stop="time",id="id",names.count="Count")
par(mfrow=c(1,3)) 
plot(covrp)

# with strata, each strata in matrix column, provides basis for fast Bootstrap
covrpS <- covarianceRecurrentS(rr,1,2,status="status",death="death",
        start="entry",stop="time",strata="strata",id="id",names.count="Count")

## ---- eval=FALSE--------------------------------------------------------------
#  times <- seq(500,5000,500)
#  
#  coo1 <- covarianceRecurrent(rr,1,2,status="status",start="entry",stop="time")
#  #
#  mug <- Cpred(cbind(coo1$time,coo1$EN1N2),times)[,2]
#  mui <- Cpred(cbind(coo1$time,coo1$EIN1N2),times)[,2]
#  mu2.1 <- Cpred(cbind(coo1$time,coo1$mu2.1),times)[,2]
#  mu2.i <- Cpred(cbind(coo1$time,coo1$mu2.i),times)[,2]
#  mu1.2 <- Cpred(cbind(coo1$time,coo1$mu1.2),times)[,2]
#  mu1.i <- Cpred(cbind(coo1$time,coo1$mu1.i),times)[,2]
#  cbind(times,mu2.1,mu2.i)
#  cbind(times,mu1.2,mu1.i)

## ---- eval=FALSE--------------------------------------------------------------
#  bt1 <- BootcovariancerecurrenceS(rr,1,2,status="status",start="entry",stop="time",K=100,times=times)
#  #bt1 <- Bootcovariancerecurrence(rr,1,2,status="status",start="entry",stop="time",K=K,times=times)
#  
#  BCoutput <- list(bt1=bt1,mug=mug,mui=mui,
#          bse.mug=bt1$se.mug,bse.mui=bt1$se.mui,
#          dmugi=mug-mui,
#  	bse.dmugi=apply(bt1$EN1N2-bt1$EIN1N2,1,sd),
#  	mu2.1 = mu2.1 , mu2.i = mu2.i , dmu2.i=mu2.1-mu2.i,
#  	mu1.2 = mu1.2 , mu1.i = mu1.i , dmu1.i=mu1.2-mu1.i,
#  	bse.mu2.1=apply(bt1$mu2.i,1,sd), bse.mu2.1=apply(bt1$mu2.1,1,sd),
#  	bse.dmu2.i=apply(bt1$mu2.1-bt1$mu2.i,1,sd),
#  	bse.mu1.2=apply(bt1$mu1.2,1,sd), bse.mu1.i=apply(bt1$mu1.i,1,sd),
#  	bse.dmu1.i=apply(bt1$mu1.2-bt1$mu1.i,1,sd)
#  	)

## ---- eval=FALSE--------------------------------------------------------------
#  tt  <- BCoutput$dmugi/BCoutput$bse.dmugi
#  cbind(times,2*(1-pnorm(abs(tt))))

## ---- eval=FALSE--------------------------------------------------------------
#  t21  <- BCoutput$dmu1.i/BCoutput$bse.dmu1.i
#  t12  <- BCoutput$dmu2.i/BCoutput$bse.dmu2.i
#  cbind(times,2*(1-pnorm(abs(t21))),2*(1-pnorm(abs(t12))))

## ---- eval=FALSE--------------------------------------------------------------
#  par(mfrow=c(1,2))
#  matplot(BCoutput$bt1$time,BCoutput$bt1$EN1N2,type="l",lwd=0.3)
#  matplot(BCoutput$bt1$time,BCoutput$bt1$EIN1N2,type="l",lwd=0.3)

## ---- eval=FALSE--------------------------------------------------------------
#    data(base1cumhaz)
#    data(base4cumhaz)
#    data(drcumhaz)
#    dr <- drcumhaz
#    base1 <- base1cumhaz
#    base4 <- base4cumhaz
#  
#    par(mfrow=c(1,3))
#    var.z <- c(0.5,0.5,0.5)
#    # death related to  both causes in same way
#    cor.mat <- corM <- rbind(c(1.0, 0.0, 0.0), c(0.0, 1.0, 0.0), c(0.0, 0.0, 1.0))
#    rr <- simRecurrentII(200,base1,base4,death.cumhaz=dr,var.z=var.z,cor.mat=cor.mat,dependence=2)
#    rr <- count.history(rr,types=1:2)
#    cor(attr(rr,"z"))
#    coo <- covarianceRecurrent(rr,1,2,status="status",start="entry",stop="time")
#    plot(coo,main ="Scenario I")

## ---- eval=FALSE--------------------------------------------------------------
#    var.z <- c(0.5,0.5,0.5)
#    # death related to  both causes in same way
#    cor.mat <- corM <- rbind(c(1.0, 0.0, 0.5), c(0.0, 1.0, 0.5), c(0.5, 0.5, 1.0))
#    rr <- simRecurrentII(200,base1,base4,death.cumhaz=dr,var.z=var.z,cor.mat=cor.mat,dependence=2)
#    rr <- count.history(rr,types=1:2)
#    coo <- covarianceRecurrent(rr,1,2,status="status",start="entry",stop="time")
#    par(mfrow=c(1,3))
#    plot(coo,main ="Scenario II")

## ---- eval=FALSE--------------------------------------------------------------
#    var.z <- c(0.5,0.5,0.5)
#    # positive dependence for N1 and N2 all related in same way
#    cor.mat <- corM <- rbind(c(1.0, 0.5, 0.5), c(0.5, 1.0, 0.5), c(0.5, 0.5, 1.0))
#    rr <- simRecurrentII(200,base1,base4,death.cumhaz=dr,var.z=var.z,cor.mat=cor.mat,dependence=2)
#    rr <- count.history(rr,types=1:2)
#    coo <- covarianceRecurrent(rr,1,2,status="status",start="entry",stop="time")
#    par(mfrow=c(1,3))
#    plot(coo,main="Scenario III")

## ---- eval=FALSE--------------------------------------------------------------
#    var.z <- c(0.5,0.5,0.5)
#    # negative dependence for N1 and N2 all related in same way
#    cor.mat <- corM <- rbind(c(1.0, -0.4, 0.5), c(-0.4, 1.0, 0.5), c(0.5, 0.5, 1.0))
#    rr <- simRecurrentII(200,base1,base4,death.cumhaz=dr,var.z=var.z,cor.mat=cor.mat,dependence=2)
#    rr <- count.history(rr,types=1:2)
#    coo <- covarianceRecurrent(rr,1,2,status="status",start="entry",stop="time")
#    par(mfrow=c(1,3))
#    plot(coo,main="Scenario IV")

## -----------------------------------------------------------------------------
sessionInfo()