mets (version 1.3.2)

recurrentMarginal: Fast recurrent marginal mean when death is possible

Description

Fast Marginal means of recurrent events. Using the Lin and Ghosh (2000) standard errors. Fitting two models for death and recurent events these are combined to prducte the estimator $$ \int_0^t S(u|x=0) dR(u|x=0) $$ the mean number of recurrent events, here $$ S(u|x=0) $$ is the probability of survival for the baseline group, and $$ dR(u|x=0) $$ is the hazard rate of an event among survivors for the baseline. Here $$ S(u|x=0) $$ is estimated by $$ exp(-\Lambda_d(u|x=0) $$ with $$\Lambda_d(u|x=0) $$ being the cumulative baseline for death.

Usage

recurrentMarginal(recurrent, death, fixbeta = NULL, km = TRUE, ...)

Arguments

recurrent

phreg object with recurrent events

death

phreg object with deaths

fixbeta

to force the estimation of standard errors to think of regression coefficients as known/fixed

km

if true then uses Kaplan-Meier for death, otherwise exp(- Nelson-Aalen )

...

Additional arguments to lower level funtions

Author

Thomas Scheike

Details

Assumes no ties in the sense that jump times needs to be unique, this is particularly so for the stratified version.

References

Ghosh and Lin (2002) Nonparametric Analysis of Recurrent events and death, Biometrics, 554--562.

Examples

data(base1cumhaz)
data(base4cumhaz)
data(drcumhaz)
dr <- drcumhaz
base1 <- base1cumhaz
base4 <- base4cumhaz
rr <- simRecurrent(1000,base1,death.cumhaz=dr)
rr$x <- rnorm(nrow(rr)) 
rr$strata <- floor((rr$id-0.01)/500)

##  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)

########################################################################
###   with strata     ##################################################
########################################################################
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)

########################################################################
###   CIF  #############################################################
########################################################################
### use of function to compute cumulative incidence (cif) with robust standard errors
 data(bmt)
 bmt$id <- 1:nrow(bmt)
 xr  <- phreg(Surv(time,cause==1)~cluster(id),data=bmt)
 dr  <- phreg(Surv(time,cause!=0)~cluster(id),data=bmt)

 out <- recurrentMarginal(xr,dr,km=TRUE)
 bplot(out,se=TRUE,ylab="cumulative incidence")