Fast recurrent marginal mean when death is possible
Source:R/recurrent.marginal.R
recurrentMarginal.RdFast 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.
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
Details
Assumes no ties in the sense that jump times needs to be unique, this is particularly so for the stratified version.
References
Cook, R. J. and Lawless, J. F. (1997) Marginal analysis of recurrent events and a terminating event. Statist. Med., 16, 911–924. 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")
