mets (version 1.3.7)

resmeanIPCW: Restricted IPCW mean for censored survival data

Description

Simple and fast version for IPCW regression for just one time-point thus fitting the model $$E( min(T, t) | X ) = exp( X^T beta) $$ or in the case of competing risks data $$E( I(epsilon=1) (t - min(T ,t)) | X ) = exp( X^T beta) $$ thus given years lost to cause, see binreg for the arguments.

Usage

resmeanIPCW(formula, data, outcome = c("rmst", "rmtl"), ...)

Arguments

formula

formula with outcome on Event form

data

data frame

outcome

can do either rmst regression ('rmst') or years-lost regression ('rmtl')

...

Additional arguments to binreg

Author

Thomas Scheike

Details

When the status is binary assumes it is a survival setting and default is to consider outcome Y=min(T,t), if status has more than two levels, then computes years lost due to the specified cause, thus using the response $$ Y = (t-min(T,t)) I(status=cause) $$

Based on binomial regresion IPCW response estimating equation: $$ X ( \Delta(min(T,t)) Y /G_c(min(T,t)) - exp( X^T beta)) = 0 $$ for IPCW adjusted responses. Here $$ \Delta(min(T,t)) = I ( min(T ,t) \leq C ) $$ is indicator of being uncensored. Concretely, the uncensored observations at time t will count those with an event (of any type) before t and those with a censoring time at t or further out. One should therefore be a bit careful when data has been constructed such that some of the event times T are equivalent to t.

Can also solve the binomial regresion IPCW response estimating equation: $$ h(X) X ( \Delta(min(T,t)) Y /G_c(min(T,t)) - exp( X^T beta)) = 0 $$ for IPCW adjusted responses where $h$ is given as an argument together with iid of censoring with h.

By using appropriately the h argument we can also do the efficient IPCW estimator estimator.

Variance is based on $$ \sum w_i^2 $$ also with IPCW adjustment, and naive.var is variance under known censoring model.

When Ydirect is given it solves : $$ X ( \Delta(min(T,t)) Ydirect /G_c(min(T,t)) - exp( X^T beta)) = 0 $$ for IPCW adjusted responses.

The actual influence (type="II") function is based on augmenting with $$ X \int_0^t E(Y | T>s) /G_c(s) dM_c(s) $$ and alternatively just solved directly (type="I") without any additional terms.

Censoring model may depend on strata.

Examples

library(mets)
data(bmt); bmt$time <- bmt$time+runif(nrow(bmt))*0.001
# E( min(T;t) | X ) = exp( a+b X) with IPCW estimation 
out <- resmeanIPCW(Event(time,cause!=0)~tcell+platelet+age,bmt,
                time=50,cens.model=~strata(platelet),model="exp")
summary(out)

## weighted GLM version   RMST
out2 <- logitIPCW(Event(time,cause!=0)~tcell+platelet+age,bmt,
            time=50,cens.model=~strata(platelet),model="exp",outcome="rmst")
summary(out2)

### time-lost
outtl <- resmeanIPCW(Event(time,cause!=0)~tcell+platelet+age,bmt,
                time=50,cens.model=~strata(platelet),model="exp",outcome="rmtl")
summary(outtl)

### same as Kaplan-Meier for full censoring model 
bmt$int <- with(bmt,strata(tcell,platelet))
out <- resmeanIPCW(Event(time,cause!=0)~-1+int,bmt,time=30,
                             cens.model=~strata(platelet,tcell),model="lin")
estimate(out)
out1 <- phreg(Surv(time,cause!=0)~strata(tcell,platelet),data=bmt)
rm1 <- resmean.phreg(out1,times=30)
summary(rm1)

### years lost regression
outl <- resmeanIPCW(Event(time,cause!=0)~-1+int,bmt,time=30,outcome="years-lost",
                             cens.model=~strata(platelet,tcell),model="lin")
estimate(outl)

## competing risks years-lost for cause 1  
out <- resmeanIPCW(Event(time,cause)~-1+int,bmt,time=30,cause=1,
                            cens.model=~strata(platelet,tcell),model="lin")
estimate(out)
## same as integrated cumulative incidence 
rmc1 <- cif.yearslost(Event(time,cause)~strata(tcell,platelet),data=bmt,times=30)
summary(rmc1)