mets (version 1.3.5)

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, ...)

Arguments

formula

formula with outcome on Event form

data

data frame

...

Additional arguments to lower level funtions

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

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)

### 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)

## 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)