resmeanIPCW: Restricted IPCW mean for censored survival data

In kkholst/mets: Analysis of Multivariate Event Times

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.

Usage

resmeanIPCW(
  formula,
  data,
  cause = 1,
  time = NULL,
  type = c("II", "I"),
  beta = NULL,
  offset = NULL,
  weights = NULL,
  cens.weights = NULL,
  cens.model = ~+1,
  se = TRUE,
  kaplan.meier = TRUE,
  cens.code = 0,
  no.opt = FALSE,
  method = "nr",
  model = "exp",
  augmentation = NULL,
  h = NULL,
  MCaugment = NULL,
  Ydirect = NULL,
  ...
)

Arguments

formula	formula with outcome (see coxph)
data	data frame
cause	cause of interest
time	time of interest
type	of estimator
beta	starting values
offset	offsets for partial likelihood
weights	for score equations
cens.weights	censoring weights
cens.model	only stratified cox model without covariates
se	to compute se's based on IPCW
kaplan.meier	uses Kaplan-Meier for IPCW in contrast to exp(-Baseline)
cens.code	gives censoring code
no.opt	to not optimize
method	for optimization
model	exp or linear
augmentation	to augment binomial regression
h	h for estimating equation
MCaugment	iid of h and censoring model
Ydirect	to bypass the construction of the response Y=min(T,tau) and use this instead
...	Additional arguments to lower level funtions

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.

Author(s)

Thomas Scheike

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)

kkholst/mets documentation built on May 4, 2024, 1:26 p.m.