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.
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,
...
)formula with outcome (see coxph)
data frame
cause of interest
time of interest
of estimator
starting values
offsets for partial likelihood
for score equations
censoring weights
only stratified cox model without covariates
to compute se's based on IPCW
uses Kaplan-Meier for IPCW in contrast to exp(-Baseline)
gives censoring code
to not optimize
for optimization
exp or linear
to augment binomial regression
h for estimating equation
iid of h and censoring model
to bypass the construction of the response Y=min(T,tau) and use this instead
Additional arguments to lower level funtions
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
Based on binomial regresion IPCW response estimating equation: $$ X ( \Delta (min(T , t))/G_c(min(T_i,t)) - exp( X^T beta)) = 0 $$ for IPCW adjusted responses. Here $$ \Delta(min(T,t)) I ( min(T ,t) \leq C ) $$ is indicator of being uncensored.
Can also solve the binomial regresion IPCW response estimating equation: $$ h(X) X ( \Delta (min(T, t))/G_c(min(T_i,t)) - exp( X^T beta)) = 0 $$ 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 : $$ X ( \Delta( min(T,t)) Ydirect /G_c(min(T_i,t)) - exp( X^T beta)) = 0 $$ 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.
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)
#>
#> n events
#> 408 245
#>
#> 408 clusters
#> coeffients:
#> Estimate Std.Err 2.5% 97.5% P-value
#> (Intercept) 3.014391 0.063784 2.889376 3.139406 0.0000
#> tcell 0.106875 0.139461 -0.166463 0.380212 0.4435
#> platelet 0.246943 0.098921 0.053061 0.440825 0.0125
#> age -0.185972 0.043746 -0.271712 -0.100231 0.0000
#>
#> exp(coeffients):
#> Estimate 2.5% 97.5%
#> (Intercept) 20.37668 17.98209 23.0901
#> tcell 1.11279 0.84665 1.4626
#> platelet 1.28011 1.05449 1.5540
#> age 0.83030 0.76207 0.9046
#>
#>
### 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)
#> Estimate Std.Err 2.5% 97.5% P-value
#> inttcell=0, platelet=0 13.60 0.8316 11.97 15.23 3.829e-60
#> inttcell=0, platelet=1 18.90 1.2696 16.41 21.39 4.004e-50
#> inttcell=1, platelet=0 16.19 2.4061 11.48 20.91 1.705e-11
#> inttcell=1, platelet=1 17.77 2.4536 12.96 22.58 4.464e-13
out1 <- phreg(Surv(time,cause!=0)~strata(tcell,platelet),data=bmt)
rm1 <- resmean.phreg(out1,times=30)
summary(rm1)
#> strata times rmean se.rmean years.lost
#> tcell=0, platelet=0 0 30 13.60292 0.8315433 16.39708
#> tcell=0, platelet=1 1 30 18.90123 1.2693327 11.09877
#> tcell=1, platelet=0 2 30 16.19119 2.4006162 13.80881
#> tcell=1, platelet=1 3 30 17.76608 2.4422050 12.23392
## 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)
#> Estimate Std.Err 2.5% 97.5% P-value
#> inttcell=0, platelet=0 12.105 0.8508 10.438 13.773 6.162e-46
#> inttcell=0, platelet=1 6.884 1.1741 4.583 9.185 4.536e-09
#> inttcell=1, platelet=0 7.261 2.3533 2.648 11.873 2.033e-03
#> inttcell=1, platelet=1 5.780 2.0925 1.679 9.882 5.738e-03
## same as integrated cumulative incidence
rmc1 <- cif.yearslost(Event(time,cause)~strata(tcell,platelet),data=bmt,times=30)
summary(rmc1)
#> strata times intF11 intF12 se.intF11 se.intF12
#> tcell=0, platelet=0 0 30 12.105159 4.291923 0.8508126 0.6161430
#> tcell=0, platelet=1 1 30 6.884176 4.214597 1.1741014 0.9057117
#> tcell=1, platelet=0 2 30 7.260734 6.548077 2.3532796 1.9703431
#> tcell=1, platelet=1 3 30 5.780373 6.453549 2.0924990 2.0815267
#> total.years.lost
#> tcell=0, platelet=0 16.39708
#> tcell=0, platelet=1 11.09877
#> tcell=1, platelet=0 13.80881
#> tcell=1, platelet=1 12.23392