Estimates the percentage of the years lost that is due to a cause and how covariates affects this percentage by doing ICPW regression.
Usage
binregRatio(
formula,
data,
cause = 1,
time = NULL,
beta = NULL,
type = c("II", "I"),
offset = NULL,
weights = NULL,
cens.weights = NULL,
cens.model = ~+1,
se = TRUE,
kaplan.meier = TRUE,
cens.code = 0,
no.opt = FALSE,
method = "nr",
augmentation = NULL,
outcome = c("cif", "rmtl"),
model = c("logit", "exp", "lin"),
Ydirect = NULL,
...
)Arguments
- formula
formula with outcome (see
coxph)- data
data frame
- cause
cause of interest (numeric variable)
- time
time of interest
- beta
starting values
- type
"II" adds augmentation term, and "I" classical outcome IPCW regression
- 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
- augmentation
to augment binomial regression
- outcome
can do CIF regression "cif"=F(t|X), "rmtl"=E( t- min(T, t) | X)"
- model
logit, exp or lin(ear)
- Ydirect
use this Y instead of outcome constructed inside the program, should be a matrix with two column for numerator and denominator.
- ...
Additional arguments to lower level funtions
Details
Let the years lost be $$Y1= t- min(T ,) $$ and the years lost due to cause 1 $$Y2= I(epsilon==1) ( t- min(T ,t) $$ , then we model the ratio $$logit( E(Y2 | X)/E(Y1 | X)) = X^T \beta $$. Estimation is based on on binomial regresion IPCW response estimating equation: $$ X ( \Delta^{ipcw}(t) Y2 expit(X^T \beta) - Y1 ) = 0 $$ where $$\Delta^{ipcw}(t) = I((min(t,T)< C)/G_c(min(t,T)-)$$ is IPCW adjustment of the response $$Y(t)= I(T \leq t, \epsilon=1 )$$.
(type="I") sovlves this estimating equation using a stratified Kaplan-Meier for the censoring distribution. For (type="II") the default an additional censoring augmentation term $$X \int E(Y(t)| T>s)/G_c(s) d \hat M_c$$ is added.
The variance is based on the squared influence functions that are also returned as the iid component. naive.var is variance under known censoring model.
Censoring model may depend on strata (cens.model=~strata(gX)).
Examples
library(mets)
data(bmt); bmt$time <- bmt$time+runif(408)*0.001
rmst30 <- rmstIPCW(Event(time,cause!=0)~platelet+tcell+age,bmt,time=30,cause=1)
rmst301 <- rmstIPCW(Event(time,cause)~platelet+tcell+age,bmt,time=30,cause=1)
rmst302 <- rmstIPCW(Event(time,cause)~platelet+tcell+age,bmt,time=30,cause=2)
estimate(rmst30)
#> Estimate Std.Err 2.5% 97.5% P-value
#> (Intercept) 2.6104 0.05744 2.49777 2.7229 0.000e+00
#> platelet 0.2450 0.08434 0.07971 0.4103 3.672e-03
#> tcell 0.1459 0.11873 -0.08680 0.3786 2.191e-01
#> age -0.1729 0.03794 -0.24723 -0.0985 5.217e-06
estimate(rmst301)
#> Estimate Std.Err 2.5% 97.5% P-value
#> (Intercept) 2.4449 0.07291 2.3020 2.5878272 1.617e-246
#> platelet -0.4519 0.16739 -0.7800 -0.1238273 6.940e-03
#> tcell -0.4937 0.25146 -0.9866 -0.0008631 4.960e-02
#> age 0.2747 0.06538 0.1466 0.4028551 2.648e-05
estimate(rmst302)
#> Estimate Std.Err 2.5% 97.5% P-value
#> (Intercept) 1.45849 0.1362 1.1915 1.7255 9.623e-27
#> platelet -0.01890 0.2224 -0.4548 0.4170 9.323e-01
#> tcell 0.40759 0.2648 -0.1113 0.9265 1.237e-01
#> age 0.04577 0.1191 -0.1877 0.2792 7.008e-01
## percentage of total cumulative incidence due to cause 1
rmtlratioI <- rmtlRatio(Event(time,cause)~platelet+tcell+age,bmt,time=30,cause=1)
summary(rmtlratioI)
#> n events
#> 408 154
#>
#> 408 clusters
#> coeffients:
#> Estimate Std.Err 2.5% 97.5% P-value
#> (Intercept) 0.977110 0.178192 0.627860 1.326361 0.0000
#> platelet -0.412122 0.323292 -1.045763 0.221520 0.2024
#> tcell -0.855519 0.419219 -1.677174 -0.033865 0.0413
#> age 0.217628 0.168419 -0.112468 0.547724 0.1963
#>
#> exp(coeffients):
#> Estimate 2.5% 97.5%
#> (Intercept) 2.65677 1.87360 3.7673
#> platelet 0.66224 0.35142 1.2480
#> tcell 0.42506 0.18690 0.9667
#> age 1.24312 0.89363 1.7293
#>
#>
pp <- predict(rmtlratioI,bmt)
ppb <- cbind(pp,bmt)
## percentage of total cumulative incidence due to cause 1
cifratio <- binregRatio(Event(time,cause)~platelet+tcell+age,bmt,time=30,cause=1)
summary(cifratio)
#> n events
#> 408 154
#>
#> 408 clusters
#> coeffients:
#> Estimate Std.Err 2.5% 97.5% P-value
#> (Intercept) 0.91179 0.17554 0.56774 1.25585 0.0000
#> platelet -0.46503 0.31924 -1.09072 0.16066 0.1452
#> tcell -1.06112 0.41571 -1.87590 -0.24634 0.0107
#> age 0.21199 0.16115 -0.10386 0.52784 0.1884
#>
#> exp(coeffients):
#> Estimate 2.5% 97.5%
#> (Intercept) 2.48878 1.76427 3.5108
#> platelet 0.62812 0.33597 1.1743
#> tcell 0.34607 0.15322 0.7817
#> age 1.23614 0.90135 1.6953
#>
#>
pp <- predict(cifratio,bmt)
rmtlratioI <- binregRatio(Event(time,cause)~platelet+tcell+age,bmt,
time=30,cause=1,outcome="rmtl")
summary(rmtlratioI)
#> n events
#> 408 154
#>
#> 408 clusters
#> coeffients:
#> Estimate Std.Err 2.5% 97.5% P-value
#> (Intercept) 0.977110 0.178192 0.627860 1.326361 0.0000
#> platelet -0.412122 0.323292 -1.045763 0.221520 0.2024
#> tcell -0.855519 0.419219 -1.677174 -0.033865 0.0413
#> age 0.217628 0.168419 -0.112468 0.547724 0.1963
#>
#> exp(coeffients):
#> Estimate 2.5% 97.5%
#> (Intercept) 2.65677 1.87360 3.7673
#> platelet 0.66224 0.35142 1.2480
#> tcell 0.42506 0.18690 0.9667
#> age 1.24312 0.89363 1.7293
#>
#>
pp <- predict(rmtlratioI,bmt)
ppb <- cbind(pp,bmt)