Under two-stage randomization we can estimate the average treatment effect E(Y(i,j)) of treatment regime (i,j). The estimator can be agumented in different ways: using the two randomizations and the dynamic censoring augmetatation. The treatment's must be given as factors.
Usage
binregTSR(
formula,
data,
cause = 1,
time = NULL,
cens.code = 0,
response.code = NULL,
augmentR0 = NULL,
treat.model0 = ~+1,
augmentR1 = NULL,
treat.model1 = ~+1,
augmentC = NULL,
cens.model = ~+1,
estpr = c(1, 1),
response.name = NULL,
offset = NULL,
weights = NULL,
cens.weights = NULL,
beta = NULL,
kaplan.meier = TRUE,
no.opt = FALSE,
method = "nr",
augmentation = NULL,
outcome = c("cif", "rmst", "rmst-cause"),
model = "exp",
Ydirect = NULL,
return.dataw = 0,
pi0 = 0.5,
pi1 = 0.5,
cens.time.fixed = 1,
outcome.iid = 1,
meanCs = 0,
...
)Arguments
- formula
formula with outcome (see
coxph)- data
data frame
- cause
cause of interest
- time
time of interest
- cens.code
gives censoring code
- response.code
code of status of survival data that indicates a response at which 2nd randomization is performed
- augmentR0
augmentation model for 1st randomization
- treat.model0
logistic treatment model for 1st randomization
- augmentR1
augmentation model for 2nd randomization
- treat.model1
logistic treatment model for 2ndrandomization
- augmentC
augmentation model for censoring
- cens.model
stratification for censoring model based on observed covariates
- estpr
estimate randomization probabilities using model
- response.name
can give name of response variable, otherwise reads this as first variable of treat.model1
- offset
not implemented
- weights
not implemented
- cens.weights
can be given
- beta
starting values
- kaplan.meier
for censoring weights, rather than exp cumulative hazard
- no.opt
not implemented
- method
not implemented
- augmentation
not implemented
- outcome
can be c("cif","rmst","rmst-cause")
- model
not implemented, uses linear regression for augmentation
- Ydirect
use this Y instead of outcome constructed inside the program (e.g. I(T< t, epsilon=1)), see binreg for more on this
- return.dataw
to return weighted data for all treatment regimes
- pi0
set up known randomization probabilities
- pi1
set up known randomization probabilities
- cens.time.fixed
to use time-dependent weights for censoring estimation using weights
- outcome.iid
to get iid contribution from outcome model (here linear regression working models).
- meanCs
(0) indicates that censoring augmentation is centered by CensAugment.times/n
- ...
Additional arguments to lower level funtions
Details
The solved estimating eqution is $$ ( I(min(T_i,t) < G_i)/G_c(min(T_i ,t)) I(T \leq t, \epsilon=1 ) - AUG_0 - AUG_1 + AUG_C - p(i,j)) = 0 $$ where using the covariates from augmentR0 $$ AUG_0 = \frac{A_0(i) - \pi_0(i)}{ \pi_0(i)} X_0 \gamma_0$$ and using the covariates from augmentR1 $$ AUG_1 = \frac{A_0(i)}{\pi_0(i)} \frac{A_1(j) - \pi_1(j)}{ \pi_1(j)} X_1 \gamma_1$$ and the censoring augmentation is $$ AUG_C = \int_0^t \gamma_c(s)^T (e(s) - \bar e(s)) \frac{1}{G_c(s) } dM_c(s) $$ where $$ \gamma_c(s)$$ is chosen to minimize the variance given the dynamic covariates specified by augmentC.
In the observational case, we can use propensity score modelling and outcome modelling (using linear regression).
Standard errors are estimated using the influence function of all estimators and tests of differences can therefore be computed subsequently.
Examples
library(mets)
ddf <- mets:::gsim(200,covs=1,null=0,cens=1,ce=2)
bb <- binregTSR(Event(entry,time,status)~+1+cluster(id),ddf$datat,time=2,cause=c(1),
cens.code=0,treat.model0=A0.f~+1,treat.model1=A1.f~A0.f,
augmentR1=~X11+X12+TR,augmentR0=~X01+X02,
augmentC=~A01+A02+X01+X02+A11t+A12t+X11+X12+TR,
response.code=2)
summary(bb)
#> Simple estimator :
#> coef
#> A0.f=1, response*A1.f=1 0.5973346 0.06741269
#> A0.f=1, response*A1.f=2 0.7989301 0.06842393
#> A0.f=2, response*A1.f=1 0.3327747 0.07150476
#> A0.f=2, response*A1.f=2 0.3240653 0.07402359
#>
#> First Randomization Augmentation :
#> coef
#> A0.f=1, response*A1.f=1 0.5870854 0.06725571
#> A0.f=1, response*A1.f=2 0.8046055 0.06813286
#> A0.f=2, response*A1.f=1 0.3294242 0.07116377
#> A0.f=2, response*A1.f=2 0.3200976 0.07455184
#>
#> Second Randomization Augmentation :
#> coef
#> A0.f=1, response*A1.f=1 0.5961775 0.06499758
#> A0.f=1, response*A1.f=2 0.8035470 0.06483341
#> A0.f=2, response*A1.f=1 0.3372532 0.07258110
#> A0.f=2, response*A1.f=2 0.3121596 0.07871542
#>
#> 1st and 2nd Randomization Augmentation :
#> coef
#> A0.f=1, response*A1.f=1 0.5936725 0.06223468
#> A0.f=1, response*A1.f=2 0.8084049 0.06466502
#> A0.f=2, response*A1.f=1 0.3401991 0.07134539
#> A0.f=2, response*A1.f=2 0.3133418 0.07761599
#>