mets (version 1.3.4)

binregTSR: 2 Stage Randomization for Survival Data or competing Risks Data

Description

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,
  ...
)

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).

...

Additional arguments to lower level funtions

Author

Thomas Scheike

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

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)