Average Treatment effect for censored competing risks data using Binomial Regression

Under the standard causal assumptions we can estimate the average treatment effect E(Y(1) - Y(0)). We need Consistency, ignorability ( Y(1), Y(0) indep A given X), and positivity.

Usage

binregATE(
  formula,
  data,
  cause = 1,
  time = NULL,
  beta = NULL,
  treat.model = ~+1,
  cens.model = ~+1,
  offset = NULL,
  weights = NULL,
  cens.weights = NULL,
  se = TRUE,
  type = c("II", "I"),
  kaplan.meier = TRUE,
  cens.code = 0,
  no.opt = FALSE,
  method = "nr",
  augmentation = NULL,
  outcome = c("cif", "rmst", "rmtl"),
  model = c("default", "logit", "exp", "lin"),
  Ydirect = NULL,
  typeATE = "II",
  ...
)

Arguments

formula

formula with outcome (see coxph)

data

data frame

cause

cause of interest

time

time of interest

beta

starting values

treat.model

logistic treatment model given covariates

cens.model

only stratified cox model without covariates

offset

offsets for partial likelihood

weights

for score equations

cens.weights

censoring weights

se

to compute se's with IPCW adjustment, otherwise assumes that IPCW weights are known

type

"II" adds augmentation term, and "I" classic binomial regression

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

for augment binomial regression

outcome

can do CIF regression "cif"=F(t|X), "rmst"=E( min(T, t) | X) , or E( I(epsilon==cause) ( t - mint(T,t)) ) | X) depending on the number of the number of causes.

model

exp or linear model for E( min(T, t) | X)=exp(X^t beta), or E( I(epsilon==cause) ( t - mint(T,t)) ) | X)=exp(X^t beta)

Ydirect

use this outcome Y with IPCW vesion

typeATE

"II" to censor augment the estimating equation

...

Additional arguments to lower level funtions (binreg that fits outcome model)

Details

The first covariate in the specification of the competing risks regression model must be the treatment variable that should be coded as a factor. If the factor has more than two levels then it uses the mlogit for propensity score modelling. If there are no censorings this is the same as ordinary logistic regression modelling.

Estimates the ATE using the the standard binary double robust estimating equations that are IPCW censoring adjusted. Rather than binomial regression we also consider a IPCW weighted version of standard logistic regression logitIPCWATE.

typeATE="II" will augment the estimating equation with $$ (A/\pi(X)) \int E( O(t) | T \geq t, S(X))/ G_c(t,S(X)) d \hat M_c(s) $$ when estimating the mean outcome for the treated.

Author

Thomas Scheike

Examples

library(mets); data(bmt)
dfactor(bmt)  <-  ~.

brs <- binregATE(Event(time,cause)~tcell.f+platelet+age,bmt,time=50,cause=1,
  treat.model=tcell.f~platelet+age)
summary(brs)
#>    n events
#>  408    160
#> 
#>  408 clusters
#> coeffients:
#>              Estimate   Std.Err      2.5%     97.5% P-value
#> (Intercept) -0.199112  0.130982 -0.455831  0.057607  0.1285
#> tcell.f1    -0.637221  0.356617 -1.336177  0.061735  0.0740
#> platelet    -0.344504  0.245974 -0.826604  0.137596  0.1613
#> age          0.437222  0.107263  0.226991  0.647454  0.0000
#> 
#> exp(coeffients):
#>             Estimate    2.5%  97.5%
#> (Intercept)  0.81946 0.63392 1.0593
#> tcell.f1     0.52876 0.26285 1.0637
#> platelet     0.70857 0.43753 1.1475
#> age          1.54840 1.25482 1.9107
#> 
#> Average Treatment effects (G-formula) :
#>            Estimate   Std.Err      2.5%     97.5% P-value
#> treat0     0.428748  0.027511  0.374828  0.482668  0.0000
#> treat1     0.289931  0.065905  0.160761  0.419102  0.0000
#> treat:1-0 -0.138817  0.071772 -0.279487  0.001854  0.0531
#> 
#> Average Treatment effects (double robust) :
#>            Estimate   Std.Err      2.5%     97.5% P-value
#> treat0     0.428159  0.027612  0.374040  0.482278  0.0000
#> treat1     0.250414  0.064791  0.123426  0.377402  0.0001
#> treat:1-0 -0.177745  0.070145 -0.315226 -0.040263  0.0113
#> 
#> 

brsi <- binregATE(Event(time,cause)~tcell.f+tcell.f*platelet+tcell.f*age,bmt,time=50,cause=1,
  treat.model=tcell.f~platelet+age)
summary(brsi)
#>    n events
#>  408    160
#> 
#>  408 clusters
#> coeffients:
#>                    Estimate   Std.Err      2.5%     97.5% P-value
#> (Intercept)       -0.161478  0.133240 -0.422623  0.099667  0.2255
#> tcell.f1          -1.029704  0.513385 -2.035920 -0.023489  0.0449
#> platelet          -0.490119  0.270795 -1.020867  0.040630  0.0703
#> age                0.445946  0.112205  0.226028  0.665864  0.0001
#> tcell.f1:platelet  0.956586  0.694975 -0.405540  2.318713  0.1687
#> tcell.f1:age      -0.154714  0.427213 -0.992036  0.682609  0.7172
#> 
#> exp(coeffients):
#>                   Estimate    2.5%   97.5%
#> (Intercept)        0.85089 0.65533  1.1048
#> tcell.f1           0.35711 0.13056  0.9768
#> platelet           0.61255 0.36028  1.0415
#> age                1.56197 1.25361  1.9462
#> tcell.f1:platelet  2.60280 0.66662 10.1626
#> tcell.f1:age       0.85666 0.37082  1.9790
#> 
#> Average Treatment effects (G-formula) :
#>            Estimate   Std.Err      2.5%     97.5% P-value
#> treat0     0.427718  0.027557  0.373706  0.481729  0.0000
#> treat1     0.265587  0.069738  0.128903  0.402272  0.0001
#> treat:1-0 -0.162130  0.074795 -0.308726 -0.015535  0.0302
#> 
#> Average Treatment effects (double robust) :
#>            Estimate   Std.Err      2.5%     97.5% P-value
#> treat0     0.428133  0.027614  0.374012  0.482255  0.0000
#> treat1     0.253093  0.066785  0.122196  0.383990  0.0002
#> treat:1-0 -0.175040  0.072033 -0.316223 -0.033857  0.0151
#> 
#>