Average treatment effect (ATE) based on the Cox and Fine-Gray model
In mets: Analysis of Multivariate Event Times

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
library(mets)

ATE

Computing the G-estimation based on the Cox or Fine-Gray model : [ \hat S(t,A=a) = n^{-1} \sum_i S(t,A=a,X_i) ] and this estimator has influence function [ S(t,A=a,X_i) - S(t,A=a) + E( D_{A_0(t), \beta} S(t,A=a,X_i) ) \epsilon_i(t) ] where $\epsilon_i(t)$ is the iid decomposition of $(\hat A(t) - A(t), \hat \beta- \beta)$.

set.seed(100)

data(bmt); bmt$time <- bmt$time+runif(nrow(bmt))*0.001
dfactor(bmt) <- tcell~tcell
bmt$event <- (bmt$cause!=0)*1

fg1 <- cifreg(Event(time,cause)~tcell+platelet+age,bmt,cause=1,
          cox.prep=TRUE,propodds=NULL)
summary(survivalG(fg1,bmt,50))

fg2 <- cifreg(Event(time,cause)~tcell+platelet+age,bmt,cause=2,
          cox.prep=TRUE,propodds=NULL)
summary(survivalG(fg2,bmt,50))

ss <- phreg(Surv(time,event)~tcell+platelet+age,bmt)
summary(survivalG(ss,bmt,50))

Comparing with binomial-regression ATE

br1 <- binregATE(Event(time,cause)~tcell+platelet+age,bmt,cause=1,
         time=40,treat.model=tcell~platelet+age)
summary(br1)

sr1 <- binregATE(Event(time,event)~tcell+platelet+age,bmt,cause=1,
         time=40, treat.model=tcell~platelet+age)
summary(sr1)