In kkholst/mets: Analysis of Multivariate Event Times

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

G-computation for the Cox and Fine-Gray models

Computing the standardized estimate (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 $(\hat A(t) - A(t), \hat \beta- \beta)$.

These estimates have a causal interpration under the assumption of no-unmeasured confounders, and even without the causal assumptions this standardization can still be a useful summary measure.

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)
sss <- survivalG(ss,bmt,50)
summary(sss)

Gtime <- survivalGtime(ss,bmt)
plot(Gtime)

G-computation for the binomial regression

We compare with the similar estimates using the Doubly Robust estimating equations using binregATE. The standardization from the G-computation can also be computed using a specialized function that takes less memory and is quicker (for large data).

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

## relative risk effect 
estimate(coef=sr1$riskDR,vcov=sr1$var.riskDR,f=function(p) p[2]/p[1],null=1)

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

and using the specialized function

br1 <- binreg(Event(time,cause)~tcell+platelet+age,bmt,cause=1,time=40)
Gbr1 <- binregG(br1,data=bmt)
summary(Gbr1)

## contrasting average age to +2-sd age, Avalues
Gbr2 <- binregG(br1,data=bmt,varname="age",Avalues=c(0,2))
summary(Gbr2)