Implements integrative analyses for the average treatment effect combining main data with unmeasured confounders and validation data with supplementary information on these confounders.

devtools::install_github("shuyang1987/IntegrativeCI")

Under the unconfoundedness assumption with completely observed confounders, the smaller validation data allow for constructing consistent estimators for causal effects, but the big main data can only give error-prone estimators in general.

The integrative estimator leverages the information in the big main data to improve the estimation efficiencies yet preserve the consistencies of the initial estimators based solely on the validation data. Specifically, it exploits the difference of the error-prone estimators applied to the main data and the validation data, which is consistent for zero assuming that the main data and the validation data are representative of the same target population.

The framework applies to asymptotically normal estimators, including the commonly-used regression imputation, (augmented) weighting, and matching estimators.

Yang, S. and Ding, P. (2018). Combining multiple observational data sources to estimate causal effects. (https://arxiv.org/abs/1801.0080)

The function implementing the integrative average treatment effect is IntegrativeCI::IntegrativeATE().

set.seed(1)

n<-1000  # the (combined) main sample size (Samples 1 and 2)
n2<-500  # the validation sample size (Sample 2)

## generate covariates (x,u)

x<-runif(n,0,2)
u<-2*sin(x)+runif(n,0,1)

## generate treatment A

lps<-cbind(1,x,u)%*%c(0,-1,1)
ps<-exp(lps)/(1+exp(lps))
A<-rbinom(n,1,ps)

## generate potential and observed outcomes

loc.a1<-which(A==1)
loc.a0<-which(A==0)
y1<- -x+2*u+rnorm(n,0,1)
y0<- -x+1*u+rnorm(n,0,1)
y<-y1*A+y0*(1-A)
true<-mean(y1-y0)

## generate indicator of membership of the validation sample (Sample 2)

I<-rep(1,n)
I[((1+(n-n2)):n)]<-0

## u is not observed for Sample 1
loc1<-which(I==1)
u[loc1]<-NA

method_val <-c("reg")
method_ep<-c("reg","ipw")

true
#> [1] 1.839584
out<-IntegrativeCI::IntegrativeATE(I,x,u,y,A,method_val,method_ep,nboot=50)
out$est
#>          [,1]
#> [1,] 1.860912
out$ve
#>            [,1]
#> [1,] 0.00753725
out$ve_boot
#>             [,1]
#> [1,] 0.007406224