ui_causal: Uncertainty intervals for Average Causal Effects

In ui: Uncertainty Intervals and Sensitivity Analysis for Missing Data

Uncertainty intervals for Average Causal Effects

Description

This function allows you to derive uncertainty intervals for the average causal effect (ACE) or the average causal effect on the treated (ACT). The function uses a regression imputation estimator and a doubly robust estimator. The uncertainty intervals can be used as a sensitivity analysis to unconfoundedness. Note that rho=0 render the same results as assuming no unobserved confounding.

Usage

ui_causal(
  out_formula,
  treat_formula,
  data,
  rho = c(-0.3, 0.3),
  rho0 = NULL,
  rho1 = NULL,
  ACT = FALSE,
  sand = TRUE,
  gridn = 21,
  plot = TRUE,
  rho_plotrange = c(-0.5, 0.5),
  alpha = 0.05
)

Arguments

out_formula	Formula for the outcome regression models
treat_formula	Formula for the propensity score model (regression model for treatment assignment).
data	data.frame containing the variables in the formula.
rho	Pre-specified interval for rho0 and rho1.
rho0	Pre-specified value of rho0, if an interval it has to be the same as rho1.
rho1	Pre-specified value of rho1, if an interval it has to be the same as rho0.
ACT	If TRUE Average Causal effect of the Treated is calculated, if FALSE Average Causal effect is calculated. Default is FALSE.
sand	Specifies which estimator of the standard errors should be used for OR, see details.
gridn	Number of fixed points within the rho interval for which sigma0 and sigma1 should be estimated.
plot	If TRUE the function runs slightly slower but you will be able to plot your results using profile.uicausal.
rho_plotrange	an interval larger than rho for the plot using profile.uicausal.
alpha	Default 0.05 corresponding to a confidence level of 0.95 for CI and UI.

Details

In order to visualize the results, you can use profile.uicausal. Details about estimators can be found in Genbäck and de Luna (2018)

The standard errors are calculated with the following estimators:

DR ACE - simplified sandwich estimator

DR ACT - sandwich estimator

OR ACE - if sand=TRUE sandwich estimator (default and recommended), if sand=FALSE large sample variance

OR ACT - if sand=TRUE sandwich estimator (default and recommended), if sand=FALSE large sample variance

Value

A list containing:

call	The matched call
rho0	The rage of rho0 from which the ui is calculated
rho1	If ACT==FALSE,range of rho1 from which the ui is calculated
out_model0	Outcome regression model for non-treated.
out_model1	Outcome regression model for treated.
treat_model	Regression model for treatment mechanism (propensity score).
sigma0	Consistent estimate of sigma0 for different values of rho0
sigma1	Consistent estimate of sigma1 for different values of rho1
dr	DR inference, confidence intervals for different pre-specified values of rho for the OR estimator, uncertainty interval, coefficient estimates, confounding bias, indentification bounds, standard error etc.
or	OR inference, confidence intervals for different pre-specified values of rho for the OR estimator, uncertainty interval, coefficient estimates, confounding bias, indentification bounds, standard error etc.

Author(s)

Minna Genbäck

References

Genbäck, M., de Luna, X. (2018). Causal Inference Accounting for Unobserved Confounding after Outcome Regression and Doubly Robust Estimation. Biometrics. DOI: 10.1111/biom.13001

Examples

library(MASS)
n<-500
delta<-c(-0.3,0.65)
rho<-0.3
X<-cbind(rep(1,n),rnorm(n))
x<-X[,-1]
s0<-2
s1<-3
error<-mvrnorm(n, c(0,0,0), matrix(c(1,0.6,0.9,0.6,4,0.54,0.9,0.54,9), ncol=3))
zstar<-X%*%delta+error[,1]
z<- zstar>0
y1<-ifelse(x< (-1),0.2*x-0.1*x^2, ifelse(x< 1,0.3*x, ifelse(x<3,0.4-0.1*x^2,-0.2-0.1*x)))+error[,3]
y0<-ifelse(x<1.5, x-0.4*x^2, ifelse(x<2, -0.15-0.25*x+0.5*x^2, 1.85-0.25*x))+error[,2]
y<-y0
y[z==1]<-y1[z==1]
data<-data.frame(y,z,x)


ui<-ui_causal(y~x, z~x, data=data, rho=c(0,0.3), ACT=FALSE)
ui
profile(ui)
mean(y1-y0)

ui<-ui_causal(y~x, z~x, data=data, rho=c(0,0.3), ACT=TRUE)
ui
profile(ui)
profile(ui,profile="ui")
mean(y1[z==1]-y0[z==1])

ui documentation built on June 25, 2026, 5:09 p.m.