ui.causal: Uncertainty intervals for Average Causal Effects
In ui: Uncertainty Intervals and Sensitivity Analysis for Missing Data

Description Usage Arguments Details Value Author(s) References Examples

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.

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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)

`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 `plot.uicausal`.
`rho.plotrange`	an interval larger than `rho` for the plot using `plot.uicausal`.
`alpha`	Default 0.05 corresponding to a confidence level of 95 for CI and UI.

In order to visualize the results, you can use plot.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

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 interval, 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 interval, standard error etc.

Minna Genbäck

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

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
plot(ui)
profile(ui)
mean(y1-y0)

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