An R6Class of AIPW for estimating the average causal effects with users' inputs of exposure, outcome, covariates and related libraries for estimating the efficient influence function.


AIPW object


An AIPW object is constructed by new() with users' inputs of data and causal structures, then it fit() the data using the libraries in Q.SL.library and g.SL.library with k_split cross-fitting, and provides results via the summary() method. After using fit() and/or summary() methods, propensity scores and inverse probability weights by exposure status can be examined with plot.p_score() and plot.ip_weights(), respectively.

If outcome is missing, analysis assumes missing at random (MAR) by estimating propensity scores of I(A=a, observed=1) with all covariates W. (W.Q and W.g are disabled.) Missing exposure is not supported.

See examples for illustration.


AIPW$new(Y = NULL, A = NULL, W = NULL, W.Q = NULL, W.g = NULL, Q.SL.library = NULL, g.SL.library = NULL, k_split = 10, verbose = TRUE, = FALSE)

Constructor Arguments

YIntegerA vector of outcome (binary (0, 1) or continuous)
AIntegerA vector of binary exposure (0 or 1)
WDataCovariates for both exposure and outcome models.
W.QDataCovariates for the outcome model (Q).
W.gDataCovariates for the exposure model (g).
Q.SL.librarySL.libraryAlgorithms used for the outcome model (Q).
g.SL.librarySL.libraryAlgorithms used for the exposure model (g).
k_splitIntegerNumber of folds for splitting (Default = 10).
verboseLogicalWhether to print the result (Default = TRUE) to save and (Default = FALSE)

Constructor Argument Details

W, W.Q & W.g

It can be a vector, matrix or data.frame. If and only if W == NULL, W would be replaced by W.Q and W.g.

Q.SL.library & g.SL.library

Machine learning algorithms from SuperLearner libraries or sl3 learner object (Lrnr_base)


It ranges from 1 to number of observation-1. If k_split=1, no cross-fitting; if k_split>=2, cross-fitting is used (e.g., k_split=10, use 9/10 of the data to estimate and the remaining 1/10 leftover to predict). NOTE: it's recommended to use cross-fitting.

This option allows users to save the fitted sl object (libs$ & libs$ for debug use. Warning: Saving the SuperLearner fitted object may cause a substantive storage/memory use.

Public Methods

fit()Fit the data to the AIPW objectfit.AIPW
stratified_fit()Fit the data to the AIPW object stratified by Astratified_fit.AIPW
summary()Summary of the average treatment effects from AIPWsummary.AIPW_base
plot.p_score()Plot the propensity scores by exposure statusplot.p_score
plot.ip_weights()Plot the inverse probability weights using truncated propensity scoresplot.ip_weights

Public Variables

VariableGenerated byReturn
nConstructorNumber of observations
stratified_fittedstratified_fit()Fit the outcome model stratified by exposure status
obs_estfit() & summary()Components calculating average causal effects
estimatessummary()A list of Risk difference, risk ratio, odds ratio
resultsummary()A matrix contains RD, ATT, ATC, RR and OR with their SE and 95%CI
g.plotplot.p_score()A density plot of propensity scores by exposure status
ip_weights.plotplot.ip_weights()A box plot of inverse probability weights
libsfit()SuperLearner or sl3 libraries and their fitted objects
sl.fitConstructorA wrapper function for fitting SuperLearner or sl3
sl.predictConstructorA wrapper function using to predict

Public Variable Details


An indicator for whether the outcome model is fitted stratified by exposure status in the fit() method. Only when using stratified_fit() to turn on stratified_fit = TRUE, summary outputs average treatment effects among the treated and the controls.


After using fit() and summary() methods, this list contains the propensity scores (p_score), counterfactual predictions (mu, mu1 & mu0) and efficient influence functions (aipw_eif1 & aipw_eif0) for later average treatment effect calculations.


This plot is generated by ggplot2::geom_density


This plot uses truncated propensity scores stratified by exposure status (ggplot2::geom_boxplot)


Zhong Y, Kennedy EH, Bodnar LM, Naimi AI (2021). AIPW: An R Package for Augmented Inverse Probability Weighted Estimation of Average Causal Effects. American Journal of Epidemiology.

Robins JM, Rotnitzky A (1995). Semiparametric efficiency in multivariate regression models with missing data. Journal of the American Statistical Association.

Chernozhukov V, Chetverikov V, Demirer M, et al (2018). Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal.

Kennedy EH, Sjolander A, Small DS (2015). Semiparametric causal inference in matched cohort studies. Biometrika.


#> Loading required package: nnls
#> Loading required package: gam
#> Loading required package: splines
#> Loading required package: foreach
#> Loaded gam 1.22-2
#> Super Learner
#> Version: 2.0-28.1
#> Package created on 2021-05-04

#create an object
aipw_sl <- AIPW$new(Y=rbinom(100,1,0.5), A=rbinom(100,1,0.5),
                    W.Q=rbinom(100,1,0.5), W.g=rbinom(100,1,0.5),

#fit the object
# or use `aipw_sl$stratified_fit()` to estimate ATE and ATT/ATC

#calculate the results
aipw_sl$summary(g.bound = 0.025)

#check the propensity scores by exposure status after truncation