Nonparametric estimators of the average treatment effect with doubly-robust confidence intervals and hypothesis tests
Author: David Benkeser
drtmle is an R package that computes marginal means of an outcome
under fixed levels of a treatment. The package computes targeted minimum
loss-based (TMLE) estimators that are doubly robust, not only with
respect to consistency, but also with respect to asymptotic normality,
as discussed in Benkeser, et al.
(2017).
This property facilitates construction of doubly-robust confidence
intervals and hypothesis tests.
The package additionally includes methods for computing valid confidence intervals for an inverse probability of treatment weighted (IPTW) estimator of the average treatment effect when the propensity score is estimated via super learning, as discussed in van der Laan (2014).
Install the current stable release from CRAN via
install.packages("drtmle")A developmental release may be installed from GitHub via
devtools with:
devtools::install_github("benkeser/drtmle")Suppose the data consist of a vector of baseline covariates (W), a
multi-level treatment assignment (A), and a continuous or
binary-valued outcome (Y). The function drtmle may be used to
estimate a_0). The resulting targeted minimum loss-based estimates
are doubly robust with respect to both consistency and asymptotic
normality. The function computes doubly robust covariance estimates that
can be used to construct doubly robust confidence intervals for marginal
means and contrasts between means. A simple example on simulated data is
shown below. We refer users to the
vignette
for more information and further examples.
# load packages
library(drtmle)
#> drtmle: TMLE with doubly robust inference
#> Version: 1.1.1
library(SuperLearner)
#> Loading required package: nnls
#> Loading required package: gam
#> Loading required package: splines
#> Loading required package: foreach
#> Loaded gam 1.20.1
#> Super Learner
#> Version: 2.0-28
#> Package created on 2021-05-04
# simulate simple data structure
set.seed(12345)
n <- 200
W <- data.frame(W1 = runif(n,-2,2), W2 = rbinom(n,1,0.5))
A <- rbinom(n, 1, plogis(-2 + W$W1 - 2*W$W1*W$W2))
Y <- rbinom(n, 1, plogis(-2 + W$W1 - 2*W$W1*W$W2 + A))
# estimate the covariate-adjusted marginal mean for A = 1 and A = 0
# here, we do not properly estimate the propensity score
fit1 <- drtmle(W = W, A = A, Y = Y, # input data
a_0 = c(0, 1), # return estimates for A = 0 and A = 1
SL_Q = "SL.npreg", # use kernel regression for E(Y | A = a, W)
glm_g = "W1 + W2", # use misspecified main terms glm for E(A | W)
SL_Qr = "SL.npreg", # use kernel regression to guard against
# misspecification of outcome regression
SL_gr = "SL.npreg", # use kernel regression to guard against
# misspecification of propensity score
returnModels = TRUE # for visualizing fits later
)
# print the output
fit1
#> $est
#>
#> 0 0.1752271
#> 1 0.2866095
#>
#> $cov
#> 0 1
#> 0 9.039683e-04 4.591974e-05
#> 1 4.591974e-05 8.823850e-03
# get confidence intervals for marginal means
# truth is E[Y(1)] = 0.29, E[Y(0)] = 0.15
ci_fit1 <- ci(fit1)
# print the output
ci_fit1
#> $drtmle
#> est cil ciu
#> 0 0.175 0.116 0.234
#> 1 0.287 0.102 0.471
# get confidence intervals for ate
# truth is E[Y(1)] - E[Y(0)] = 0.14
ci_ate1 <- ci(fit1, contrast = c(-1, 1))
# print the output
ci_ate1
#> $drtmle
#> est cil ciu
#> E[Y(1)]-E[Y(0)] 0.111 -0.081 0.304This method requires estimation of additional univariate regressions to
ensure doubly robust confidence intervals and hypothesis tests. The
method for estimation are input via SL.Qr and SL.gr or glm.Qr and
glm.gr if parametric models are desired). These additional fits can be
visualized by the plot method for drtmle.
layout(t(1:3))
plot(fit1, ask = FALSE)The package additionally includes a function for computing valid confidence intervals about an inverse probability of treatment weight (IPTW) estimator when super learning is used to estimate the propensity score.
# fit iptw
fit2 <- adaptive_iptw(Y = Y, A = A, W = W, a_0 = c(0, 1),
SL_g = c("SL.glm", "SL.mean", "SL.step.interaction"),
SL_Qr = "SL.npreg")
#> Loading required package: nloptr
# print the output
fit2
#> $est
#>
#> 0 0.1734251
#> 1 0.2438025
#>
#> $cov
#> 0 1
#> 0 8.607877e-04 8.982892e-05
#> 1 8.982892e-05 2.308177e-02
# compute a confidence interval for margin means
ci_fit2 <- ci(fit2)
# print the output
ci_fit2
#> $iptw_tmle
#> est cil ciu
#> 0 0.173 0.116 0.231
#> 1 0.244 -0.054 0.542
# compute a confidence interval for the ate
ci_ate2 <- ci(fit2, contrast = c(-1, 1))
# print the output
ci_ate2
#> $iptw_tmle
#> est cil ciu
#> E[Y(1)]-E[Y(0)] 0.07 -0.232 0.373If you encounter any bugs or have any specific feature requests, please file an issue.
After using the drtmle R package, please cite the following:
@Manual{drtmlepackage,
title = {drtmle: Doubly-Robust Nonparametric Estimation and Inference},
author = {David Benkeser},
note = {R package version 1.0.0},
doi = {10.5281/zenodo.844836}
}
@article{benkeser2017improved,
year = {2017},
author = {Benkeser, David C and Carone, Marco and van der Laan, Mark J
and Gilbert, Peter B},
title = {Doubly-robust nonparametric inference on the average
treatment effect},
journal = {Biometrika},
volume = {104}, number = {4},
pages = {863–880},
doi = {10.1093/biomet/asx053}
}
© 2016- David C. Benkeser
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Copyright (c) 2016- David C. Benkeser
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