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, Carone, van der Laan & Gilbert, 2017 (accepted Biometrika; working paper). 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 E[E(Y ∣ A = a0, W)] for user-selected values of a0 (via option 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, quietly = TRUE)
#> drtmle: TMLE with doubly robust inference
#> Version: 1.0.2
library(SuperLearner, quietly = TRUE)
#> Super Learner
#> Version: 2.0-23-9000
#> Package created on 2017-07-20
# simulate simple data structure
set.seed(1234)
n <- 200
W <- data.frame(W1 = runif(n,-2,2), W2 = rbinom(n,1,0.5))
A <- rbinom(n, 1, plogis(-2 + W$W1 - 2*W$W2))
Y <- rbinom(n, 1, plogis(-2 + W$W1 - 2*W$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
)
# print the output
fit1
#> $est
#>
#> 0 0.1403428
#> 1 0.2158854
#>
#> $cov
#> 0 1
#> 0 0.0008075554 0.0002582092
#> 1 0.0002582092 0.0014881480
# get confidence intervals for marginal means
ci_fit1 <- ci(fit1)
# print the output
ci_fit1
#> $drtmle
#> est cil ciu
#> 0 0.140 0.085 0.196
#> 1 0.216 0.140 0.291
# get confidence intervals for ate
ci_ate1 <- ci(fit1,contrast = c(-1, 1))
# print the output
ci_ate1
#> $drtmle
#> est cil ciu
#> E[Y(1)]-E[Y(0)] 0.076 -0.007 0.158The 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 0.1377524
#> 1 0.1943633
#>
#> $cov
#> 0 1
#> 0 0.0007623723 0.0002181465
#> 1 0.0002181465 0.0106635990
# compute a confidence interval for margin means
ci_fit2 <- ci(fit2)
# print the output
ci_fit2
#> $iptw_tmle
#> est cil ciu
#> 0 0.138 0.084 0.192
#> 1 0.194 -0.008 0.397
# 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)] 0.057 -0.149 0.262If you encounter any bugs or have any specific feature requests, please file an issue.
After using the drtmle R package, please cite the following:
@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}
}
© 2016-2017 David C. Benkeser
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Copyright (c) 2016-2017 David C. Benkeser
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