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R/drtmle

Travis-CI Build Status AppVeyor Build Status Coverage Status CRAN CRAN downloads Project Status: Active - The project has reached a stable, usable state and is being actively developed. MIT license DOI

Nonparametric estimators of the average treatment effect with doubly-robust confidence intervals and hypothesis tests

Author: David Benkeser

Description

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).

Installation

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")

Usage

Doubly-robust inference for the average treatment effect

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 $E[E(Y \mid A = a_0, W)]$ for user-selected values of $a_0$ (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)
#> 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 0.304

This 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)

Inference for super learner-based IPTW

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 0.373

Issues

If you encounter any bugs or have any specific feature requests, please file an issue.

Citation

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}
}

License

© 2016- David C. Benkeser

The contents of this repository are distributed under the MIT license. See below for details:

The MIT License (MIT)

Copyright (c) 2016- David C. Benkeser

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.