Efficient Causal Mediation Analysis for the Natural and Interventional Effects
Authors: Nima Hejazi, Iván Díaz, and Kara Rudolph
What’s medoutcon?
The medoutcon R package provides facilities for efficient estimation of path-specific (in)direct effects that measure the impact of a treatment variable A on an outcome variable Y, through a direct path (through A only) and an indirect path (through a set of mediators M only). In the presence of an intermediate mediator-outcome confounder Z, itself affected by the treatment A, these correspond to the interventional (in)direct effects described by Dı́az et al. (2020), though similar (yet less general) effect definitions and/or estimation strategies have appeared in VanderWeele, Vansteelandt, and Robins (2014), Rudolph et al. (2017), Zheng and van der Laan (2017), and Benkeser and Ran (2021). When no intermediate confounders are present, these effect definitions simplify to the well-studied natural (in)direct effects, and our estimators are analogs of those formulated by Zheng and van der Laan (2012). Both an efficient one-step bias-corrected estimator with cross-fitting (Pfanzagl and Wefelmeyer 1985; Zheng and van der Laan 2011; Chernozhukov et al. 2018) and a cross-validated targeted minimum loss estimator (TMLE) (van der Laan and Rose 2011; Zheng and van der Laan 2011) are made available. medoutcon integrates with the sl3 R package (Coyle et al. 2021) to leverage statistical machine learning in the estimation procedure.
Installation
Install the most recent stable release from GitHub via remotes:
remotes::install_github("nhejazi/medoutcon")Example
To illustrate how medoutcon may be used to estimate stochastic interventional (in)direct effects of the exposure (A) on the outcome (Y) in the presence of mediator(s) (M) and a mediator-outcome confounder (Z), consider the following example:
library(data.table)
library(tidyverse)
#> ── Attaching packages ─────────────────────────────────────────────────────── tidyverse 1.3.2 ──
#> ✔ ggplot2 3.3.6 ✔ purrr 0.3.4
#> ✔ tibble 3.1.8 ✔ dplyr 1.0.10
#> ✔ tidyr 1.2.1 ✔ stringr 1.4.1
#> ✔ readr 2.1.2 ✔ forcats 0.5.2
#> ── Conflicts ────────────────────────────────────────────────────────── tidyverse_conflicts() ──
#> ✖ dplyr::between() masks data.table::between()
#> ✖ dplyr::filter() masks stats::filter()
#> ✖ dplyr::first() masks data.table::first()
#> ✖ dplyr::lag() masks stats::lag()
#> ✖ dplyr::last() masks data.table::last()
#> ✖ purrr::transpose() masks data.table::transpose()
library(medoutcon)
#> medoutcon v0.1.6: Efficient Natural and Interventional Causal Mediation Analysis
set.seed(1584)
# produces a simple data set based on ca causal model with mediation
make_example_data <- function(n_obs = 1000) {
## baseline covariates
w_1 <- rbinom(n_obs, 1, prob = 0.6)
w_2 <- rbinom(n_obs, 1, prob = 0.3)
w_3 <- rbinom(n_obs, 1, prob = pmin(0.2 + (w_1 + w_2) / 3, 1))
w <- cbind(w_1, w_2, w_3)
w_names <- paste("W", seq_len(ncol(w)), sep = "_")
## exposure
a <- as.numeric(rbinom(n_obs, 1, plogis(rowSums(w) - 2)))
## mediator-outcome confounder affected by treatment
z <- rbinom(n_obs, 1, plogis(rowMeans(-log(2) + w - a) + 0.2))
## mediator -- could be multivariate
m <- rbinom(n_obs, 1, plogis(rowSums(log(3) * w[, -3] + a - z)))
m_names <- "M"
## outcome
y <- rbinom(n_obs, 1, plogis(1 / (rowSums(w) - z + a + m)))
## construct output
dat <- as.data.table(cbind(w = w, a = a, z = z, m = m, y = y))
setnames(dat, c(w_names, "A", "Z", m_names, "Y"))
return(dat)
}
# set seed and simulate example data
example_data <- make_example_data()
w_names <- str_subset(colnames(example_data), "W")
m_names <- str_subset(colnames(example_data), "M")
# quick look at the data
head(example_data)
#> W_1 W_2 W_3 A Z M Y
#> 1: 1 0 1 0 0 0 1
#> 2: 0 1 0 0 0 1 0
#> 3: 1 1 1 1 0 1 1
#> 4: 0 1 1 0 0 1 0
#> 5: 0 0 0 0 0 1 1
#> 6: 1 0 1 1 0 1 0
# compute one-step estimate of the interventional direct effect
os_de <- medoutcon(W = example_data[, ..w_names],
A = example_data$A,
Z = example_data$Z,
M = example_data[, ..m_names],
Y = example_data$Y,
effect = "direct",
estimator = "onestep")
os_de
#> Interventional Direct Effect
#> Estimator: onestep
#> Estimate: -0.065
#> Std. Error: 0.054
#> 95% CI: [-0.17, 0.041]
# compute targeted minimum loss estimate of the interventional direct effect
tmle_de <- medoutcon(W = example_data[, ..w_names],
A = example_data$A,
Z = example_data$Z,
M = example_data[, ..m_names],
Y = example_data$Y,
effect = "direct",
estimator = "tmle")
tmle_de
#> Interventional Direct Effect
#> Estimator: tmle
#> Estimate: -0.06
#> Std. Error: 0.058
#> 95% CI: [-0.173, 0.053]For details on how to use data adaptive regression (machine learning) techniques in the estimation of nuisance parameters, consider consulting the vignette that accompanies the package.
Contributions
Contributions are very welcome. Interested contributors should consult our contribution guidelines prior to submitting a pull request.
Citation
After using the medoutcon R package, please cite the following:
@article{diaz2020nonparametric,
title={Non-parametric efficient causal mediation with intermediate
confounders},
author={D{\'\i}az, Iv{\'a}n and Hejazi, Nima S and Rudolph, Kara E
and {van der Laan}, Mark J},
year={2020},
url = {https://arxiv.org/abs/1912.09936},
doi = {10.1093/biomet/asaa085},
journal={Biometrika},
volume = {108},
number = {3},
pages = {627--641},
publisher={Oxford University Press}
}
@article{hejazi2022medoutcon-joss,
author = {Hejazi, Nima S and Rudolph, Kara E and D{\'\i}az,
Iv{\'a}n},
title = {{medoutcon}: Nonparametric efficient causal mediation
analysis with machine learning in {R}},
year = {2022},
doi = {10.21105/joss.03979},
url = {https://doi.org/10.21105/joss.03979},
journal = {Journal of Open Source Software},
publisher = {The Open Journal}
}
@software{hejazi2022medoutcon-rpkg,
author={Hejazi, Nima S and D{\'\i}az, Iv{\'a}n and Rudolph, Kara E},
title = {{medoutcon}: Efficient natural and interventional causal
mediation analysis},
year = {2022},
doi = {10.5281/zenodo.5809519},
url = {https://github.com/nhejazi/medoutcon},
note = {R package version 0.1.6}
}License
© 2020-2022 Nima S. Hejazi
The contents of this repository are distributed under the MIT license. See below for details:
MIT License
Copyright (c) 2020-2022 Nima S. Hejazi
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.References
sl3: Modern Machine Learning Pipelines for Super Learning (version 1.4.4). https://doi.org/10.5281/zenodo.1342293.
