Targeted Learning for Causal Mediation Analysis
Authors: Nima Hejazi, James Duncan, David McCoy, and Mark van der Laan
What’s tmle3mediate?
tmle3mediate is an adapter/extension R package in the tlverse ecosystem that provides support for causal mediation analysis, for a range of target parameters applicable in settings with mediating variables. Causal effects for which estimation machinery is provided include the popular natural (in)direct effects (Robins and Greenland 1992; Zheng and van der Laan 2012; VanderWeele 2015), and the less restrictive population intervention (in)direct effects (Dı́az and Hejazi 2020). By building on the core tlverse grammar exposed by the tmle3 R package, tmle3mediate accommodates targeted maximum likelihood (or targeted minimum loss-based) estimation of these causal effect parameters through a unified interface. For a general discussion of the framework of targeted minimum loss-based estimation and its relationship to statistical causal inference, the motivated reader may consider consulting van der Laan and Rose (2011) and van der Laan and Rose (2018). A practical and accessible introduction using the tlverse software ecosystem is provided in van der Laan et al. (2021) (see https://tlverse.org/tlverse-handbook).
Installation
Install the most recent stable release from GitHub via remotes:
remotes::install_github("tlverse/tmle3mediate")Example
To illustrate how tmle3mediate may be used to estimate the effect of applying a stochastic intervention to the treatment (A) while keeping the mediator(s) (Z) fixed, consider the following example:
library(data.table)
library(origami)
library(sl3)
library(tmle3)
library(tmle3mediate)
# produces a simple data set based on ca causal model with mediation
make_mediation_data <- function(n_obs = 1000) {
# baseline covariate -- simple, binary
W <- rbinom(n_obs, 1, prob = 0.50)
# create treatment based on baseline W
A <- as.numeric(rbinom(n_obs, 1, prob = W / 4 + 0.1))
# single mediator to affect the outcome
z1_prob <- 1 - plogis((A^2 + W) / (A + W^3 + 0.5))
Z <- rbinom(n_obs, 1, prob = z1_prob)
# create outcome as a linear function of A, W + white noise
Y <- Z + A - 0.1 * W + rnorm(n_obs, mean = 0, sd = 0.25)
# full data structure
data <- as.data.table(cbind(Y, Z, A, W))
setnames(data, c("Y", "Z", "A", "W"))
return(data)
}
# set seed and simulate example data
set.seed(75681)
example_data <- make_mediation_data(100)
node_list <- list(W = "W", A = "A", Z = "Z", Y = "Y")
# consider an incremental propensity score intervention that triples (i.e.,
# delta = 3) the individual-specific odds of receiving treatment
delta_ipsi <- 3
# make learners for nuisance parameters
g_learners <- e_learners <- m_learners <- phi_learners <-
Lrnr_cv$new(Lrnr_glm$new(), full_fit = TRUE)
learner_list <- list(Y = m_learners, A = g_learners)
# compute one-step estimate for an incremental propensity score intervention
tmle_spec <- tmle_medshift(delta = delta_ipsi,
e_learners = e_learners,
phi_learners = phi_learners,
max_iter = 5)
tmle_out <- tmle3(tmle_spec, example_data, node_list, learner_list)
tmle_out
#> A tmle3_Fit that took 5 step(s)
#> type param init_est tmle_est se lower upper
#> 1: PIDE E[Y_{A=NULL}] 0.7938906 0.7927072 0.203954 0.3929648 1.19245
#> psi_transformed lower_transformed upper_transformed
#> 1: 0.7927072 0.3929648 1.19245Contributions
Contributions are very welcome. Interested contributors should consult our contribution guidelines prior to submitting a pull request.
Citation
After using the tmle3mediate R package, please cite the following:
@software{hejazi2021tmle3mediate-rpkg,
author = {Hejazi, Nima S and Duncan, James and McCoy, David and
{van der Laan}, Mark J},
title = {{tmle3mediate}: Targeted Learning for Causal Mediation
Analysis},
year = {2021},
doi = {},
url = {https://github.com/tlverse/tmle3mediate},
note = {R package version 0.0.3}
}Funding
The development of this software was supported in part through UC Berkeley’s Biomedical Big Data training program, made possible by grant T32 LM012417 from the National Institutes of Health.
License
The contents of this repository are distributed under the GPL-3 license. See file LICENSE for details.
References
Dı́az, Iván, and Nima S Hejazi. 2020. “Causal Mediation Analysis for Stochastic Interventions.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 82 (3): 661–83. https://doi.org/10.1111/rssb.12362.
Dı́az, Iván, Nima S Hejazi, Kara E Rudolph, and Mark J van der Laan.
- “Non-Parametric Efficient Causal Mediation with Intermediate Confounders.” Biometrika. https://doi.org/10.1093/biomet/asaa085.
Robins, James M, and Sander Greenland. 1992. “Identifiability and Exchangeability for Direct and Indirect Effects.” Epidemiology, 143–55.
van der Laan, Mark J, Jeremy R Coyle, Nima S Hejazi, Ivana Malenica, Rachael V Phillips, and Alan E Hubbard. 2021. Targeted Learning in R: Causal Data Science with the tlverse Software Ecosystem. CRC Press. https://tlverse.org/tlverse-handbook.
van der Laan, Mark J, and Sherri Rose. 2011. Targeted Learning: Causal Inference for Observational and Experimental Data. Springer Science & Business Media.
———. 2018. Targeted Learning in Data Science: Causal Inference for Complex Longitudinal Studies. Springer Science & Business Media.
VanderWeele, Tyler. 2015. Explanation in Causal Inference: Methods for Mediation and Interaction. Oxford University Press.
Zheng, Wenjing, and Mark J van der Laan. 2012. “Targeted Maximum Likelihood Estimation of Natural Direct Effects.” International Journal of Biostatistics 8 (1). https://doi.org/10.2202/1557-4679.1361.
