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 1.3.1 ──
#> ✔ ggplot2 3.3.5     ✔ purrr   0.3.4
#> ✔ tibble  3.1.6     ✔ dplyr   1.0.7
#> ✔ tidyr   1.1.4     ✔ stringr 1.4.0
#> ✔ readr   2.1.1     ✔ forcats 0.5.1
#> ── 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: -0.075
#> Std. Error: 0.056
#> 95% CI: [-0.186, 0.035]

# 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: -0.078
#> Std. Error: 0.059
#> 95% CI: [-0.193, 0.037]

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.


Issues

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


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}
    }

References

Benkeser, David, and Jialu Ran. 2021. “Nonparametric Inference for Interventional Effects with Multiple Mediators.” Journal of Causal Inference. https://doi.org/10.1515/jci-2020-0018.

Chernozhukov, Victor, Denis Chetverikov, Mert Demirer, Esther Duflo, Christian Hansen, Whitney Newey, and James Robins. 2018. “Double/Debiased Machine Learning for Treatment and Structural Parameters.” The Econometrics Journal 21 (1). https://doi.org/10.1111/ectj.12097.

Coyle, Jeremy R, Nima S Hejazi, Ivana Malenica, Rachael V Phillips, and Oleg Sofrygin. 2021. sl3: Modern Machine Learning Pipelines for Super Learning (version 1.4.4). https://doi.org/10.5281/zenodo.1342293.

Dı́az, Iván, Nima S Hejazi, Kara E Rudolph, and Mark J van der Laan. 2020. “Non-Parametric Efficient Causal Mediation with Intermediate Confounders.” Biometrika 108 (3): 627–41. https://doi.org/10.1093/biomet/asaa085.

Pfanzagl, J, and W Wefelmeyer. 1985. “Contributions to a General Asymptotic Statistical Theory.” Statistics & Risk Modeling 3 (3-4): 379–88. https://doi.org/10.1007/978-1-4612-5769-1.

Rudolph, Kara E, Oleg Sofrygin, Wenjing Zheng, and Mark J van der Laan. 2017. “Robust and Flexible Estimation of Stochastic Mediation Effects: A Proposed Method and Example in a Randomized Trial Setting.” Epidemiologic Methods 7 (1). https://doi.org/10.1515/em-2017-0007.

van der Laan, Mark J, and Sherri Rose. 2011. Targeted Learning: Causal Inference for Observational and Experimental Data. Springer Science & Business Media.

VanderWeele, Tyler J, Stijn Vansteelandt, and James M Robins. 2014. “Effect Decomposition in the Presence of an Exposure-Induced Mediator-Outcome Confounder.” Epidemiology 25 (2): 300. https://doi.org/10.1097/ede.0000000000000034.

Zheng, Wenjing, and Mark J van der Laan. 2011. “Cross-Validated Targeted Minimum-Loss-Based Estimation.” In Targeted Learning: Causal Inference for Observational and Experimental Data, 459–74. Springer. https://doi.org/10.1007/978-1-4419-9782-1_27.

———. 2012. “Targeted Maximum Likelihood Estimation of Natural Direct Effects.” International Journal of Biostatistics 8 (1). https://doi.org/10.2202/1557-4679.1361.

———. 2017. “Longitudinal Mediation Analysis with Time-Varying Mediators and Exposures, with Application to Survival Outcomes.” Journal of Causal Inference 5 (2). https://doi.org/10.1515/jci-2016-0006.