Efficient Causal Mediation Analysis with Intermediate Confounders

Authors: Nima Hejazi, Iván Díaz, and Kara Rudolph


What’s medoutcon?

The medoutcon R package provides facilities for efficient estimation of stochastic (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. While the proposed approach is similar to those appearing in VanderWeele, Vansteelandt, and Robins (2014), Rudolph et al. (2017), and Zheng and van der Laan (2017), medoutcon is designed as a software implementation to accompany the methodology proposed in Díaz et al. (2020). 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. 2020) 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)
library(medoutcon)
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")
summary(os_de)
#>        lwr_ci     param_est        upr_ci     param_var      eif_mean 
#>       -0.1884       -0.0726        0.0433        0.0035   -4.4100e-17 
#>     estimator         param 
#>       onestep direct_effect

# 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")
summary(tmle_de)
#>        lwr_ci     param_est        upr_ci     param_var      eif_mean 
#>        -0.203       -0.0859        0.0311        0.0036    4.4084e-03 
#>     estimator         param 
#>          tmle direct_effect

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 = {},
      journal={},
      volume={},
      number={},
      pages={},
      publisher={}
    }

    @manual{hejazi2020medoutcon,
      author={Hejazi, Nima S and D{\'\i}az, Iv{\'a}n and Rudolph, Kara E},
      title = {{medoutcon}: Efficient causal mediation analysis under
        intermediate confounding},
      year  = {2020},
      url = {https://github.com/nhejazi/medoutcon},
      note = {R package version 0.1.0}
    }

References

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, and Oleg Sofrygin. 2020. “sl3: Modern Pipelines for Machine Learning and Super Learning.” https://github.com/tlverse/sl3. https://doi.org/10.5281/zenodo.1342293.

Díaz, Iván, Nima S Hejazi, Kara E Rudolph, and Mark J van der Laan.

  1. “Non-Parametric Efficient Causal Mediation with Intermediate Confounders.” https://arxiv.org/abs/1912.09936.

Pfanzagl, J, and W Wefelmeyer. 1985. “Contributions to a General Asymptotic Statistical Theory.” Statistics & Risk Modeling 3 (3-4): 379–88.

Rudolph, Kara E, Oleg Sofrygin, Wenjing Zheng, and Mark J van der Laan.

  1. “Robust and Flexible Estimation of Stochastic Mediation Effects: A Proposed Method and Example in a Randomized Trial Setting.” Epidemiologic Methods 7 (1). De Gruyter.

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 (Cambridge, Mass.) 25 (2). NIH Public Access: 300.

Zheng, Wenjing, and Mark J van der Laan. 2011. “Cross-Validated Targeted Minimum-Loss-Based Estimation.” In Targeted Learning, 459–74. Springer.

———. 2017. “Longitudinal Mediation Analysis with Time-Varying Mediators and Exposures, with Application to Survival Outcomes.” Journal of Causal Inference 5 (2). De Gruyter.