Targeted Learning for Causal Mediation Analysis

Authors: Nima Hejazi, James Duncan, David McCoy, and Mark van der Laan

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).

Install the most recent stable release from GitHub via remotes:

remotes::install_github("tlverse/tmle3mediate")

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           1.19245

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

Contributions are very welcome. Interested contributors should consult our contribution guidelines prior to submitting a pull request.

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}
    }

• R/medshift - An R package providing tools to estimate the causal effect of stochastic treatment regimes in the mediation setting, including classical (G-computation, IPW) and doubly robust (one-step) estimators. This is an implementation of the methodology explored by Dı́az and Hejazi (2020).

• R/medoutcon - An R package providing doubly robust estimators (one-step, TMLE) of the interventional (in)direct effects, which are defined by joint static and stochastic interventions applied to the exposure and mediators, respectively. These effect definitions are similar to but more general than the natural (in)direct effects. This is an implementation of the methodology explored by Dı́az et al. (2020).

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.

The contents of this repository are distributed under the GPL-3 license. See file LICENSE for details.