AIPTW and TMLE estimates of interventional mediation effects

This function computes multiply robust estimates of interventional mediation effects with two mediators. Two such estimates are produced, an augmented inverse probability of treatment weighted (AIPTW) estimator and a targeted minimum loss estimator (TMLE). The AIPTW was found to perform better in most simulations.

intermed(
  Y,
  C,
  M1,
  M2,
  A,
  DeltaA = as.numeric(!is.na(A)),
  DeltaM = as.numeric(!is.na(M1)),
  a = 1,
  a_star = 0,
  SL_Qbar = NULL,
  SL_g = NULL,
  SL_Q_M = NULL,
  n_SL = 1,
  glm_Qbar = NULL,
  glm_g = NULL,
  glm_Q_M = NULL,
  tolg = 0.01,
  tol = 1/(sqrt(length(Y)) * log(length(Y))),
  targeted_se = FALSE,
  return_models = FALSE,
  cvFolds = 1,
  use_future = FALSE,
  Qbar_n = NULL,
  Q_M_n = NULL,
  gn = NULL,
  max_iter = 50,
  verbose = FALSE,
  stratify = FALSE,
  ...
)

Arguments

Y	A vector of continuous or binary outcomes.
C	A `data.frame` of named covariates.
M1	A `vector` of mediators.
M2	A `vector` of mediators.
A	A vector of binary treatment assignment (assumed to be equal to 0 or 1).
DeltaA	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed).
DeltaM	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed).
a	The label for the treatment. The effects estimates returned pertain to estimation of interventional effects of `a` versus `a_star`.
a_star	The label for the treatment. The effects estimates returned pertain to estimation of interventional effects of `a` versus `a_star`.
SL_Qbar	A vector of characters or a list describing the Super Learner library to be used for the outcome regression.
SL_g	A vector of characters or a list describing the Super Learner library to be used for the propensity score.
SL_Q_M	A list with two named entries `M1` and `M2`, specifying super learner libraries for estimation of the pooled hazard regression that is mapped into an estimate of the mediator distributions.
n_SL	The number of repeated super learner runs to execute for each regression.
glm_Qbar	A character describing a formula to be used in the call to `glm` for the outcome regression. The formula may include `colnames(C)`, `"A"` (if `stratify = FALSE`), `"M1"`, and `"M2"` as terms in the formula.
glm_g	A character describing a formula to be used in the call to `glm` for the outcome regression. The formula may include `colnames(C)`, in the formula.
glm_Q_M	A list with two named entries `M1` and `M2`, specifying the regression formula for estimation of the pooled hazard regression that is mapped into an estimate of the mediator distributions. The formula for `M1` can include `"A"` (if `stratify = FALSE`) and `colnames(C)`, while the formula for `M2` can additionally include `M1`.
tolg	The truncation level for the propensity score
tol	The tolerance for stopping the iterative targeting procedure.
targeted_se	A boolean indicating whether to return the standard error estimates based on targeted nuisance parameters or the initial estimates of nuisance parameters.
return_models	A boolean indicating whether to return the fitted models for each of the nuisance regressions. If `TRUE` then the output will include a list with named entries `g` (propensity score fit), `Qbar` (outcome regression fit), and `Q_M` (mediator distribution fits).
cvFolds	Number of cross-validation folds to use if CVTMLE and CV-one step are desired
use_future	A boolean indicating whether to use the `future` package to parallelize computations
Qbar_n	Power users may wish to pass in their own properly formatted list of the outcome regression so that nuisance parameters can be fitted outside of `intermed`.
Q_M_n	Power users may wish to pass in their own properly formatted list of the mediator distributions so that nuisance parameters can be fitted outside of `intermed`.
gn	Power users may wish to pass in their own properly formatted list of the propensity score so that nuisance parameters can be fitted outside of `intermed`.
max_iter	The maximum number of iterations for the TMLE
verbose	A boolean indicating whether to print status updates.
all_mediator_values	All combinations of M1 and M2

Value

An object of class "intermed".

aiptw: A list of point estimates and estimated covariance matrix from the one-step estimator
tmle: A list of point estimates and estimated covariance matrix from the TMLE
plugin: Plugin estimates of the mediation effects
fm: Fitted models if return_models = TRUE, NULL otherwise

Details

Under the hood, the function fits several nuisance regressions and combines them into the final estimate. Users have several options for fitting these regressions as described below. In particular, SuperLearner can be used to flexibly estimate the regressions.