Compute the Shift Parameter Estimate and the Efficient Influence Function

Usage

eif(
  Y,
  Qn,
  Hn,
  estimator = c("tmle", "onestep"),
  fluc_mod_out = NULL,
  C_samp = rep(1, length(Y)),
  ipc_weights = rep(1, length(Y))
)

Arguments

Y: A numeric vector of the observed outcomes.
Qn: An object providing the value of the outcome evaluated after imposing a shift in the treatment. This object is passed in after being constructed by a call to the internal function est_Q.
Hn: An object providing values of the auxiliary ("clever") covariate, constructed from the treatment mechanism and required for targeted minimum loss-based estimation. This object object should be passed in after being constructed by a call to the internal function est_Hn.
estimator: The type of estimator to be fit, either "tmle" for targeted maximum likelihood estimation or "onestep" for a one-step estimator.
fluc_mod_out: An object giving values of the logistic tilting model for targeted minimum loss estimation. This type of object should be the output of the internal routines to perform this step of the TML estimation procedure, as given by fit_fluctuation.
C_samp: Indicator for missingness due to exclusion from second-phase sample. Used for compatibility with the IPCW-TML estimation routine.
ipc_weights: A numeric vector that gives inverse probability of censoring weights for each observation. These are generated by invoking the routines for estimating the censoring mechanism.

Value

A list containing the parameter estimate, estimated variance based on the efficient influence function (EIF), the estimate of the EIF incorporating inverse probability of censoring weights, and the estimate of the EIF without the application of such weights.

Details

Estimate the value of the causal parameter alongside statistical inference for the parameter estimate based on the efficient influence function of the target parameter, which takes the following form: