Iterative IPCW Update Procedure of Augmented Efficient Influence Function

Iterative IPCW Update Procedure of Augmented Efficient Influence Function

ipcw_eif_update(
  data_internal,
  C_samp,
  V,
  ipc_mech,
  ipc_weights,
  Qn_estim,
  Hn_estim,
  estimator = c("tmle", "onestep"),
  fluctuation = NULL,
  flucmod_tol = 50,
  eif_reg_type = c("hal", "glm")
)

Arguments

data_internal

A data.table containing of the observations selected into the second-phase sample.

C_samp

A numeric indicator for missingness due to exclusion the from second-stage sample.

V

A data.table giving the values across all observations of all variables that play a role in the censoring mechanism.

ipc_mech

A numeric vector of the censoring mechanism estimates all of the observations, only for the two-phase sampling mechanism. Note well that these values do NOT account for censoring from loss to follow-up.

ipc_weights

A numeric vector of inverse probability of censoring weights, including such weights for censoring due to loss to follow-up. Without loss to follow-up, these are equivalent to C_samp / ipc_mech in an initial run of this procedure.

Qn_estim

A data.table corresponding to the outcome regression. This is produced by invoking the internal function est_Q.

Hn_estim

A data.table corresponding to values produced in the computation of the auxiliary ("clever") covariate. This is produced easily by invoking 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.

fluctuation

A character giving the type of regression to be used in traversing the fluctuation submodel. The choices are "weighted" and "standard".

flucmod_tol

A numeric indicating the largest value to be tolerated in the fluctuation model for the targeted minimum loss estimator.

eif_reg_type

Whether a flexible nonparametric function ought to be used in the dimension-reduced nuisance regression of the targeting step for the censored data case. By default, the method used is a nonparametric regression based on the Highly Adaptive Lasso (from hal9001). Set this to "glm" to instead use a simple linear regression model. In this step, the efficient influence function (EIF) is regressed against covariates contributing to the censoring mechanism (i.e., EIF ~ V | C = 1).

Value

A list containing the estimated outcome mechanism, the fitted fluctuation model for TML updates, the updated inverse probability of censoring weights (IPCW), the updated estimate of the efficient influence function, and the estimated IPCW component of the EIF.

Details

An adaptation of the IPCW-TMLE for iteratively constructing an efficient inverse probability of censoring weighted TML or one-step estimator. The efficient influence function of the parameter and updating the IPC weights in an iterative process, until a convergence criteria is satisfied.