moi_missing: Mean Imputation Among Missing Outcomes

Description

Estimates the mean of a given parametric imputation model among observations with a missing outcome and a given treatment. Specifically, it provides estimates of \(E[U(X,A,Z;\theta)|A=a, \Delta=0]\), for an imputation model \(U\), where \(X\) denotes baseline covariates, \(A\) denotes the treatment, \(Z\) denotes post randomization covariates, and \(\Delta\) denotes a non-missing indicator. Influence function based standard errors are also provided.

Usage

moi_missing(
  data,
  id,
  delta,
  treatment.model,
  imputation.model,
  imputation.subset = NULL,
  imputation.augmentation = FALSE,
  missing.model = NULL,
  imputation.augmentation.model = NULL,
  extended.output = FALSE
)

Value

A list with components:

estimate: A lava::estimate object with coefficients \(E[U|A=1,\Delta=0]\) and \(E[U|A=0,\Delta=0]\) and the associated influence functions.
imputation.model: The fitted imputation model.
imputation.subset: The imputation.subset expression.
levels: Treatment levels (character).
IC3: (only if extended.output = TRUE and imputation.augmentation = TRUE) Named list (one entry per treatment level) giving the per-level augmentation contribution to the influence function.
IC_epsilon: (only if extended.output = TRUE) Influence function for the imputation-model parameters.

Arguments

id: A vector with subject IDs
treatment.model: A learner object for the binary treatment, used to extract the treatment variable and its levels.
imputation.model: A learner object of class 'learner_glm' used to fit the imputation model. The learner must specify the outcome variable and model formula. If the learner was constructed with user-supplied weights, those weights are multiplied by the imputation.subset indicator (excluded rows receive zero weight).
missing.model: learner object specifying the model for the probability of the outcome being observed/non-missing
imputation.augmentation.model: learner object specifying the model for the imputation augmentation
extended.output: Logical. If TRUE, the returned list also includes the augmentation component IC3 of the influence function (only when imputation.augmentation = TRUE) and the imputation-model influence function IC_epsilon. Default is FALSE.