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Augmented IPW (AIPW) estimator for regression parameters

estimate_beta_aipw.Rd

Fits a regression model for Y using an augmented inverse probability weighting (AIPW) estimator in the setting of an outcome-dependent right-censored covariate. The outcome model is specified by model, typically of the form y ~ AW + Z1 + ... + Zp, where AW = A - X.

Usage

estimate_beta_aipw(
  data_yXZ,
  model,
  model_weights,
  model_xz,
  aw_var = "AW",
  lbound = 0,
  ubound = 50
)

Arguments

data_yXZ

A data frame containing at least:

  • y: outcome,

  • A: auxiliary covariate used to form AW = A - X,

  • W: observed covariate W = min(X, C),

  • D: indicator I(X <= C),

  • columns for the covariates in model,

  • columns for the covariates in model_weights and model_xz.

model

A formula specifying the outcome regression model, e.g. y ~ AW + Z or y ~ AW + Z1 + Z2.

model_weights

A formula specifying the censoring model for C | (Y, Z, ...). Typically a right-hand-side only formula, such as ~ y + Z, which is internally expanded to Surv(W, 1 - D) ~ y + Z.

model_xz

A formula specifying the covariate structure for X | Z. Typically right-hand-side only, e.g. ~ Z, meaning log E[X | Z] depends on those covariates. Only the RHS is used.

aw_var

Character string giving the name of the exposure covariate in model that equals A - X (default "AW"). This must appear in model and in data_yXZ.

lbound, ubound

Numeric lower and upper bounds for the numerical integration over X in the augmentation term (defaults: 0 and 50).

Value

A list with components

beta_est

A 1 x p matrix of estimated regression coefficients \(\hat \beta\).

psi_est

Scalar, estimated residual standard deviation \(\hat \psi\).

Details

The AIPW estimator combines:

  • An IPW component based on a censoring model for C | (Y, Z, ...) specified by model_weights.

  • An augmentation component that integrates over the conditional distribution X | Z specified by gamma_x and model_xz.

The function solves the AIPW estimating equations for the regression parameters \(\beta\), treating the nuisance models as plug-in, and returns \(\hat \beta\) along with a plug-in estimate of the residual standard deviation \(\hat \psi\).