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Sandwich variance estimator for the AIPW estimator

var_beta_aipw.Rd

Computes a plug-in sandwich variance estimator for the AIPW regression estimator under outcome-dependent right-censoring of a covariate. The outcome model is specified by model, typically of the form y ~ AW + Z1 + ... + Zp, where AW = A - X.

Usage

var_beta_aipw(data_yXZ, theta, lbound = 0, ubound = 50)

Arguments

data_yXZ

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),

  • all covariates appearing in model,

  • all covariates appearing in model_weights and model_xz.

theta

Numeric vector c(beta, psi) from the AIPW estimator, where beta has length equal to the number of columns in model.matrix(model, data_yXZ) and psi is the residual standard deviation.

lbound, ubound

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

Value

A list with components

beta_est

Estimated regression coefficients \(\beta\).

psi_est

Estimated residual standard deviation \(\psi\).

se_beta

Sandwich standard errors for \(\beta\).

Details

The AIPW estimator combines:

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

  • an augmentation component based on an AFT model for X | Z specified by gamma_x and model_xz.

This function takes the estimated parameter vector theta = c(beta, psi) from estimate_beta_aipw_est and computes a sandwich variance for \(\beta\), treating the nuisance model parameters as plug-in.