AIPW lambda-close estimator — estimate_beta_aipw

Fits a regression model for y using an augmented IPW estimator with a closed-form ("lambda-close") augmentation under a normal approximation for X. This implementation assumes the outcome model is y ~ AW + Z, where AW = A - X, and uses a single covariate Z in the outcome model.

Usage

estimate_beta_aipw_lambda(
  data_yXZ = dat,
  model = model,
  model_weights = model_weights,
  aw_var = "AW"
)

Arguments

data_yXZ: Data frame containing at least y, A, AW, W, D, Z, and the weight variables myp_ywz_oracle, myp_ywz, myp_uniform, myp_ywz_logit. Assumes the outcome model is y ~ AW + Z.
model: Formula for the outcome, currently assumed to be y ~ AW + Z. The function checks that the design matrix has exactly three columns: intercept, AW, and Z, in that order.
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.
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.

Value

A list with components:

beta_est: 1 x 4 matrix: \((\hat\beta_0, \hat\beta_1, \hat\beta_2, \hat\psi)\).
se_est: 1 x 3 matrix of standard errors for \(\beta_0, \beta_1, \beta_2\) based on the geex sandwich estimator.

Details

The estimator combines:

an IPW component using weights D / p, where p is chosen via myweight, and
a closed-form augmentation term derived under a normal approximation for X.