Sandwich variance estimator for the IPW estimator

Computes a sandwich variance estimator for the IPW regression estimator, allowing for a general outcome model y ~ AW + Z1 + ... + Zp and a possibly different censoring model for C | (Y, Z, ...) specified by model_weights. The censoring model is fit via a Weibull AFT model using survreg, and the corresponding Gumbel parameterization for log(W) is used to construct the weights \(\pi(Y, W, Z)\).

Usage

var_beta_ipw(data_yXZ, theta, model, model_weights)

Arguments

data_yXZ

A data frame containing at least the outcome y, the covariates in the outcome model model, the observed covariate W, the event indicator D, and the covariates appearing in the censoring model model_weights.

theta

Numeric vector of parameter estimates \((\beta, \psi)\) from the IPW estimator. The length of theta must be equal to p_beta + 1, where p_beta is the number of regression coefficients in model.

model

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

model_weights

A formula specifying the censoring model used to estimate the IPW weights. Typically of the form ~ y + Z1 + Z2 (right-hand-side only). Internally this is expanded to Surv(W, 1 - D) ~ y + Z1 + Z2. If a full Surv formula is provided, only its right-hand side is used.

Value

A list with components

beta_est

Estimated regression coefficients \(\beta\).

psi_est

Estimated residual standard deviation \(\psi\).

se_beta

Sandwich standard errors for \(\beta\).

sandwich_var

Full sandwich variance matrix for the stacked nuisance parameter vector \(\xi = (\beta, \alpha)\), where \(\alpha\) are the parameters of the censoring model.

Details

The parameter vector theta is assumed to be of the form \(\theta = (\beta, \psi)\), where:

• \(\beta\) are the regression coefficients in the outcome model,

• \(\psi\) is the residual standard deviation on the original scale.