Estimating equations for g-estimation of structural nested mean models

Estimates the parameters of a structural nested mean model via g-estimation. Supports both inefficient (X = NULL) and efficient (X provided) g-estimators, and both linear and log-linear (Poisson) structural mean models.

Usage

ee_gestimation_snmm(
  theta,
  y,
  A,
  W,
  V,
  X = NULL,
  model = "linear",
  weights = NULL
)

Arguments

theta

Numeric vector. For the inefficient g-estimator, length is b + c (SMM parameters + PS model parameters). For the efficient g-estimator, length is b + c + d (SMM + PS + outcome model parameters).

y

Numeric vector of n observed outcomes.

A

Numeric vector of n binary treatment indicators (0/1).

W

Numeric n-by-c design matrix for the propensity score model.

V

Numeric n-by-b design matrix for the structural mean model. Should NOT include A itself.

X

Optional n-by-d design matrix for the outcome model (efficient g-estimator). Default NULL (inefficient g-estimator).

model

Character string: "linear" or "poisson". Default "linear".

weights

Optional numeric vector of n weights. Default NULL.

Value

A matrix of estimating equation contributions. The structural mean model rows are named SNM phi_0 through SNM phi_(b-1), matching the zero-based subscripts the literature gives those parameters. The propensity score rows are named W_1 through W_c, and, for the efficient g-estimator, the outcome model rows are named X_1 through X_d.

Examples

# A confounded binary treatment whose true effect on the outcome is -2.
set.seed(42)
n <- 500
W <- rbinom(n, 1, 0.5)
A <- rbinom(n, 1, 0.25 + 0.5 * W)
Y <- 5 + 2 * W - 2 * A + rnorm(n)

W_ps <- cbind(1, W) # Propensity score design matrix

# An intercept-only structural mean model gives a single causal contrast.
# Build it with rep() so the column has one entry per observation.
V <- cbind(rep(1, n))

psi <- function(theta) {
  ee_gestimation_snmm(theta, y = Y, A = A, W = W_ps, V = V, model = "linear")
}

# theta holds the structural mean model coefficient, which is the causal
# effect, followed by the two propensity score coefficients.
m <- m_estimate(stacked_equations = psi, init = rep(0, 3))
coef(m)
#> SNM phi_0       W_1       W_2 
#> -2.066667 -1.024504  2.234017