Estimating equation for extended Rogan-Gladen correction

Extended version that conditions sensitivity and specificity on covariates using logistic regression models.

Usage

ee_rogan_gladen_extended(theta, y, y_star, r, X, weights = NULL)

Arguments

theta

Numeric vector of length 1 + 2*p: corrected proportion, then p sensitivity model parameters, then p specificity model parameters.

y

Numeric vector of gold-standard measurements (validation sample where r = 0).

y_star

Numeric vector of mismeasured outcome values.

r

Numeric indicator: 1 for main study, 0 for validation.

X

Numeric n-by-p design matrix for sensitivity/specificity models.

weights

Optional numeric vector of n weights. Default NULL.

Value

A (1+2*p)-by-n matrix, with rows named corrected_proportion, then sens_1 through sens_p for the sensitivity model, then spec_1 through spec_p for the specificity model.

Examples

# A validation design of the kind ee_rogan_gladen() takes, with sensitivity
# and specificity now modeled by logistic regression. The design matrix here
# is intercept only, so both models estimate a single log-odds.
set.seed(1)
n <- 500
y_true <- rbinom(n, 1, 0.3)
y_star <- ifelse(y_true == 1, rbinom(n, 1, 0.9), 1 - rbinom(n, 1, 0.85))
r <- c(rep(0, 200), rep(1, 300))

# The gold standard is observed only in the validation sample, so the main
# study positions carry a 0 placeholder, as on ee_rogan_gladen().
y <- ifelse(r == 0, y_true, 0)
X <- cbind(rep(1, n))

psi <- function(theta) {
  ee_rogan_gladen_extended(theta, y = y, y_star = y_star, r = r, X = X)
}

m <- m_estimate(stacked_equations = psi, init = c(0.5, 1, 1))

# Corrected prevalence, then the sensitivity and specificity intercepts
coef(m)
#> corrected_proportion               sens_1               spec_1 
#>            0.2963931            2.0614230            1.7176515