% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/compute_estimands_Parast_et_al_2024.R
\name{compute_estimands_Parast_et_al_2024}
\alias{compute_estimands_Parast_et_al_2024}
\title{Monte Carlo Computation of the Estimands for the Simulation Study in Parast et al. (2024)}
\usage{
compute_estimands_Parast_et_al_2024(MC_samples)
}
\arguments{
\item{MC_samples}{Integer. The number of Monte Carlo samples to generate per setting.}
}
\value{
A data frame containing the Monte Carlo estimates for each setting:
\itemize{
  \item \code{setting}: The index of the simulation setting.
  \item \code{U_Y_MC}, \code{U_S_MC}, \code{delta_MC}: Parameters of interest from \insertCite{parast2024rank;textual}{BSET}.
  \item \code{V_Y_MC}, \code{V_S_MC}, \code{theta_MC}: Parameters of interest from \insertCite{carlotti2026bayesian;textual}{BSET}.
}
}
\description{
This function iterates through the four simulation settings defined in Parast
et al. (2024) and estimates the true values of \eqn{U_Y}, \eqn{U_S},
\eqn{\delta}, \eqn{V_Y}, \eqn{V_S}, and \eqn{\theta} using a Monte Carlo
dataset generated according to the specified data-generating processes.
}
\details{
The settings are defined as follows:
\itemize{
  \item Setting 1: \strong{Useless surrogate (Gaussian model)}
    \deqn{Y_1 \sim \mathcal{N}(5, 3), \quad Y_0 \sim \mathcal{N}(3, 3),}
    \deqn{S_1 \sim \mathcal{N}(2/3, 1), \quad S_0 \sim \mathcal{N}(2/3, 1).}
  \item Setting 2: \strong{Perfect surrogate (Gaussian model)}
    \deqn{Y_1 \sim \mathcal{N}(6, 3), \quad Y_0 \sim \mathcal{N}(5/2, 3),}
    \deqn{S_1 = Y_1 + \mathcal{N}(0, 1/10), \quad S_0 = Y_0 + \mathcal{N}(0, 1/10).}
  \item Setting 3: \strong{Imperfect surrogate (Gaussian model)}
    \deqn{S_1 \sim \mathcal{N}(5, 3), \quad S_0 \sim \mathcal{N}(3, 3),}
    \deqn{Y_1 = S_1 + \mathcal{N}(1.5, 0.6), \quad Y_0 = S_0 + \mathcal{N}(0, 0.6).}
  \item Setting 4: \strong{Misspecified model (non-Gaussian model)}
    \deqn{S_1 \sim \exp(\mathcal{N}(2.5, 1.5)), \quad S_0 \sim \exp(\mathcal{N}(0.5, 1.5)),}
    \deqn{Y_1 = 2 + 6/5 \sqrt{S_1} + 3/10 \exp(S_1 / 500) + \exp(\mathcal{N}(0, 0.3)),}
    \deqn{Y_0 = 4/5 \sqrt{S_0} + 1/5 \exp(S_0 / 50) + \exp(\mathcal{N}(0, 0.3)).}
}
This function is generally not intended to be called directly by the user.
It is provided as a utility for computing the true parameter values for the
simulation settings described in \insertCite{parast2024rank;textual}{BSET}.
}
\references{
\insertRef{parast2024rank}{BSET}
}
