Monte Carlo Integration in Simple and Complex Simulation Designs

TL;DR

This paper demonstrates how Monte Carlo integration can be used to accurately compute true parameter values in both simple and complex simulation studies, with practical pseudocode and R code provided.

Contribution

It introduces general pseudocode and strategies for applying Monte Carlo integration to estimate true values in complex simulation designs, including causal mediation analysis.

Findings

Monte Carlo integration effectively estimates true parameter values.

Strategies to minimize Monte Carlo error are discussed.

R code implementation is provided for practical use.

Abstract

Simulation studies are used to evaluate and compare the properties of statistical methods in controlled experimental settings. In most cases, performing a simulation study requires knowledge of the true value of the parameter, or estimand, of interest. However, in many simulation designs, the true value of the estimand is difficult to compute analytically. Here, we illustrate the use of Monte Carlo integration to compute true estimand values in simple and complex simulation designs. We provide general pseudocode that can be replicated in any software program of choice to demonstrate key principles in using Monte Carlo integration in two scenarios: a simple three variable simulation where interest lies in the marginally adjusted odds ratio; and a more complex causal mediation analysis where interest lies in the controlled direct effect in the presence of mediator-outcome confounders affected by the exposure. We discuss general strategies that can be used to minimize Monte Carlo error, and to serve as checks on the simulation program to avoid coding errors. R programming code is provided illustrating the application of our pseudocode in these settings.