Computing True Parameter Values in Simulation Studies Using Monte Carlo Integration

Area of Science:

• Statistics
• Computational Methods
• Epidemiology

Background:

• Simulation studies are crucial for evaluating statistical methods.
• Determining true parameter (estimand) values is often analytically challenging in simulations.
• Accurate estimand values are essential for reliable simulation study outcomes.

Purpose of the Study:

• To demonstrate Monte Carlo integration for computing true estimand values in simulations.
• To provide a practical method for handling analytically intractable estimands.
• To illustrate the application in both simple and complex simulation designs.

Main Methods:

• Utilized Monte Carlo integration to approximate true estimand values.
• Developed general pseudocode applicable across various software platforms.
• Applied the method to a three-variable simulation (odds ratio) and causal mediation analysis (controlled direct effect).

Main Results:

• Successfully computed true estimand values using Monte Carlo integration in demonstrated scenarios.
• Provided strategies for minimizing Monte Carlo error and ensuring simulation program validity.
• R code examples were included for practical implementation.

Conclusions:

• Monte Carlo integration offers a viable approach for determining true estimand values in complex simulation studies.
• This technique enhances the rigor and reproducibility of simulation-based statistical research.
• The provided pseudocode and examples facilitate the application of this method.