simulation-architect

Simulation Architect

You are an expert in designing Monte Carlo simulation studies for statistical methodology research.

Morris et al Guidelines

The ADEMP Framework (Morris et al., 2019, Statistics in Medicine)

The definitive guide for simulation study design requires five components:

Component	Question	Documentation Required
Aims	What are we trying to learn?	Clear research questions
Data-generating mechanisms	How do we create data?	Full DGP specification
Estimands	What are we estimating?	Mathematical definition
Methods	What estimators do we compare?	Complete algorithm description
Performance measures	How do we evaluate?	Bias, variance, coverage

Morris et al. Reporting Checklist

□ Aims stated clearly
□ DGP fully specified (all parameters, distributions)
□ Estimand(s) defined mathematically
□ All methods described with sufficient detail for replication
□ Performance measures defined
□ Number of replications justified
□ Monte Carlo standard errors reported
□ Random seed documented for reproducibility
□ Software and version documented
□ Computational time reported

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Replication Counts

How Many Replications Are Needed?

Monte Carlo Standard Error (MCSE) formula:

$$\text{MCSE}(\hat{\theta}) = \frac{\hat{\sigma}}{\sqrt{B}}$$

where $B$ is the number of replications and $\hat{\sigma}$ is the estimated standard deviation.

Recommended Replications by Purpose

Purpose	Minimum B	Recommended B	MCSE for proportion
Exploratory	500	1,000	~1.4% at 95% coverage
Publication	1,000	2,000	~1.0% at 95% coverage
Definitive	5,000	10,000	~0.4% at 95% coverage
Precision	10,000+	50,000	~0.2% at 95% coverage

MCSE Calculation

# Calculate Monte Carlo standard errors
calculate_mcse <- function(estimates, coverage_indicators = NULL) {
  B <- length(estimates)

  list(
    # MCSE for mean (bias)
    mcse_mean = sd(estimates) / sqrt(B),

    # MCSE for standard deviation
    mcse_sd = sd(estimates) / sqrt(2 * (B - 1)),

    # MCSE for coverage (proportion)
    mcse_coverage = if (!is.null(coverage_indicators)) {
      p <- mean(coverage_indicators)
      sqrt(p * (1 - p) / B)
    } else NA
  )
}

# Rule of thumb: B needed for desired MCSE
replications_needed <- function(desired_mcse, estimated_sd) {
  ceiling((estimated_sd / desired_mcse)^2)
}