simulation-architect

name	simulation-architect
description	Design and implementation of comprehensive simulation studies

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

---

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 *   p  B
      
  



replications_needed  desired_mcse estimated_sd 
  estimated_sd  desired_mcse

---

R Code Templates

Complete Simulation Template

# Full simulation study template following Morris et al. guidelines
run_simulation_study <- function(
  n_sims = 2000,
  n_vec = c(200, 500, 1000),
  seed = 42,
  parallel = TRUE,
  n_cores = parallel::detectCores() - 1
) {

  set.seed(seed)

  # Define parameter grid
  params <- expand.grid(
    n = n_vec,
    effect_size = c(0, 0.14, 0.39),
    model_spec = c("correct", "misspecified")
  )

  # Setup parallel processing
   parallel 
    cl  parallelmakeClustern_cores
    doParallelregisterDoParallelcl
    parallelstopClustercl
  

  
  results  foreach
    i  nrowparams
    .combine  rbind
    .packages   
    

    scenario  paramsi 
    sim_results  replicaten_sims 
      data  generate_dgpscenario
      estimates  apply_methodsdata
      evaluate_performanceestimates truth  scenarioeffect_size
     simplify  

    summarize_scenariosim_results scenario
  

  
  results  add_monte_carlo_errorsresults n_sims

  results



add_monte_carlo_errors  results B 
  results 
    mutate
      mcse_bias  empirical_se  B
      mcse_coverage  coverage    coverage  B
      mcse_rmse  rmse    B
    

Parallel Simulation Template

# Memory-efficient parallel simulation
run_parallel_simulation <- function(scenario, n_sims, n_cores = 4) {
  library(future)
  library(future.apply)

  plan(multisession, workers = n_cores)

  results <- future_replicate(n_sims, {
    data <- generate_dgp(scenario$n, scenario$params)
    est <- estimate_effect(data)
    list(
      estimate = est$point,
      se = est$se,
      covered = abs(est$point - scenario$truth) < 1.96 * est$se
    )
  }, simplify = 

  plansequential  

  
  estimates  sapplyresults `[[` 
  ses  sapplyresults `[[` 
  covered  sapplyresults `[[` 

  
    bias  meanestimates  scenariotruth
    empirical_se  sdestimates
    mean_se  meanses
    coverage  meancovered
    mcse_bias  sdestimates  n_sims
    mcse_coverage  meancovered    meancovered  n_sims
  

---

Core Principles (Morris et al., 2019)

ADEMP Framework

1. Aims: What question does the simulation answer?
2. Data-generating mechanisms: How is data simulated?
3. Estimands: What is being estimated?
4. Methods: What estimators are compared?
5. Performance measures: How is performance assessed?

Data-Generating Process Design

Standard Mediation DGP

generate_mediation_data <- function(n, params) {
  # Confounders
  X <- rnorm(n)

  # Treatment (binary)
  ps <- plogis(params$gamma0 + params$gamma1 * X)
  A <- rbinom(n, 1, ps)

  # Mediator
  M <- params$alpha0 + params$alpha1 * A + params$alpha2 * X +
       rnorm(n, sd = params$sigma_m)

  # Outcome
  Y <- params$beta0 + params$beta1 * A + params$beta2 * M +
       params$beta3 * X + params$beta4 * A * M 
       rnormn sd  paramssigma_y

  data.frameY  Y A  A M  M X  X

DGP Variations to Consider

• Linearity: Linear vs nonlinear relationships
• Model specification: Correct vs misspecified
• Error structure: Homoscedastic vs heteroscedastic
• Interaction: No interaction vs A×M interaction
• Confounding: Measured vs unmeasured
• Treatment: Binary vs continuous
• Mediator: Continuous vs binary vs count

Parameter Grid Design

Sample Size Selection

Size	Label	Purpose
100-200	Small	Stress test
500	Medium	Typical study
1000-2000	Large	Asymptotic behavior
5000+	Very large	Efficiency comparison

Effect Size Selection

Effect	Interpretation
0	Null (Type I error)
0.1	Small
0.3	Medium
0.5	Large

Recommended Grid Structure

params <- expand.grid(
  n = c(200, 500, 1000, 2000),
  effect = c(0, 0.14, 0.39, 0.59),  # Small/medium/large per Cohen
  confounding = c(0, 0.3, 0.6),
  misspecification = c(FALSE, TRUE)
)

Performance Metrics

Primary Metrics

Metric	Formula	Target	MCSE Formula
Bias	$\bar{\hat\psi} - \psi_0$	≈ 0	$\sqrt{\text{Var}(\hat\psi)/n_{sim}}$
Empirical SE	$\text{SD}(\hat\psi)$	—	Complex
Average SE	$\bar{\widehat{SE}}$	≈ Emp SE	$\text{SD}(\widehat{SE})/\sqrt{n_{sim}}$
Coverage	$\frac{1}{n_{sim}}\sum I(\psi_0 \in CI)$	≈ 0.95	$\sqrt{p(1-p)/n_{sim}}$
MSE	$\text{Bias}^2 + \text{Var}$	Minimize	—
Power	% rejecting $H_0$	Context-dependent	$\sqrt{p(1-p)/n_{sim}}$

Relative Metrics (for method comparison)

• Relative bias: $\text{Bias}/\psi_0$ (when $\psi_0 \neq 0$)
• Relative efficiency: $\text{Var}(\hat\psi_1)/\text{Var}(\hat\psi_2)$
• Relative MSE: $\text{MSE}_1/\text{MSE}_2$

Replication Guidelines

Minimum Replications

Metric	Minimum	Recommended
Bias	1000	2000
Coverage	2000	5000
Power	1000	2000

Monte Carlo Standard Error

Always report MCSE for key metrics:

• Coverage MCSE at 95%: $\sqrt{0.95 \times 0.05 / n_{sim}} \approx 0.007$ for $n_{sim}=1000$
• Need ~2500 reps for MCSE < 0.005

R Implementation Template

#' Run simulation study
#' @param scenario Parameter list for this scenario
#' @param n_rep Number of replications
#' @param seed Random seed
run_simulation <- function(scenario, n_rep = 2000, seed = 42) {
  set.seed(seed)

  results <- future_map(1:n_rep, function(i) {
    # Generate data
    data <- generate_data(scenario$n, scenario$params)

    # Fit methods
    fit1 <- method1(data)
    fit2 <- method2(data)

    # Extract estimates
    tibble(
      rep = i,
      method = c("method1" 
      estimate  fit1est fit2est
      se  fit1se fit2se
      ci_lower  estimate    se
      ci_upper  estimate    se
    
   .options  furrr_optionsseed   
    bind_rows

  
  results 
    group_bymethod 
    summarize
      bias  meanestimate  scenariotrue_value
      emp_se  sdestimate
      avg_se  meanse
      coverage  meanci_lower  scenariotrue_value 
                      ci_upper  scenariotrue_value
      mse  bias  emp_se
      .groups  
    

Results Presentation

Standard Table Format

Table X: Simulation Results (n_rep = 2000)

                    Method 1                    Method 2
n       Bias   SE    Cov   MSE      Bias   SE    Cov   MSE
-----------------------------------------------------------
200     0.02   0.15  0.94  0.023    0.01   0.12  0.95  0.014
500     0.01   0.09  0.95  0.008    0.00   0.08  0.95  0.006
1000    0.00   0.06  0.95  0.004    0.00   0.05  0.95  0.003

Note: Cov = 95% CI coverage. MCSE for coverage ≈ 0.005.

Visualization Guidelines

• Use faceted plots for multiple scenarios
• Show confidence bands for metrics
• Compare methods side-by-side
• Log scale for MSE if range is large

Checkpoints and Reproducibility

Checkpointing Strategy

# Save results incrementally
if (i %% 100 == 0) {
  saveRDS(results_so_far,
          file = sprintf("checkpoint_%s_rep%d.rds", scenario_id, i))
}

Reproducibility Requirements

1. Set seed explicitly
2. Record package versions (sessionInfo())
3. Use furrr_options(seed = TRUE) for parallel
4. Save full results, not just summaries
5. Document any manual interventions

Common Pitfalls

Design Pitfalls

• Too few replications for coverage assessment
• Unrealistic parameter combinations
• Missing null scenario (effect = 0)
• No misspecification scenarios

Implementation Pitfalls

• Not setting seeds properly in parallel
• Ignoring convergence failures
• Not checking for numerical issues
• Insufficient burn-in for MCMC methods

Reporting Pitfalls

• Missing MCSE
• Not reporting convergence failures
• Cherry-picking scenarios
• Inadequate description of DGP

Key References

• Morris et al 2019
• Burton et al
• White