power-optimization-patterns

Power Optimization Patterns

When to Use This Skill

• Optimizing sample size for target power
• Selecting design parameters (randomization ratio, event count)
• Trading off between competing objectives
• Performing sensitivity analysis
• Finding optimal regions across scenarios

Clinical Trial Optimization Framework

Problem Formulation

Components:

• Data Model D(θ): Parameterized by θ (treatment effects, rates, etc.)
• Analysis Model A(λ): Parameterized by λ (sample size, events, etc.)
• Criterion ψ(λ | θ): Power or other metric

Objective: Find λ* that optimizes ψ(λ | θ) subject to constraints.

Direct Optimization

Sample Size Determination

Objective: Find minimum n such that Power(n) ≥ target

Binary Search Algorithm:

find_sample_size <- function(target_power, effect_size, alpha = 0.025,
                            n_low = 50, n_high = 500, n_sims = 10000) {

  while (n_high - n_low > 5) {
    n_mid <- round((n_low + n_high) / 2)

    # Run CSE with n_mid
    data.model <- DataModel() +
      OutcomeDist(outcome.dist = "NormalDist") +
      SampleSize(n_mid) +
      Sample(id = "Control", outcome.par = parameters(mean = 0, sd = 1)) +
      Sample(id = "Treatment", outcome.par = parameters(mean = effect_size, sd = 1))

    analysis.model <- AnalysisModel() +
      Test(id = "Primary", samples = samples("Control", "Treatment"), method = "TTest")

    evaluation.model <- EvaluationModel() +
      Criterion(id = "Power", method = "MarginalPower",
                tests = tests("Primary"), labels = "Power",
                par = parameters(alpha = alpha))

    results <- CSE(data.model, analysis.model, evaluation.model,
                   SimParameters(n.sims = n_sims, proc.load = "full", seed = 12345))

    power <- results$simulation.results$Power

    if (power >= target_power) {
      n_high <- n_mid
    } else {
      n_low <- n_mid
    }
  }

  return(n_high)
}

Event Count Optimization (TTE)

# Grid search over event counts
event_grid <- seq(200, 400, by = 25)
power_results <- numeric(length(event_grid))

for (i in seq_along(event_grid)) {
  results <- sim_fixed_n(
    n_sim = 10000,
    sample_size = 500,
    target_event = event_grid[i],
    enroll_rate = enroll_rate,
    fail_rate = fail_rate,
    timing_type = 2
  )
  power_results[i] <- mean(results$z < qnorm(0.025))
}

# Find minimum events for 90% power
min_events <- event_grid[min(which(power_results >= 0.90))]