power-optimization-patternslisted

# 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:** ```r 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 = "Ma