Power Simulations of Rare Event Counts and Introduction to the ‘Power Lift’ Metric

Objectives: This study addresses the significant challenge of estimating statistical power for experiments involving rare but impactful events, where traditional power analysis models, assuming normal distribution, inadequately estimate required sample sizes. It introduces a simulation framework leveraging Poisson regression models to better capture the dynamics of rare event occurrences and their impact on power calculations.Methods: Using Poisson distributions, a comprehensive simulation framework systematically assesses the interplay between sample size, effect size, and event occurrence rates. This approach is calibrated against real-world criminological constraints to ensure relevance and applicability. A key innovation is the "power lift" metric, devised to provide a more stable estimation of the required sample sizes by addressing the inherent instability in power simulations for rare events.Results: The simulation reveals intricate relationships between effect size, sample size, and event rates, underscoring the challenge of achieving sufficient statistical power in studies of rare events. The "power lift" metric emerges as a robust tool for determining sample size requirements, offering greater stability across various scenarios. Results are operationalized through user-friendly simulation code and a quick reference table, providing practical tools for researchers.Conclusions: The study advances a methodological framework for power analysis in the context of rare events in criminology. By integrating the "power lift" metric and a Poisson regression-based simulation framework, it offers researchers a more accurate and reliable means of estimating sample sizes for statistically robust investigations into rare but socially significant events.