group-sequential-methodslisted

# Group Sequential Methods ## When to Use This Skill - Designing group sequential trials with interim analyses - Implementing alpha spending functions - Setting futility stopping rules - Calculating information fractions - Using sim_gs_n() for GS simulations - Integrating with gsDesign2 package ## Fundamental Concepts ### Group Sequential Design A group sequential design allows for: - **Early stopping for efficacy**: If treatment effect is larger than expected - **Early stopping for futility**: If treatment effect is unlikely to reach significance - **Reduced expected sample size**: When treatment effect is present ### Information Fraction Information fraction at analysis k: ``` I_k / I_K = (events at analysis k) / (total planned events) ``` For time-to-event trials, information ≈ number of events. ### Type I Error Spending The key constraint is that the design controls the overall Type I error at the planned alpha level. Spending functions define cumulative alpha spending over information time, and boundaries are derived using the joint distribution of sequential test statistics. They are not obtained by simply assigning independent nominal alpha levels to each look. ## Alpha Spending Functions ### O'Brien-Fleming (OBF) **Properties:** - Conservative at early analyses - Nearly full alpha at final analysis - Difficult to stop early - Maintains nominal Type I error **Formula:** ``` α*(t) = 2 - 2Φ(z_{α/2} / √t) ``` **When to Use:** - Want maximum power at final a