The FORSS Framework for Sample Size and Power Calculations With Win Statistics for Hierarchical Endpoints

TL;DR

The FORSS framework offers a computationally efficient, formula-based method for sample size and power calculations in clinical trials with hierarchical endpoints using win statistics.

Contribution

It introduces a flexible, super-sample approach that improves upon existing methods by reducing computational burden and allowing for realistic endpoint dependence modeling.

Findings

FORSS closely matches empirical power in simulations.

Type I error rates are maintained near 5%.

Endpoint dependence significantly impacts sample size planning.

Abstract

Win statistics have gained increasing popularity as primary analysis methods for clinical trials with hierarchical endpoints (HEs) as primary endpoints. However, existing sample size and power calculation approaches in trial design still face several limitations and challenges: simulation-based approaches are computationally intensive, while existing formula-based methods often rely on simplifying assumptions such as independence among HEs, or require specification of overall win statistics and tie probability that are difficult to elicit a priori in practice. To address these challenges, we propose the FORSS framework, a FORmula-based Super-Sample approach that allows investigators to specify marginal treatment effects using familiar metrics (e.g., hazard ratios, mean differences, and risk differences) together with a flexible joint working distribution for the HEs. Rather than repeatedly simulating full trials at each candidate sample size, FORSS uses super-samples to estimate the population-level plug-in quantities required by analytical formulas for both power and sample size calculation. We evaluated the performance of the proposed FORSS through extensive simulation studies. The results show that the formula-based FORSS closely matches empirical power across a wide range of scenarios while maintaining Type~I error rates near the nominal 5\% level. An illustration based on the HEART-FID trial further shows that endpoint-dependence specifications can materially affect projected power and required sample size when planning trials with HEs.