Calculating power for the Finkelstein and Schoenfeld test statistic for a composite endpoint with two components

The Finkelstein and Schoenfeld (FS) test is a popular generalized pairwise comparison approach to analyze prioritized composite endpoints (eg, components are assessed in order of clinical importance). Power and sample size estimation for the FS test, however, are generally done via simulation studies. This simulation approach can be extremely computationally burdensome, compounded by increasing number of composite endpoints and with increasing sample size. Here we propose an analytical solution to calculate power and sample size for commonly encountered two-component hierarchical composite endpoints. The power formulas are derived assuming underlying distributions in each of the component outcomes on the population level, which provide a computationally efficient and practical alternative to the standard simulation approach. Monte Carlo simulation results demonstrate that performance of the proposed power formulas are consistent with that of the simulation approach, and have generally desirable objective properties including robustness to mis-specified distributional assumptions. We demonstrate the application of the proposed formulas by calculating power and sample size for the Transthyretin Amyloidosis Cardiomyopathy Clinical Trial.