Generalizing the Finkelstein-Schoenfeld Test to Incorporate Multiple Alternating Thresholds

Composite endpoints consisting of both terminal and non-terminal events, such as death and hospitalization, are frequently used in cardiovascular clinical trials. The Finkelstein-Schoenfeld (FS) test provides a way to employ a hierarchical structure to combine fatal and non-fatal events by giving death information an absolute priority, which may limit the contribution of clinically meaningful non-fatal events. To provide a more flexible alternative, we propose the Finkelstein-Schoenfeld with Multiple Thresholds (FS-MT) test, which extends the standard FS test by incorporating multiple thresholds applied sequentially and alternating across endpoints. A weighted adaptive approach is also developed to help determine the thresholds in FS-MT. The proposed approach retains the statistical properties of the FS test while allowing more flexible use of information from lower-priority events. We evaluate the operating characteristics of the proposed test through simulations that vary the follow-up time, the correlation between events, and the treatment effect sizes. A case study based on the Digitalis Investigation Group clinical trial data is presented to further illustrate our proposed method. An R package ``FSMT'' that implements the proposed methodology has been developed.