Clinically Interpretable Time-To-Event Testing in Randomized Clinical Trials: Milestone Survival Combined With...

The log-rank test and hazard ratio (HR) are widely used to compare survival curves in event-driven randomized clinical trials (RCTs). The optimality of the log-rank test and interpretation of the HR rely on the proportional hazards (PH) assumption, which is frequently violated in oncology due to delayed, waning, or crossing hazards. Although combination procedures built from weighted log-rank tests improve robustness to non-PH, hazard-based summaries remain difficult to interpret clinically. We propose combination tests that integrate two clinically interpretable estimands: the between-group difference in milestone survival probability $S\left(\tau \right)$ and in restricted mean survival time (RMST) $\mu (0,\tau )$ . Using Monte Carlo simulations under a milestone-based design (uniform follow-up to $\tau$ ) and supplementary event-driven designs, we compared the proposed combinations with the log-rank and MaxCombo tests across diverse survival patterns, sample sizes, and censoring rates. We evaluated Type I error and power. The milestone combination procedures showed rejection probabilities close to the nominal level under the estimand-null configurations examined and showed competitive to superior power in non-PH settings, including transient effects and crossing hazards. Applications to three oncology RCTs illustrate that, when HRs hover near unity while absolute estimands differ, the milestone combinations can detect benefits at clinically meaningful horizons. These findings support aligning design, estimands, and analysis around a prespecified milestone. Careful selection of $\tau$ is essential to balance information and interpretability. Milestone-based combination tests provide a viable, patient-centered alternative or complement to HR-centric methods, particularly when non-PH is anticipated.