A Milestone-Based Framework for Characterizing Time-Varying Treatment Effects in Immunotherapy Trials

Referee: [Methods] Methods section (description of tau-based summary): The definition, derivation, and statistical properties of the tau-based summary for short-term treatment ordering on the pre-milestone subpopulation are not provided; it is unclear whether this functional correctly orders treatments or identifies hazard reversal without additional assumptions on the underlying hazard processes or independent censoring.

Authors: We appreciate this observation. The tau-based summary is intended as a rank-based measure (analogous to Kendall's tau) that compares the ordering of survival times between treatment arms within the pre-milestone group to detect crossings or reversals in the cumulative incidence. In the revised manuscript, we will add a formal definition, derivation from the joint survival distribution, and discussion of its properties, including the assumption of independent censoring and how it identifies hazard reversals when the integrated difference in hazards changes sign. This will clarify its use without requiring proportional hazards. revision: yes

Referee: [Methods] Methods and Application sections (milestone time point): The framework relies on pre-specifying a single clinically meaningful milestone t* such that P(T > t*) cleanly separates long-term from short-term effects, but no justification, sensitivity analysis to modest shifts in t*, or discussion of information loss is given; this choice is load-bearing for the central separation claim.

Authors: We agree that the choice of t* is critical. In the revision, we will justify the choices of t* for each trial based on clinical literature and trial characteristics (e.g., 12 or 24 months for immunotherapy benefit emergence). We will also include sensitivity analyses showing how the milestone survival probabilities and tau summaries change with small perturbations in t* (such as ±2 or ±3 months) and discuss the trade-off in information loss versus interpretability. These additions will be made to the Methods and Results sections. revision: yes

Referee: [Results] Results section: No simulation studies are included to evaluate the framework's performance under controlled scenarios with known time-varying hazards, varying censoring rates, or competing risks, leaving the reliability of the milestone survival probabilities and tau-summary unverified despite the use of reconstructed KM data from the three trials.

Authors: The primary aim of the manuscript is to introduce the framework and illustrate its application to real trial data to demonstrate clinical interpretability. However, we recognize the importance of simulation-based validation. In the revised version, we will incorporate a simulation study section that assesses the framework under scenarios with non-proportional hazards, different censoring mechanisms, and sample sizes, to verify the accuracy of the estimates and the tau-summary's ability to detect reversals. revision: yes

Referee: [Application] Application section (data handling): The analysis uses reconstructed individual-level data from published Kaplan-Meier curves in CheckMate 067, 227, and CLEAR without explicit discussion of how right-censoring or potential reconstruction inaccuracies are incorporated into the tau-based calculations or milestone probabilities.

Authors: We will revise the Application section to include a detailed description of the data reconstruction method (using the algorithm of Guyot et al. or similar), how the reconstructed data preserve the original censoring information from the KM curves, and the potential limitations due to reconstruction error. We will also explain that the milestone probabilities are directly estimated from the KM curves, and the tau-summary is computed on the reconstructed event times, with bootstrap for inference to account for variability. revision: yes