Round 13: response to reviewers

Protocol version reviewed: 0.13.0. Revised version: 0.14.0.

Verdicts: GPT-6 Astra MAJOR REVISION; Fable 5.1 ACCEPT; Grok 4.7 MAJOR REVISION. All three addressed the same under specified pooling sentence. Every comment is answered below and recorded in ../comments.csv.

Summary of main changes

• Piecewise integration is written as one specified model: identical reported interval boundaries across covering arms (otherwise unavailable), y_a ~ N(mu + Z u_a, V_a) with one arm level random effect per event, priors PR15 and PR16, a one arm rule, and summaries from joint predictive draws.
• The exponential approximation is the one interval special case of the same model.
• Scenario uncertainty from arm specific draws; count variance stated as an approximation; reference arm heterogeneity prior PR17.

GPT-6 Astra (gpt-6-astra)

C13-1 (major; Competing risks; priors). Multivariate pooling lacked common coordinates and a between arm covariance.

Response (revised). Agreed; your conservative restriction adopted: piecewise integration requires identical reported interval boundaries across all covering arms through the horizon, otherwise the route is unavailable. The model is now written: y_a ~ N(mu + Z u_a, V_a) with one arm level random effect per event shared across intervals (the structure fable-5.1 proposed), u_ak ~ N(0, tau_k^2), priors PR15 (mu) and PR16 (tau_k) with sensitivity priors, hazards per year, and a one arm rule. We used this structure rather than an unstructured covariance with an LKJ prior because with two to five covering arms a free between arm covariance over intervals and events is weakly identified, and a proportional deviation of each arm hazard function is the usual form of baseline risk heterogeneity.

C13-2 (minor; Competing risks; absolute effects). Scenario uncertainty targeted the predictive distribution.

Response (revised). Agreed; your text adopted: scenario values remain empirical percentiles of arms own cumulative incidences, with uncertainty from arm specific draws N(y_a, V_a) recomputed per draw.

C13-3 (minor; Competing risks). Count variance stated as exact.

Response (revised). Agreed; the working normal approximation with variance approximately 1/d_k and zero covariance under its standard assumptions.

Fable 5.1 (fable-5.1)

F13-1 (minor; Competing risks; priors). Multivariate model structure and prior.

Response (revised). Agreed; your structure (one shared random effect per event per arm) adopted with priors PR15 and PR16. Because identical interval boundaries are now required (C13-1), no observation equation across different partitions is needed. PR17 also settles the reference arm heterogeneity prior deferred in round 12.

F13-2 (minor; Competing risks). Scenario values tied to the wrong distribution.

Response (revised). Agreed; see C13-2.

F13-note (note; Absolute effects). Point estimate versus median of draws.

Response (revised). Adopted: the displayed reference cumulative incidence is the median of the integrated draws.

Grok 4.7 (grok-4.7)

G13-M1 (major; Competing risks). No mean for a reported interval covering several grid intervals; displayed incidence unspecified.

Response (revised (alternative)). Resolved by requiring identical reported interval boundaries across covering arms (C13-1), so every coordinate maps to one common interval and no observation equation across partitions is needed; the displayed reference cumulative incidence is the median of the joint predictive draws of the integrated incidence, as you proposed. Your length weighted observation equation was not needed under this restriction; it remains the natural amendment if unequal partitions must be accommodated.

G13-1 (minor; Competing risks; absolute effects). Scenario uncertainty.

Response (revised). Agreed; see C13-2.