Peer review round 13: LivingGLP1 protocol 0.13.0 (reviewer grok-4.7)

1. Round 12 comments

G12-M1. Partly resolved. The two defects named in the comment are corrected in Competing risks, Piecewise integration, lines 615 to 641. For curves, (g) maps the ordinates to the log hazards and (J) is the Jacobian of (g), so (J\Sigma J^{\mathsf{T}}) is the covariance of those log hazards. For reported counts with valid person time, the two event log hazards are independent with variance (1/d_k), and a zero count makes the route unavailable. Copies of one reported interval are one coordinate, and the uncertainty of the integrated cumulative incidence uses joint predictive draws. Adopting that structure is right. Those sentences still give no observation equation that places the coordinates on the common grid at lines 597 to 605, so the shared draw cannot be fitted when arms have different interval ends. That remainder is Major 1.

The other edits in this passage and in Data items are sound. "Where published" qualifies the curves (lines 419 to 420). An author supplied covariance is paired with the authors' ordinate estimates, and digitized ordinates are inverted only with a published covariance at the same times (lines 621 to 626 and 423 to 425). Those are the ordinates inside (g).

2. New issues

Major 1. The multivariate model has no mean for a reported interval that covers several grid intervals. File: protocol/protocol.qmd, Competing risks, Piecewise integration, lines 597 to 605 and 629 to 641.

The grid is the union of the covering arms' reported ends, so unequal partitions are the ordinary case. Each arm's log hazard vector is indexed by that arm's reported intervals. The fitted object is a reference hazard on each grid interval, the median of its marginal predictive distribution. No sentence states the mean of a reported interval log hazard given the grid hazards it covers.

The carrying rule at lines 603 to 605 copies one draw onto every contained grid interval. With one coordinate, the within-arm variance of the difference between those copies is zero. A normal likelihood then requires the corresponding grid means to be equal. An arm whose only reported interval runs from time zero to the analyzed horizon would force a constant reference hazard on the whole grid and remove the piecewise model this bullet exists to fit.

The same sentences leave the displayed incidence unspecified. The point hazard on each grid interval is a marginal predictive median. Cumulative incidence is a nonlinear function of both hazards. Absolute effects (lines 974 to 976) takes the reference risk as the median of the predictive distribution. That summary is the median of the joint draws of the integrated incidence.

Replace the carrying sentence at lines 603 to 605 with: "an arm's hazards are constant within each of its own reported intervals. A reported interval that contains several grid intervals is one observation in the model below, with one draw and one variance."

Replace the passage from "Uncertainty: for reported first" through "no interval or arm is omitted." with:

"Uncertainty: for reported first event counts with valid person time, the log hazards of the two events, and of distinct reported intervals, are independent, with (\mathrm{Var}(\log h_k) = 1/d_k) and (d_k) the reported count of event (k) on that interval. A zero count for either event makes the route unavailable. For curve inversion, event counts are not inferred from curve increments and numbers at risk, because within interval censoring leaves them unidentified. A reported or author supplied covariance (\Sigma) of the ordinates that enter the formulas is required, for both events and every interval end that is used, including the analyzed horizon when that ordinate is used, together with the authors' estimates of those ordinates when (\Sigma) is author supplied. Digitized values are inverted only with a published covariance at the same times. When event free survival is published instead of the competing cumulative incidence, the ordinates are the target cumulative incidence and the event free survival. Let (g) map these ordinates to the vector of log hazards of both events on the arm's reported intervals. The within-arm covariance of that vector is (J\Sigma J^{\mathsf{T}}), where (J) is the Jacobian of (g). Each covering arm contributes one multivariate normal likelihood on that vector. The random effects parameters are the reference log hazards of both events on the common grid. The mean of a reported interval log hazard is the logarithm of the length-weighted average of the exponentiated grid log hazard means on the grid intervals it contains. That reported interval enters once, with the variance of its own coordinate. The reference hazard on each grid interval is the median of its marginal predictive distribution. The displayed reference cumulative incidence is the median of the joint predictive draws of the integrated incidence, and the uncertainty of that incidence uses the same draws, so a copied interval stays one draw. The between-arm covariance of the grid log hazards is the prior to be added to priors.csv by the deferred reference arm amendment before the first analysis. When any covering arm lacks qualifying inputs, positive finite hazards, or a finite covariance of the form specified for its input, this route is unavailable and another eligible route is kept. No constants are added and no interval or arm is omitted."

Minor 1. Scenario uncertainty is tied to the pooled predictive distribution. File: protocol/protocol.qmd, Competing risks, lines 636 to 638, and Absolute effects, lines 976 to 981.

Lines 636 to 638 take the uncertainty of the scenario values from the joint predictive distribution of the pooled reference hazards. Absolute effects defines each scenario as the 25th or 75th percentile of the covering arms' own cumulative incidences at the analyzed horizon: the reported Aalen-Johansen value when that is the source, otherwise the incidence from that arm's own qualifying hazards. The uncertainty of an arm incidence built from its piecewise hazards is the joint distribution of that arm's coordinates.

After the displayed reference cumulative incidence sentence in the Major 1 replacement, add: "Each scenario value remains the 25th or 75th percentile, across covering arms, of those arms' own cumulative incidences. An arm incidence computed from its piecewise hazards uses joint draws of that arm's own log hazard coordinates, so a copied interval stays one draw."

3. Checks and registration

The authoritative tables match the version 0.12.0 snapshot except protocol/amendments.csv row A012 (2026-10-13, version 0.13.0, Competing risks and data items, before results). outcomes.csv has 77 outcomes. The outcomes section and the subtitle both say version 0.13.0, dated 2026-10-13, after twelve rounds. search/strategies/concepts.yaml remains version 1.2.0. R/search_strategy.R builds the PubMed, Europe PMC, OpenAlex, and ClinicalTrials.gov queries from the class terms, agent terms, mechanism block, and PubMed vocabulary. The Chinese term list remains the manual CNKI and Wanfang list. The iGlarLixi switching row remains a template (is_template yes) and stays excluded from every network until a strategy is recorded. The point inversion formulas are unchanged. Under constant hazards 0.04 and 0.02 per year for one year they still return those hazards: (S(1) = \exp(-0.06)), the cumulative incidences are (0.04/0.06) and (0.02/0.06) times (1 - \exp(-0.06)), and the Aalen-Johansen split returns 0.04 and 0.02. The Quarto file was read and was not rendered.

The two matters deferred from round 12 stay outside the verdict. Reported Aalen-Johansen values will often miss the analyzed horizon, and priors.csv still has no heterogeneity prior for the reference arm meta-analysis. The new model makes that prior a prior on the between-arm covariance of the grid log hazards of both events. Setting the numerical prior by amendment before the first analysis is acceptable. The observation equation in Major 1 belongs in the registered text, because it fixes the estimand.

Team names, affiliations, postal address, funding, competing interests, confirmation of Embase access, PRESS review by a human information specialist, verification of the Chinese terms by a Chinese-reading team member, and confirmation and locking of provisional thresholds by clinical advisors and patient partners remain conditions on the administrative checklist. This verdict is based on the methods. With the piecewise likelihood written as in Major 1 and Minor 1, the methods are acceptable for registration once the administrative conditions are completed.

VERDICT: MAJOR REVISION