{"id":"abcb3f68-4760-447a-a6a4-3787abf13ccb","arxiv_id":"1908.07265","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A robust Bayesian hierarchical model for piecewise exponential data leverages historical controls in time-to-event trial analysis and design using individual or summary data.","lead":"This paper extends Bayesian meta-analytic-predictive priors to time-to-event endpoints, letting clinical trials borrow historical control data when patient-level data are unavailable. The method is illustrated on ovarian and lung cancer trial data, where it can reduce control-arm sample sizes.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Appendix A Step 4's event-count extraction equation is algebraically wrong, so the NSCLC historical data and all design operating characteristics in §3.2 rest on an invalid transformation; this must be corrected and re-run before the aggregate-data claim is accepted.","rationale":"The central claim requires that aggregate KM data can be converted into Poisson sufficient statistics (events and exposure) that are accurate enough for hierarchical borrowing. The paper's own Appendix A, which is the only description of how this conversion was done for the NSCLC design example, contains a wrong equation. This is more specific than the general approximation caveat the reader flagged: it is a definite algebraic error. Because the MAP prior in §3.2 is derived from these extracted counts, and because Table 3 and Figure 4 are the paper's evidence that the robust design has acceptable operating characteristics, the numerical validation is compromised as printed. The methodological framework (PWE hierarchical model, robust mixture) may still be sound; the fix is to correct the extraction formula and redo the empirical work. Hence the verdict remains conditional, not rejection. The reader's weakest_assumption about mid-interval deaths and constant censoring rates is related but does not catch the explicit formula error, so agreement is partial.","tokens_in":16054,"tokens_out":11547,"duration_ms":118993,"concrete_test":"Simulate a piecewise-exponential sample (e.g., N=200 with known hazards), compute the true interval event counts d_i and the Kaplan-Meier survival estimates S(t_i). Apply Appendix A Step 4 as printed to solve for d_i and compare with the true counts; the error will be large and systematic. Then re-extract the seven NSCLC KM curves from the original publications using the correct relation log(S(t_{i+1})/S(t_i)) = log(1 - d_i/n_i) and re-run the MAC analyses and the 2000-trial operating-characteristic simulations of §3.2. If the prior ENE and Table 3 change materially, the current reported numbers must be revised.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Appendix A Step 4 states log(S_hat(t_{i+1})) - log(S_hat(t_i)) = 1 - d_i/n_i. This is not the Kaplan-Meier recursion: S(t_{i+1}) = S(t_i)(1 - d_i/n_i) implies the left side equals log(1 - d_i/n_i), approximately -d_i/n_i for small hazards, not 1 - d_i/n_i. The printed equation is dimensionally and algebraically wrong. If it was used to digitize the seven NSCLC Kaplan-Meier curves (§3.2, Figure 3), the implied event counts d_i are badly biased, the MAP prior (median 4.88 months, ENE 36) is distorted, and the reported type-I error, power, bias, and RMSE in Table 3 and Figure 4 are based on a prior built from incorrect summary statistics. Since the paper's central value proposition is leveraging aggregate KM data, this is a load-bearing error, not a cosmetic typo. The Fiocco example uses a different extraction (the Parmar et al. formula in §3.1) and is not directly affected, but the design application and its conclusions are.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a Bayesian meta-analytic-predictive (MAP) approach for leveraging historical control data in trials with time-to-event endpoints. The method extends the standard MAP prior for one-dimensional parameters to piecewise exponential (PWE) hazards, adding a robust exchangeability/non-exchangeability mixture to guard against prior-data conflict. The authors describe how to derive MAP priors from historical aggregate or individual data, define an effective number of events (ENE) based on expected local information ratios, and illustrate the method in two applications: a joint analysis of ovarian carcinoma trials and the design of a non-small-cell lung cancer (NSCLC) trial. The design application reports frequentist operating characteristics under several borrowing schemes.","tokens_in":16283,"tokens_out":6398,"duration_ms":63452,"significance":"If the methodology is correct, the paper addresses a practically important problem: using published Kaplan-Meier curves to borrow historical control information in time-to-event trials, which could reduce control-arm sizes while preserving frequentist properties. The hierarchical PWE model and the robust mixture extension are natural and clinically motivated, and the use of operating-characteristic simulations is appropriate. The ENE computation via expected local information ratios is a useful contribution. However, the current manuscript contains load-bearing errors in the Kaplan-Meier data-extraction formula and in the supplied WinBUGS code, so the reported NSCLC design results and the reproducibility of both applications are not yet trustworthy. These issues are correctable, but the affected analyses must be redone.","major_comments":[{"comment":"The printed equation log(S_hat(t_{i+1})) - log(S_hat(t_i)) = 1 - d_i/n_i is algebraically incorrect. The Kaplan-Meier recursion is S(t_{i+1}) = S(t_i)(1 - d_i/n_i), so the left-hand side equals log(1 - d_i/n_i), which is approximately -d_i/n_i for small hazards, not 1 - d_i/n_i. If this formula was used to digitize the seven NSCLC Kaplan-Meier curves in Section 3.2, the extracted event counts d_i are systematically wrong. Consequently the MAP prior (median 4.88 months, ENE 36) and all operating characteristics in Table 3 and Figure 4 rest on invalid summary statistics. The extraction formula must be corrected and the entire NSCLC design analysis re-run before the central design claims can be accepted.","section":"Appendix A, Step 4"},{"comment":"The supplied WinBUGS code contains several errors that affect the reported MAC analyses. In the output loop, the lines 'log(hazard[h,s,t]) <- log.hazard.base[s,t] + inprod(Xout[h,1:Ncov],beta[1:Ncov,1])' and 'log.hazard[h,s,t] <- log(hazard.base[s,t])' appear in sequence, so the second assignment overwrites the first and the covariate/treatment effect is dropped from survival outputs. Also, the expression 'step(Nstudies-1.5)' is identically 1 for Nstudies > 1, so the random effect RE[s,t] is always included, including for the predicted new study, which contradicts the intended prediction structure. Finally, when MAP.prior=TRUE the function increments Nstudies but does not expand p.exch or the NEX mean/sd matrices, so the printed Fiocco MAP-prior call in B.3.1 indexes beyond the supplied matrix dimensions and cannot run as written. Correcting these code defects and re-running the analyses is essential for the manuscript's reproducibility.","section":"Appendix B.1, WinBUGS code"}],"minor_comments":[{"comment":"The text states that the EXNEX analysis has a median survival of 2.59 months, but Table 2 reports 2.62 years; this appears to be a units typo.","section":"Section 3.1, paragraph 5"},{"comment":"The text reports the EX median survival as 2.01 years, while Table 2 gives 2.24 years; the numbers should be reconciled.","section":"Section 3.1, paragraph 5"},{"comment":"The displayed formula for ESS_ELIR is incomplete: it ends with a dangling '=' and no closed-form expression, and the definition of the Fisher information term is split awkwardly.","section":"Equation (11)"},{"comment":"All in-text citations appear as '?' placeholders, making it impossible to verify the reference list and prior literature claims; this should be fixed.","section":"General"},{"comment":"The figure labels 'Expos/Day' and 'Events' are ambiguous; the caption and text should clarify whether these are exposure per day or total exposure, and event counts per interval.","section":"Figure 3"}],"recommendation":"major_revision","confidential_remarks":"The core methodological framework is plausible and the topic is relevant, but the empirical demonstration currently rests on an incorrect data-extraction formula and on code that cannot reproduce the reported results. I recommend major revision rather than rejection because these are fixable within the scope of the paper, provided the authors correct the formula, repair the code, and re-run the affected analyses."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis is a genuine extension of the MAP borrowing framework to piecewise exponential time-to-event data, with a robust mixture for the new-trial hazards and support for aggregate Kaplan-Meier input. The ovarian analysis and the NSCLC design study illustrate the practical appeal, and the operating-characteristic simulations are the right tool for evaluating the design. The paper deserves a serious look.\n\nThe soft spots are real but uneven. The biggest is Appendix A, Step 4. The printed equation log(S_hat(t_{i+1})) - log(S_hat(t_i)) = 1 - d_i/n_i is not the Kaplan-Meier recursion. The KM recursion gives S(t_{i+1}) = S(t_i)(1 - d_i/n_i), so the left side should equal log(1 - d_i/n_i), approximately -d_i/n_i. As printed, the formula is dimensionally wrong and would produce impossible event counts if used on the NSCLC curves. If the authors used this formula to extract the seven historical curves in Section 3.2, then the MAP prior (median 4.88 months, ENE 36) and all the reported type-I error, power, bias, and RMSE in Table 3 and Figure 4 rest on invalid summary statistics. The aggregate-data claim is central to the paper, so this is load-bearing and must be corrected and re-run. The Fiocco example uses the different Parmar et al. formula in Section 3.1, so it is not affected, but the design application is.\n\nThere are also smaller issues: the text says the EX median survival is 2.01 years while Table 2 says 2.24, and the EXNEX median is reported as 2.59 months when the table says 2.62 years. The WinBUGS code in Appendix B has suspicious lines (the duplicated log-hazard statements, the step(Nstudies-1.5) logic) that make it hard to reproduce as written. The simulation results have no Monte Carlo error bars, which is minor but worth mentioning.\n\nThe method itself is sound; the hierarchical PWE model, the robust mixture, and the ENE via ELIR are all defensible. The paper is not circular about the prior. It is a method-transfer contribution within an established framework, incremental but useful. For a trialist wanting to leverage historical controls in time-to-event settings, this is a relevant read. For a referee, the paper deserves engagement, not desk rejection, but the authors need to fix the extraction error, correct the numbers, and clean up the code before the results can be trusted.\n\nIf I were handling this, I would send it to peer review with a strong request to address the Appendix A issue. My own verdict would be conditional.","headline":"Useful MAP extension to time-to-event endpoints, but the NSCLC design results rest on an algebraically wrong Kaplan-Meier extraction formula and need correction before the aggregate-data claim can be trusted.","tokens_in":16826,"tokens_out":3784,"would_cite":false,"duration_ms":36138,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62F15","62N01","62P10"],"pacs":[],"model":"deepseek-v4-flash","headline":"A Bayesian meta-analytic prior can borrow historical control data for time-to-event trials, with a robust mixture guarding against prior-data conflict.","keywords":["historical control data","meta-analytic-predictive prior","piecewise exponential model","time-to-event endpoint","robust mixture prior","effective number of events","Bayesian clinical trial design","survival analysis"],"falsifier":"Construct a simulated cohort with known piecewise hazards and a known censoring pattern, draw its Kaplan-Meier curve, apply the paper's Appendix A extraction steps to reconstruct interval event counts and exposure times, and compare them with the true values; substantial bias under realistic late-interval deaths or non-uniform censoring would show that the extracted Poisson data are not sufficient statistics, and the operating characteristics in Section 3.2 would need re-evaluation.","tokens_in":15823,"feed_emoji":"📊","tokens_out":7714,"duration_ms":72837,"temperature":0.7,"pith_summary":"This paper claims that the meta-analytic-predictive (MAP) prior, a Bayesian method for borrowing information from historical trials, can be extended from simple one-dimensional parameters to time-to-event endpoints modeled with piecewise exponential hazards. The paper shows that historical control data, even when only Kaplan-Meier curves are available in publications, can be converted into per-interval event counts and exposure times and then combined across trials into a prior for the control hazard in a new trial. To protect against the new trial differing from the historical ones, the prior can include a robust mixture component that automatically down-weights the historical data when they conflict with the new data. If this works, trialists could run smaller, faster randomized trials by using historical controls for the control arm, while still controlling error rates.","feed_headline":"Historical control data can power smaller time-to-event trials","feed_subtitle":"A robust Bayesian prior borrows published Kaplan-Meier data, cutting control-arm size while guarding against conflicting data.","key_machinery":"The load-bearing object is the interval-wise Poisson likelihood for piecewise exponential survival, in which the number of events $r_{jk}$ in trial $j$ and interval $k$ follows $\\text{Poisson}(\\lambda_{jk} E_{jk})$, with exposure times reconstructed from published Kaplan-Meier curves. Around this likelihood, the paper builds a hierarchical model on log-hazards with a first-order dynamic linear model (a random walk on the interval means) and half-normal priors on between-trial standard deviations. The robustness mechanism is a mixture of exchangeability and non-exchangeability per interval, with fixed prior weights that are updated to posterior weights depending on how similar the new data are to the historical data. Finally, the expected local-information-ratio effective sample size converts the MCMC-based MAP prior into an effective number of events for design purposes.","core_discovery":"The central discovery is a hierarchical Poisson model for piecewise exponential survival data in which, for each time interval, the log-hazards of the historical trials and of the new trial are exchangeable normal draws around a common mean with an across-trial standard deviation. The MAP prior for the new trial's control hazards is the conditional distribution of those hazards given the historical event counts and exposure times; in the meta-analytic-combined version the historical and new data are analyzed jointly, which is equivalent to the two-step MAP approach. A robust extension replaces the exchangeability assumption with a mixture: each interval of the new trial is exchangeable with probability $w$ and comes from a weakly informative non-exchangeable prior with probability $1-w$, and the weights update dynamically in the posterior. The information content of the prior is quantified by the expected local-information-ratio effective number of events, summing the effective sample sizes across intervals. Applications to ovarian carcinoma and non-small-cell lung cancer illustrate both analysis of a new trial and design of a new trial with reduced control-arm enrollment.","pith_inferences":["A testable extension would be to simulate known survival and censoring processes, generate Kaplan-Meier curves from them, and apply the paper's digitization and exposure-time reconstruction; if the reconstructed Poisson counts are biased when deaths cluster at interval boundaries or censoring is non-uniform, the MAP prior and the reported operating characteristics would shift.","The paper's EXNEX weights are fixed per interval, but the discussion hints at trial-specific weights; allowing the weights to depend on trial-level covariates could yield a meta-regression version that explains rather than merely discounts heterogeneity.","The type-I error inflation seen under full exchangeability suggests that, in a regulatory setting, the robust mixture weight should be pre-specified and its sensitivity reported, rather than chosen after seeing the new data."],"forward_implications":["In the lung cancer design example, borrowing historical control data allowed the trial to enroll 130 patients instead of 230, with the final analysis at 110 events rather than 133.","When the true control median matches the historical data, borrowing increases power substantially; in the example, power rose from about 85 percent under stratification to over 95 percent under robust borrowing.","If the true control median is misspecified, full exchangeability can inflate type-I error above 10 percent, whereas the 50-50 robust mixture keeps it much closer to the nominal 2.5 percent.","The effective number of events of the MAP prior gives a single design-time number, here 36 or 58 events in the two applications, that trialists can use to judge how much historical information is being contributed."],"supporting_citations":[{"why":"It supplies the method for extracting per-interval event counts and exposure times from published Kaplan-Meier curves, the data input for the Poisson likelihood.","marker":"Parmar et al."},{"why":"It introduces the robust MAP/MAC prior with mixture weights and establishes the equivalence of meta-analytic-combined and meta-analytic-predictive analyses used here.","marker":"Schmidli et al."},{"why":"It defines the expected local-information-ratio effective sample size used to compute the prior effective number of events for the piecewise exponential MAP prior.","marker":"Neuenschwander et al."},{"why":"It proposes the meta-analytic-predictive prior approach that this paper extends from one-dimensional parameters to piecewise exponential time-to-event data.","marker":"Spiegelhalter et al."}],"fun_headline_variants":["Historical data shrink control-arm size in time-to-event trials","Robust Bayesian prior borrows historical data to shrink control arms","Bayesian meta-analytic prior leverages historical data for smaller trials","Borrow historical control data to design smaller time-to-event trials","Robust hierarchical model uses historical data to shrink control arms"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that event counts and exposure times reconstructed from published Kaplan-Meier curves, assuming deaths at mid-interval and constant censoring within each interval, are accurate enough that the Poisson likelihood and the resulting MAP prior are not materially biased.","fun_headline_variants_meta":{"raw":{"variants":["Historical data shrink control-arm size in time-to-event trials","Robust Bayesian prior borrows historical data to shrink control arms","Bayesian meta-analytic prior leverages historical data for smaller trials","Borrow historical control data to design smaller time-to-event trials","Robust hierarchical model uses historical data to shrink control arms"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001099,"raw_usage":{"total_tokens":4562,"prompt_tokens":895,"completion_tokens":3667,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":511,"completion_tokens_details":{"reasoning_tokens":3583}},"tokens_in":511,"tokens_out":3667,"duration_ms":24035,"temperature":1.0,"reasoning_tokens":3583,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:20:52.197323+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Construct a simulated cohort with known piecewise hazards and a known censoring pattern, draw its Kaplan-Meier curve, apply the paper's Appendix A extraction steps to reconstruct interval event counts and exposure times, and compare them with the true values; substantial bias under realistic late-interval deaths or non-uniform censoring would show that the extracted Poisson data are not sufficient statistics, and the operating characteristics in Section 3.2 would need re-evaluation.","supporting_citations":[],"review_version":1}