{"id":"950cd6c5-0d11-45ba-8a5d-4ec7d18be527","arxiv_id":"1908.05091","paper_version":3,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A Bayesian method for basket trials uses Hellinger distance between subtrial posteriors to set spike-and-slab borrowing weights, improving precision and power in simulations.","lead":"This paper proposes a Bayesian method for basket trials that automatically borrows information only from patient subgroups with similar treatment effects, using a statistical distance called the Hellinger distance to decide how much to borrow. The method is designed for continuous endpoints and could help smaller subgroups in chronic disease trials gain statistical power without being overwhelmed by inconsistent data from other subgroups.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Hellinger distance is used directly as the probability of incommensurability; under equal treatment effects its sampling noise is non-negligible, so the claimed borrowed-information gains may be miscalibrated.","rationale":"The reader's weakest assumption identifies exactly the step on which the central claim rests: the Hellinger distance between operational posteriors is treated as a prior probability of incommensurability. I agree that this is the load-bearing point. The paper provides no formal derivation for w = d_H, no propagation of the estimation uncertainty in d_H, and no calibration check under the null of equal treatment effects. The simulation study is substantial and the code is available, but it does not separate the signal in d_H from finite-sample noise. Supplementary Section D gives useful illustrative examples and honestly notes that extreme sample-size imbalance and cross-subtrial variance heterogeneity are beyond scope, but it does not resolve the calibration question. A focused simulation under a global null, comparing the distribution of d_H and the resulting weights across replicates, and comparing the proposed method against a version with w fixed at zero, would directly test whether the miscalibration materially changes the claimed precision and power gains. Because this concern is real but not shown to overturn the method, the reader's CONDITIONAL verdict remains appropriate.","tokens_in":21149,"tokens_out":4593,"duration_ms":53914,"concrete_test":"Run a simulation study under the exact design of Section 4.1 with a global null (e.g., all theta_k = 0.45, or all theta_k = 0), 10,000 replicates. For each replicate, record (i) the pairwise Hellinger distances d_H defined in Eq. (6), (ii) the resulting slab probabilities w_{kk*} = d_H, (iii) the normalized weights p_{kk*} from Eq. (11), and (iv) the posterior MSE and type I error of the proposed method. Compare the null distribution of d_H to its distribution under a heterogeneous scenario such as Scenario 4. If the null distribution has median substantially above 0 and overlaps the heterogeneous distribution, the distance does not separate commensurability from sampling noise.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3 sets w_{kk*} = d_H(pi_k, pi_k*) in Eq. (5), i.e., the plug-in Hellinger distance between operational posteriors is interpreted as the prior probability that subtrials k and k* are incommensurable. This is the central calibration step: it sets the spike-and-slab mass and, through Eq. (11), the weights p_{kk*}. The distance is a random variable estimated from the same data that are later used as the likelihood in Eq. (10); no uncertainty in d_H is propagated. More importantly, d_H measures the discrepancy between finite-sample posterior distributions, not the discrepancy between true treatment effects. Even when theta_k = theta_k*, the posterior densities differ because of sampling variability; with n_k = 10 and sigma = 0.4, the standard error of the treatment-effect estimate is about 0.18, producing Hellinger distances of order 0.1-0.3 between repeated datasets with equal true effects. Thus w_{kk*} is systematically positive under perfect consistency, and under true inconsistency small samples make posteriors diffuse, compressing d_H toward 0. The claimed precision and power gains in Section 4.2 depend on w_{kk*} being a reliable prior probability, but no calibration, shrinkage, or uncertainty propagation is provided. Supplementary Section D only illustrates two simulated datasets; it does not quantify the null distribution of d_H or show that the mapping w = d_H is calibrated.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper develops a Bayesian methodology for borrowing information across patient subgroups in randomised, placebo-controlled basket trials with a continuous endpoint. After covariate adjustment via linear regression, the evidence from each subtrial is summarised by an 'operational posterior.' The Hellinger distance d_H between the operational posteriors of two subtrials is used as (i) the prior probability w_{kk*} with which a spike-and-slab prior on the precision parameter of a commensurate predictive prior is in the discounting 'slab' component (Eqs. (5)-(6)), and (ii), for K >= 3, as the input to a softmax-type transform producing combination weights p_{kk*} (Eq. (11)) that merge the (K-1) commensurate predictive priors into a normal marginal predictive prior (Eqs. (8)-(9)), which is then updated with the contemporary subtrial data (Eq. (10)). Operating characteristics are assessed by simulation under nine scenarios with K = 6 subtrials of unequal sample sizes and 10,000 replicates, comparing the proposed method with a standard hierarchical model, a no-borrowing analysis, and the EXNEX model on bias, MSE, credible interval width, an analogue of type I error, and an analogue of power. The authors report lower bias and MSE in most scenarios, narrower credible intervals when consistent sources exist, higher power in several scenarios, and the ability to up-weight the most commensurate source; type I error results are reported honestly.","tokens_in":21595,"tokens_out":35255,"duration_ms":302529,"significance":"The problem is timely and the central idea, letting a distributional discrepancy measure govern the amount of borrowing without assuming exchangeability, is attractive. If fully established, the contribution would be useful: it extends commensurate-prior borrowing to non-oncology basket trials with continuous endpoints, uses a symmetric and transformation-invariant measure, handles K >= 3 by differential weighting, and is accompanied by reproducible code and a carefully designed simulation study (nine scenarios, 10,000 replicates, including mixed-null and global-null cases). The supplementary sensitivity analyses for the tuning scale s0 and for unequal sample sizes are additional strengths, as is the explicit acknowledgment that the slab component of the spike-and-slab prior is not calibrated. However, the load-bearing calibration step w = d_H is not justified, the data are used twice in constructing the prior, and an approximation in forming the marginal predictive prior is unexamined, as detailed below. These issues must be addressed before the precision and power claims can be accepted; the manuscript is therefore of genuine interest but not yet in publishable form.","major_comments":[{"comment":"The stipulation w_{kk*} = d_H(π_{θ_k}, π_{θ_{k*}}) treats a plug-in Hellinger distance between finite-sample operational posteriors as the prior probability of incommensurability. With the essentially flat operational prior N(0, 10^2) used here, the posterior variance v is close to the sampling variance of the treatment-effect estimate, and the difference between two independent posterior means under equal true effects has variance 2v; the exponent in the Hellinger integrand then has mean 1/4, so the expected d_H under perfect consistency is around 0.4, essentially independent of n for pairs with comparable sample sizes, and larger still when posterior variances differ (for the paper's settings, v is about 0.064 at n = 10, σ = 0.4). The spike mass 1 - w_{kk*} is thus systematically well below 1 when subtrials are truly consistent, the convergence to complete pooling asserted in the note after Eq. (11) is a probability-zero idealisation, and the method borrows less than intended in the situations where borrowing is most valuable. Conversely, for genuinely discrepant effects the finite-sample noise compresses d_H for small subtrials. No calibration of the w = d_H mapping, no null-distribution analysis, and no propagation of the estimation uncertainty in d_H are provided; Supplementary Section D only illustrates two K = 2 datasets and does not quantify the sampling distribution of d_H. The Discussion's remark that the slab prior is not calibrated is welcome but does not cover this more consequential calibration. Because w_{kk*} and p_{kk*} set the amount of borrowing, the precision and power gains reported in Section 4.2 are not yet supported.","section":"Section 3, Eqs. (5)-(6)"},{"comment":"The marginal predictive prior for θ_{k*} depends on the contemporary data through the Hellinger distance d_{kk*} = d_H(π(θ_k|x_k), π(θ_{k*}|x_{k*})), which enters both w_{kk*} in Eq. (5) and p_{kk*} in Eq. (11); the notation π_MPP(θ_{k*}|x_{(-k*)}) is therefore misleading because the 'prior' is a function of x_{k*} itself. Eq. (10) then multiplies this data-dependent prior by the likelihood L(x_{k*}|θ_{k*}), using x_{k*} twice. The resulting object is not a proper Bayesian posterior, and the manuscript does not flag this plug-in or empirical-Bayes aspect. The credible-interval widths and MSE values in Section 4.2 and in Figures 1 and S2 are valid frequentist summaries of a well-defined procedure, but interpreting the narrower intervals as a Bayesian gain is not justified, and the double use could plausibly inflate the apparent precision advantage. The authors should either reframe the method explicitly as empirical Bayes or quantify the effect of the double use, for example by comparing with a version in which d_{kk*} is computed from the complementary data alone plus a held-out portion of x_{k*}.","section":"Section 3, Eqs. (6), (10)-(11)"},{"comment":"The marginal CPP in Eq. (7) is a scale mixture over the operational posterior of θ_k and the spike-and-slab prior on ν_{kk*}, so it is not exactly normal; the statement that it 'may be represented as a N(λ_k, ξ_k^2) distribution for the ease of notations' is an unexamined approximation, with no moment-matching calculation or error assessment. Relatedly, the synthesis of the (K-1) sources as a weighted sum of independent normals in Eq. (8), with variance Σ_k p^2_{kk*} ξ_k^2, is one of several possible ways to combine predictive priors (a mixture or product combination would behave differently), and no argument establishes that the convolution form is the appropriate one. The adequacy of both the normality approximation and the weighted-sum combination should be demonstrated, at least in a simple K = 3 example against the exact predictive distribution, because the resulting MPP is the prior that drives the posterior inference in Eq. (10).","section":"Section 3, Eqs. (7)-(9)"}],"minor_comments":[{"comment":"The claim that 'only information from subtrial(s) with the most commensurate treatment effect is leveraged' overstates the method, since every p_{kk*} in Eq. (11) is strictly positive and every complementary subtrial therefore contributes, however slightly, to the marginal predictive prior in Eq. (8); 'predominantly' would be accurate, and the rest of the text indeed describes down-weighting rather than elimination.","section":"Abstract / Section 1"},{"comment":"The credible-interval comparison is referenced as 'Figure S1 of the Supplementary Materials,' but the relevant figure is S2; Figure S1 displays the prior density of the CPP standard deviation under the slab prior.","section":"Section 4.2"},{"comment":"The sample-size labels in the column headers ('2 (n3 = 10)', '3 (n2 = 14)', '4 (n5 = 16)', '5 (n4 = 20)') do not match the order n_k in {10, 10, 14, 16, 20, 20} stated in Section 4.1, making the scenario table hard to read; please correct the labels and keep the subtrial numbering consistent throughout.","section":"Table 1"},{"comment":"The spike-and-slab prior is defined only through its CDF; writing the mixture explicitly as g_k(ν) = w_{kk*}/(B2 - B1) on [B1, B2] plus a point mass (1 - w_{kk*}) at ν = S would be clearer and would remove the ambiguity concerning the behaviour of the distribution on (B2, S).","section":"Section 3, Eq. (5)"},{"comment":"The choice s0 = 0.15 is motivated only as 'to leverage information from all other subtrials'; the sensitivity analysis in Supplementary Section C examines the effect of s0 on the allocated weights but not on downstream operating characteristics (MSE, power, type I error), so how the headline conclusions depend on this tuning parameter remains unclear.","section":"Section 4.1"},{"comment":"The reported Hellinger distances appear inconsistent with the stated operational posteriors. For the σ = 0.4 unequal-size example, the posteriors are given as N(0.762, 0.19^2) and N(0.863, 0.05^2); the Hellinger distance between these two normal densities is approximately 0.59, not the reported 0.08, whether 0.19 and 0.05 are read as standard deviations or as variances. The σ = 0.8 examples likewise report 0.16 where the stated densities give distances of about 0.03 and 0.61. The illustration should be recomputed or the parameter values clarified.","section":"Supplementary Section D"},{"comment":"Several typos should be corrected, including 'dφH' after Eq. (6) (should be d_H), 'contemparory' in Section 1 (should be 'contemporary'), and 'accroding' in Supplementary Section C (should be 'according').","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is well organised, clearly written, and the simulation study is a genuine strength. My substantive reservations are the two load-bearing issues in the major comments: the uncalibrated identification of the Hellinger distance with the prior probability of incommensurability, and the dependence of the marginal predictive prior on the contemporary subtrial data themselves. Both are, in principle, fixable in a major revision, ideally by adding a calibration analysis of the null distribution of d_H across the range of subtrial sample sizes the method targets, and by comparing the proposed plug-in procedure with a version that avoids the double use of x_{k*}. I would also ask the authors to re-examine the numbers in Supplementary Section D and the labelling of Table 1, which currently contain internal inconsistencies. Conditional on these points being satisfactorily addressed, I would regard the contribution as a worthwhile addition to the basket-trial methods literature."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear [Name],\n\nYou should know this paper is a workmanlike new Bayesian borrowing scheme for basket trials with continuous endpoints, and it's worth a look if you do trial design. The new trick is to use the Hellinger distance between subtrial operational posteriors to set the spike-and-slab prior mass in the commensurate-prior framework, and then to combine the point-to-point commensurate priors with a softmax weight for K≥3 subtrials. That's a real extension of the literature, and the paper is honest about its limits.\n\nWhat's good: the simulation study is broad (9 scenarios, 10,000 replicates), the code is on GitHub, and the comparisons include standard hierarchical models and EXNEX. The method plausibly gives smaller MSE and better power in the scenarios where some subtrials are consistent and others are not. The authors also note the type I error inflation in mixed-null scenarios, and the supplementary addresses rare-disease sample-size imbalances with a couple of illustrative examples. That's reasonable practice.\n\nThe soft spot is the central calibration step. Eq. (5) sets w_kk* directly equal to the Hellinger distance between the two operational posteriors and calls it the prior probability that the subtrials are incommensurable. That distance is a random variable estimated from the same data that later form the likelihood, and its uncertainty is not propagated. Under perfect consistency, the distance is positive just from sampling noise; under inconsistency, small samples compress it toward zero. The paper doesn't justify the probabilistic interpretation or provide a calibration check. This is not just cosmetic: the amount of borrowing, and thus the claimed precision and power gains, depend on that mapping. A supplementary section with two simulated datasets is not enough to establish reliability.\n\nThe normal approximation of the marginal predictive prior is also a bit quick, though expected in this kind of work. And the simulation scenarios are generated from a correlation structure that rewards methods which can identify clusters, so the favorable results are not an independent validation. These are addressable, not fatal.\n\nVerdict: this deserves a serious referee. I'd send it to peer review with a request to add a calibration study of the Hellinger distance (e.g., a simulation under the null of equal effects quantifying the distribution of w) and to discuss the double use of the data. I wouldn't cite it in my own work until that is done, but it's a solid building block for people working on basket trial methodology.\n\nBest,\n[Name]","headline":"A useful new borrowing mechanism for basket trials, undermined by an uncalibrated and double-used Hellinger-distance prior; worth peer review with a calibration study required.","tokens_in":21977,"tokens_out":4705,"would_cite":false,"duration_ms":45815,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62F15","62P10"],"pacs":[],"model":"deepseek-v4-flash","headline":"A basket trial can decide how much information each subtrial borrows from the others by measuring the Hellinger distance between their posterior treatment-effect densities, improving precision and potentially statistical power.","keywords":["basket trials","Hellinger distance","hierarchical models","precision medicine","robustness","information borrowing","commensurate priors","spike-and-slab prior"],"falsifier":"Simulate two subtrials with identical true treatment effects but strongly imbalanced sample sizes (for example $n_1 = 20$ versus $n_2 = 200$) under the paper's own data-generating model and compute the Hellinger distance between their operational posteriors over many replicates. If the average distance grows with the sample-size imbalance even though the effects are equal, the borrowing weight is systematically discounted exactly when the small subtrial needs the large subtrial's information, and the claimed calibration of distance to borrowing probability fails.","tokens_in":20979,"feed_emoji":"📊","tokens_out":16997,"duration_ms":137152,"temperature":0.7,"pith_summary":"This paper develops a Bayesian method for randomised, placebo-controlled basket trials with a continuous endpoint that lets each subtrial borrow statistical strength from the other subtrials, but only from those whose treatment effects are genuinely similar. Borrowing is controlled by a spike-and-slab prior on a precision factor, and the probability of down-weighting a source subtrial is set directly by the Hellinger distance between the two subtrials' posterior distributions of the treatment effect — a symmetric measure of dissimilarity between probability distributions, running from 0 (identical) to 1 (completely different). When three or more subtrials are analysed, the pairwise borrowed information is combined into a marginal predictive prior whose weights decay exponentially with this distance, so the most commensurate subtrial dominates. In simulations motivated by a chronic-disease basket trial, the method yields lower bias and mean squared error than standard hierarchical or EXNEX models, narrower credible intervals, and controlled error rates. The authors claim two practical advantages over alternative Bayesian models: identifying the most commensurate source of information and gauging the degree of borrowing from each specific subtrial.","feed_headline":"Similarity score decides how much basket subtrials share","feed_subtitle":"Bayesian weights from the Hellinger distance share data only between subgroups with matching treatment effects.","key_machinery":"The central object is the commensurate predictive prior (CPP) with a spike-and-slab prior on the precision factor $ν_{kk⋆}$, weighted by the Hellinger distance between operational posteriors. For a target subtrial $k⋆$ and a source subtrial $k$, the CPP is a normal prior $θ_{k⋆} | θ_k, ν_{kk⋆} ∼ N(θ_k, 1/ν²_{kk⋆})$ centred at the source's treatment effect; the precision factor $ν_{kk⋆}$ decides whether the source data are pooled in (spike at $S$) or discarded (slab uniform on $[B_1, B_2]$, set to $[0.01, 1]$ with $S = 100$ in the simulations). The weight $w_{kk⋆}$ on the slab, interpreted as the probability of incommensurability, is set equal to the Hellinger distance between the two subtrials' posterior densities, which is symmetric, bounded in $[0,1]$, and invariant to reparameterisation. For $K ≥ 3$, the pairwise CPPs are mixed into a marginal predictive prior using weights $p_{kk⋆} = exp(−d_{kk⋆}/s_0) / Σ_k exp(−d_{kk⋆}/s_0)$, whose sensitivity to the pairwise distances is controlled by the tuning constant $s_0$, chosen small enough (0.15 in the simulations) to keep discrimination between commensurate and incommensurate sources. This machinery lets the trial borrow different amounts from each subtrial without assuming exchangeability or pre-specifying clusters of similar subgroups.","core_discovery":"The central claim is that a distributional discrepancy, specifically the Hellinger distance between the posterior densities of the treatment effect in two subtrials, can serve as a direct measure of commensurability that governs information borrowing in a basket trial. The paper sets the spike-and-slab prior weight $w_{kk⋆}$ equal to the Hellinger distance $d_H(π_{θ_k}, π_{θ_{k⋆}})$: a distance near zero concentrates prior mass on the 'spike', so the complementary subtrial's data are essentially pooled in, while a distance near one concentrates mass on the 'slab', discarding the complementary data. For $K ≥ 3$ subtrials, the pairwise commensurate predictive priors are combined into a marginal predictive prior with weights $p_{kk⋆} = exp(−d_{kk⋆}/s_0)$ normalised across sources, so only the most commensurate subtrial(s) effectively contribute. Updating this marginal predictive prior with the contemporary subtrial's own data yields a robust posterior for Go/No-go decisions. Simulation results show improved precision and potentially improved power relative to no borrowing, standard hierarchical models, and EXNEX, together with the ability to identify the most commensurate source and to quantify how much each subtrial contributes.","pith_inferences":["The Hellinger distance is treated as a calibrated probability without propagating its own estimation uncertainty into the posterior; a calibration study regressing true effect differences on the derived weights across sample-size configurations would show how much miscalibration remains, especially when one subtrial is much larger than another.","The tuning constant $s_0$ acts as a temperature for the weight transformation: a principled choice could be derived by targeting a desired error-rate ceiling or a minimum power gain instead of being fixed at 0.15.","The same discrepancy-weighted borrowing idea transfers naturally to umbrella or platform trials whose arms open asynchronously, where the 'most commensurate source' could be re-selected adaptively as data accumulate, connecting this work to dynamic borrowing in sequential designs.","The method's Go/No-go criterion can be tracked against the borrowing weights in interim analyses, giving a direct way to quantify how information sharing interacts with repeated-look type I error inflation."],"forward_implications":["In a basket trial with at least three subtrials, the analysis identifies the most commensurate source subtrial(s) and assigns them the largest weight in the marginal predictive prior, so borrowing concentrates where the treatment effects genuinely match.","Estimates of a subtrial's treatment effect gain precision (narrower credible intervals, lower MSE) whenever at least one complementary subtrial has a similar effect, while inconsistent subtrials contribute little or nothing.","The method collapses to complete pooling when all pairwise Hellinger distances are zero and to no borrowing when they are near one, recovering both conventional extremes as special cases.","The same Hellinger-distance-weighted borrowing scheme can be applied to binary endpoints or other generalised linear models after fitting per-subtrial regressions, extending the approach beyond continuous endpoints.","In mixed-null and global-null scenarios, the method's analogue of the type I error rate stays well below the no-borrowing approach under the global null and below the hierarchical and EXNEX alternatives when non-null subtrials have large effects, because sharing is limited to commensurate subtrials."],"supporting_citations":[{"why":"Supplies the commensurate predictive prior and the spike-and-slab prior on the precision factor that the paper adapts from historical-data borrowing to concurrent subtrials.","marker":"Hobbs et al. (2011, 2012)"},{"why":"Source of the spike-and-slab prior distribution placed on the normal precision parameter.","marker":"Mitchell and Beauchamp (1988)"},{"why":"The robust-Bayesian divergence-measure setting from which the Hellinger distance choice is taken.","marker":"Dey and Birmiwal (1994)"},{"why":"The robust EXNEX hierarchical model that serves as the principal comparator in the simulation study.","marker":"Neuenschwander et al. (2016)"},{"why":"The pairwise exchangeability-monitoring basket design that motivates borrowing weights without full Bayesian model averaging, a close alternative.","marker":"Hobbs and Landin (2018)"},{"why":"Justifies the half-normal prior specification used for the random-effect standard deviations of the covariate coefficients.","marker":"Cunanan et al. (2019)"},{"why":"Background on Bayesian hierarchical modelling for borrowing across patient subpopulations in phase II oncology trials.","marker":"Berry et al. (2013)"}],"fun_headline_variants":["Hellinger distance tunes basket trial data sharing","Basket trials: borrow only from matching subtrials","Distance rule decides how much subtrials share","Similarity metric controls borrowing in basket trials","Let Hellinger distance set the sharing in basket trials"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the Hellinger distance between two subtrials' estimated treatment-effect distributions is a faithful, well-calibrated probability that the subtrials should not share information; if sample-size imbalance or estimation noise distorts that distance, the trial borrows the wrong amount and the claimed gains in precision and power do not follow.","fun_headline_variants_meta":{"raw":{"variants":["Hellinger distance tunes basket trial data sharing","Basket trials: borrow only from matching subtrials","Distance rule decides how much subtrials share","Similarity metric controls borrowing in basket trials","Let Hellinger distance set the sharing in basket trials"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000204,"raw_usage":{"total_tokens":1460,"prompt_tokens":1090,"completion_tokens":370,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":706,"completion_tokens_details":{"reasoning_tokens":296}},"tokens_in":706,"tokens_out":370,"duration_ms":4269,"temperature":1.0,"reasoning_tokens":296,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T13:24:04.635026+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate two subtrials with identical true treatment effects but strongly imbalanced sample sizes (for example $n_1 = 20$ versus $n_2 = 200$) under the paper's own data-generating model and compute the Hellinger distance between their operational posteriors over many replicates. If the average distance grows with the sample-size imbalance even though the effects are equal, the borrowing weight is systematically discounted exactly when the small subtrial needs the large subtrial's information, and the claimed calibration of distance to borrowing probability fails.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the commensurate predictive prior and the spike-and-slab prior on the precision factor that the paper adapts from historical-data borrowing to concurrent subtrials."},{"cited_title":"and Beauchamp, J","cited_arxiv_id":null,"evidence_quote":"Source of the spike-and-slab prior distribution placed on the normal precision parameter."},{"cited_title":"and Birmiwal, L","cited_arxiv_id":null,"evidence_quote":"The robust-Bayesian divergence-measure setting from which the Hellinger distance choice is taken."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The robust EXNEX hierarchical model that serves as the principal comparator in the simulation study."},{"cited_title":"and Landin, R","cited_arxiv_id":null,"evidence_quote":"The pairwise exchangeability-monitoring basket design that motivates borrowing weights without full Bayesian model averaging, a close alternative."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Justifies the half-normal prior specification used for the random-effect standard deviations of the covariate coefficients."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Background on Bayesian hierarchical modelling for borrowing across patient subpopulations in phase II oncology trials."}],"review_version":1}