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arxiv: 2606.23275 · v1 · pith:ALT543H5new · submitted 2026-06-22 · 📊 stat.AP

A Bayesian Phase I/II basket design with robust information borrowing to identify subtrial-specific optimal biological doses

Zhi Cao , Haiyan Zheng , Pavel Mozgunov This is my paper

Pith reviewed 2026-06-26 06:05 UTC · model grok-4.3

classification 📊 stat.AP
keywords basket trialsdose findingoptimal biological doseBayesian designinformation borrowingphase I/II trialsEXNEX priors
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The pith

A DF-EXNEX design with adaptive borrowing improves subtrial-specific OBD selection over no-borrowing alternatives in basket trials.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a Bayesian phase I/II basket design that selects optimal biological doses separately for each subtrial rather than assuming a common dose. Toxicity follows a monotone logistic model and efficacy a quadratic curve, with extended EXNEX mixture priors placed on the subtrial-specific parameters to control borrowing strength according to observed similarity. Simulations across four subtrials, five doses, and seventy scenarios show higher rates of correct OBD selection and fewer overly toxic final recommendations than a no-borrowing NEX comparator, with gains largest when subtrials are similar. A reader would care because basket trials routinely face heterogeneous dose-response relationships that pooled analysis can misjudge.

Core claim

The DF-EXNEX design employs extended exchangeability-non-exchangeability mixture priors on subtrial-specific curve parameters, allowing borrowing to adapt automatically to subtrial similarity; in large-scale simulations this yields higher correct OBD selection rates and lower rates of toxic final recommendations than a no-borrowing design, although gains can be absent or negative when true OBD locations are widely separated.

What carries the argument

Extended EXNEX mixture priors on the subtrial-specific logistic toxicity and quadratic efficacy parameters that adapt borrowing strength to data-driven similarity measures.

If this is right

  • Correct OBD selection rises and toxic recommendations fall as subtrial similarity increases.
  • A small number of mixed low/high OBD scenarios show zero or negative gains from borrowing.
  • Posterior safety and futility rules combined with a utility function define the admissible set for each subtrial.
  • Monitoring of borrowing behavior is required when true OBDs are widely separated.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same adaptive prior structure could be applied to time-to-event or ordinal endpoints without changing the core borrowing logic.
  • Real-time diagnostics on the posterior weight placed on the exchangeability component would help detect over-borrowing in ongoing trials.
  • The design's performance under model misspecification remains untested and would be a natural next simulation target.

Load-bearing premise

The simulation study assumes the logistic toxicity and quadratic efficacy models are correctly specified in every subtrial and that the seventy scenarios cover the heterogeneity range seen in actual basket trials.

What would settle it

An independent basket trial dataset in which true subtrial-specific OBD locations are known from external evidence, with the design's final recommendations compared against those known locations.

Figures

Figures reproduced from arXiv: 2606.23275 by Haiyan Zheng, Pavel Mozgunov, Zhi Cao.

Figure 1
Figure 1. Figure 1: Sequential conduct of the basket trial dose-finding design. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Various true dose-toxicity and dose-efficacy profiles used to generate subtrials with true [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Scenario-level geom-PCS gain by subtrial similarity. Each point represents one scenario. [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
read the original abstract

The objective of modern early oncology dose-finding is to identify an optimal biological dose (OBD), rather than simply the maximum tolerated dose. In basket trials, the dose-toxicity and dose-efficacy relationships may differ across biomarker or disease-defined subtrials, so a single common dose from pooled analysis may be suboptimal. We propose a flexible exchangeability-non-exchangeability (EXNEX) dose finding design (DF-EXNEX design) for subtrial-specific OBD selection in basket phase I/II trials with binary toxicity and continuous efficacy endpoints. Patient toxicity is modelled by a monotone logistic regression and efficacy by a quadratic dose-response curve. Robust borrowing is introduced through extended EXNEX mixture priors on the subtrial-specific curve parameters, allowing the strength of borrowing to adapt to the similarity of subtrials. Dose recommendation is based on an admissible set defined by posterior safety and futility rules, and an OBD-oriented utility function combining toxicity and efficacy on comparable scales. The operating characteristics were evaluated in a large-scale simulation study for the basket trial with four subtrials and five dose levels, and 70 scenarios covering all non-redundant combinations of true subtrial-specific OBD locations. Results showed that, compared with a no-borrowing NEX design, the DF-EXNEX design can increase the correct OBD selection for most scenarios while reducing overly toxic recommendation as final OBD. The improvement increased with subtrial similarity due to robust information borrowing, but a small number of mixed low/high OBD scenarios showed negative or near-zero gains, consistent with occasional over-borrowing towards intermediate doses. These results support robust borrowing for subtrial-specific OBD finding while highlighting the need to monitor borrowing behaviour when true OBDs are widely separated.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes the DF-EXNEX design for phase I/II basket trials, employing extended EXNEX mixture priors on subtrial-specific parameters to enable robust, adaptive information borrowing. Toxicity is modeled by monotone logistic regression and efficacy by a quadratic dose-response curve; final OBD selection uses an admissible set defined by posterior safety/futility rules together with an OBD-oriented utility function. Operating characteristics are assessed in a simulation study with four subtrials, five dose levels, and 70 scenarios that exhaustively vary the locations of true subtrial-specific OBDs, showing higher correct OBD selection rates and fewer overly toxic recommendations than a no-borrowing NEX comparator, with gains increasing as subtrials become more similar.

Significance. The simulation study is large (70 scenarios) and directly compares the proposed borrowing mechanism against an external no-borrowing benchmark, providing concrete evidence on when adaptive borrowing helps or occasionally harms OBD selection. If the reported gains prove robust to realistic departures from the logistic/quadratic forms, the design would offer a practical advance for basket trials that must accommodate both borrowing and heterogeneity.

major comments (2)
  1. [Simulation study] Simulation study (abstract and corresponding section): all 70 scenarios assume the logistic toxicity and quadratic efficacy models are exactly correct for every subtrial. Because both the EXNEX borrowing mechanism and the admissible-set/utility decision rule are derived under these parametric assumptions, the absence of any misspecification scenarios (non-quadratic efficacy, non-monotone or plateau toxicity, alternative links) renders the central claim—that robust borrowing improves OBD selection—conditional on correct specification and therefore incomplete.
  2. [Abstract and methods] Abstract and methods: the EXNEX mixture hyperparameters and utility-function weights are free parameters whose calibration is not described, nor are sensitivity analyses reported; this leaves open whether the observed operating-characteristic gains are sensitive to these choices.
minor comments (2)
  1. [Abstract] The abstract states that 'the improvement increased with subtrial similarity' but does not define how similarity was quantified or how the 70 scenarios were partitioned by degree of similarity.
  2. Table or figure captions for the simulation results should explicitly state the per-subtrial sample size and total enrollment used in each scenario.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. We address the major comments point by point below, and plan to revise the manuscript to incorporate the suggested improvements.

read point-by-point responses

  1. Referee: [Simulation study] Simulation study (abstract and corresponding section): all 70 scenarios assume the logistic toxicity and quadratic efficacy models are exactly correct for every subtrial. Because both the EXNEX borrowing mechanism and the admissible-set/utility decision rule are derived under these parametric assumptions, the absence of any misspecification scenarios (non-quadratic efficacy, non-monotone or plateau toxicity, alternative links) renders the central claim—that robust borrowing improves OBD selection—conditional on correct specification and therefore incomplete.

    Authors: We agree that the simulation study is limited to scenarios where the true models match the assumed logistic toxicity and quadratic efficacy forms. This is indeed a limitation for claiming robustness of the borrowing mechanism. In the revision, we will add a new subsection with misspecification scenarios, including non-quadratic efficacy (e.g., linear or plateau) and non-monotone toxicity, to evaluate the design's performance under model misspecification. We will report the results and discuss implications for the borrowing approach. revision: yes

  2. Referee: [Abstract and methods] Abstract and methods: the EXNEX mixture hyperparameters and utility-function weights are free parameters whose calibration is not described, nor are sensitivity analyses reported; this leaves open whether the observed operating-characteristic gains are sensitive to these choices.

    Authors: We will revise the methods section to provide a detailed description of how the EXNEX mixture hyperparameters (e.g., the mixture probabilities and variance components) and the utility function weights were calibrated, including any pilot studies or references used. Furthermore, we will conduct and report sensitivity analyses by varying these parameters within reasonable ranges and assessing the impact on key operating characteristics such as correct OBD selection rates. revision: yes

Circularity Check

0 steps flagged

No significant circularity; new design evaluated via forward simulation

full rationale

The paper proposes the DF-EXNEX design and assesses its performance through large-scale forward simulation of operating characteristics across 70 scenarios, comparing against an independent no-borrowing NEX comparator. No load-bearing equations, predictions, or uniqueness claims reduce by construction to fitted inputs, self-definitions, or self-citation chains; the reported gains in OBD selection are generated from external simulation benchmarks under stated parametric assumptions rather than internal reductions. This is the standard non-circular structure for a methodological design paper.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The design rests on standard Bayesian modeling assumptions plus the specific choice of logistic and quadratic functional forms; no new physical entities are postulated. Free parameters include the hyperparameters of the EXNEX mixture priors and the utility-function weights, which are not numerically specified in the abstract.

free parameters (2)
  • EXNEX mixture hyperparameters
    Control the strength of borrowing and the probability of exchangeability; their values are chosen by the authors and affect operating characteristics.
  • Utility function weights
    Scale toxicity and efficacy onto a common utility; chosen to combine the two endpoints.
axioms (2)
  • domain assumption Toxicity follows a monotone logistic regression and efficacy follows a quadratic dose-response curve in every subtrial.
    Invoked in the model specification section of the abstract; if false the posterior probabilities and OBD selection rules lose calibration.
  • domain assumption The admissible set defined by posterior safety and futility rules correctly identifies doses that are both safe and non-futile.
    Central to the dose recommendation step; the abstract does not provide external validation of these thresholds.

pith-pipeline@v0.9.1-grok · 5859 in / 1718 out tokens · 24730 ms · 2026-06-26T06:05:37.584860+00:00 · methodology

discussion (0)

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Works this paper leans on

34 extracted references · 7 canonical work pages

  1. [1]

    and Cheung, Ying Kuen and Craddock, Charles and Garcia-Corbacho, Javier and Jaki, Thomas and Lee, S

    Yap, Christina and Billingham, Lucinda J. and Cheung, Ying Kuen and Craddock, Charles and Garcia-Corbacho, Javier and Jaki, Thomas and Lee, S. Percy and Le Tourneau, Christophe and Paoletti, Xavier and Wages, Nolan A. and Wheeler, Graham M. and Zhou, Yanhong and Sydes, Matthew R. , title =. BMJ , year =

  2. [2]

    2024 , howpublished =

    2024

  3. [3]

    Jack and Siu, Lillian L

    Le Tourneau, Christophe and Lee, J. Jack and Siu, Lillian L. , title =. Journal of the National Cancer Institute , year =

  4. [4]

    and Pestana, Roberto Carmagnani and Zabor, Emily C

    Hobbs, Brian P. and Pestana, Roberto Carmagnani and Zabor, Emily C. and Kaizer, Alexander M. and Hong, David S. , title =. Journal of Clinical Oncology , volume =. 2022 , doi =. https://doi.org/10.1200/JCO.21.02285 , abstract =

    work page doi:10.1200/jco.21.02285 2022

  5. [5]

    and Cook, John D

    Thall, Peter F. and Cook, John D. , title =. Biometrics , year =

  6. [6]

    and Qin, Rui and Sargent, Daniel J

    Mandrekar, Sumithra J. and Qin, Rui and Sargent, Daniel J. , title =. Statistics in Medicine , year =

  7. [7]

    and Wathen, J

    Thall, Peter F. and Wathen, J. Kyle and Bekele, B. Nebiyou and Champlin, Richard E. and Baker, Laurence H. and Benjamin, Robert S. , title =. Statistics in Medicine , year =

  8. [8]

    Pharmaceutical Statistics , year =

    Neuenschwander, Beat and Wandel, Simon and Roychoudhury, Satrajit and Bailey, Stuart , title =. Pharmaceutical Statistics , year =

  9. [9]

    Statistics in Medicine , volume =

    Jin, Jin and Riviere, Marie-Karelle and Luo, Xiaodong and Dong, Yingwen , title =. Statistics in Medicine , volume =. doi:https://doi.org/10.1002/sim.8675 , url =. https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.8675 , year =

    work page doi:10.1002/sim.8675

  10. [10]

    and Grayling, Michael J

    Ouma, Luke O. and Grayling, Michael J. and Wason, James M. S. and Zheng, Haiyan , title =. Journal of the Royal Statistical Society: Series C (Applied Statistics) , year =

  11. [11]

    Statistical Methods in Medical Research , year =

    Chen, Xin and Zhang, Jiaxin and Yuan, Ying and others , title =. Statistical Methods in Medical Research , year =

  12. [12]

    and Takeda, Kentaro and Yuan, Ying , title =

    Wang, Shuqi and Thall, Peter F. and Takeda, Kentaro and Yuan, Ying , title =. Biometrics , year =

  13. [13]

    2025 , eprint=

    Robust Bayesian hierarchical models for basket trials enabling joint evaluation of toxicity and efficacy , author=. 2025 , eprint=

    2025

  14. [14]

    and Landin, Rodrigo , title =

    Hobbs, Brian P. and Landin, Rodrigo , title =. Statistics in Medicine , year =

  15. [15]

    2017 , howpublished =

    2017

  16. [16]

    JNCI: Journal of the National Cancer Institute , volume =

    Design of Phase II Cancer Trials Using a Continuous Endpoint of Change in Tumor Size: Application to a Study of Sorafenib and Erlotinib in Non–Small-Cell Lung Cancer , author =. JNCI: Journal of the National Cancer Institute , volume =. 2007 , month =. doi:10.1093/jnci/djm158 , publisher =

    work page doi:10.1093/jnci/djm158 2007

  17. [17]

    Circulating tumor DNA to monitor treatment response in solid tumors and advance precision oncology

    Bartolomucci, Alexandra and Nobrega, Monyse and Ferrier, Tadhg and Dickinson, Kyle and Kaorey, Nivedita and Nadeau, Am \'e lie and Castillo, Alberto and Burnier, Julia V. Circulating tumor DNA to monitor treatment response in solid tumors and advance precision oncology. NPJ Precis. Oncol

  18. [18]

    Sample sizes in dosage investigational clinical trials: a systematic evaluation

    Huang, Ji-Han and Su, Qian-Min and Yang, Juan and Lv, Ying-Hua and He, Ying-Chun and Chen, Jun-Chao and Xu, Ling and Wang, Kun and Zheng, Qing-Shan. Sample sizes in dosage investigational clinical trials: a systematic evaluation. Drug Des Devel Ther

  19. [19]

    and Gonen, Mithat and Shen, Ronglai and Hyman, David M

    Cunanan, Kristen M. and Gonen, Mithat and Shen, Ronglai and Hyman, David M. and Riely, Gregory J. and Begg, Colin B. and Iasonos, Alexia , title =. Journal of Clinical Oncology , volume =. 2017 , doi =

    2017

  20. [20]

    Hyman and Igor Puzanov and Vivek Subbiah and Jason E

    David M. Hyman and Igor Puzanov and Vivek Subbiah and Jason E. Faris and Ian Chau and Jean-Yves Blay and Jürgen Wolf and Noopur S. Raje and Eli L. Diamond and Antoine Hollebecque and Radj Gervais and Maria Elena Elez-Fernandez and Antoine Italiano and Ralf-Dieter Hofheinz and Manuel Hidalgo and Emily Chan and Martin Schuler and Susan Frances Lasserre and ...

    2015

  21. [21]

    JCO Precision Oncology , year =

    Lin, Ruitao and Zhou, Yanhong and Yan, Fangrong and Li, Daniel and Yuan, Ying , title =. JCO Precision Oncology , year =

  22. [22]

    Braun , title =

    Thomas M. Braun , title =. Chinese Clinical Oncology , volume =. 2014 , issn =

    2014

  23. [23]

    and Lu, Karen H

    Yan, Fangrong and Thall, Peter F. and Lu, Karen H. and Gilbert, Mark R. and Yuan, Ying , title =. Annals of Oncology , year =

  24. [24]

    Morris, Ian R

    Morris, Tim P. and White, Ian R. and Crowther, Michael J. , title =. Statistics in Medicine , volume =. doi:10.1002/sim.8086 , url =. https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.8086 , year =

    work page doi:10.1002/sim.8086

  25. [25]

    Biostatistics , volume =

    Mozgunov, Pavel and Jaki, Thomas and Paoletti, Xavier , title = ". Biostatistics , volume =. 2018 , month =. doi:10.1093/biostatistics/kxy045 , url =

    work page doi:10.1093/biostatistics/kxy045 2018

  26. [26]

    and Horton, Bethany Jablonski and Conaway, Mark R

    Wages, Nolan A. and Horton, Bethany Jablonski and Conaway, Mark R. and Petroni, Gina R. , title =. Contemporary Clinical Trials , year =

  27. [27]

    2024 , eprint=

    Partial Ordering Bayesian Logistic Regression Model for Phase I Combination Trials and Computationally Efficient Approach to Operational Prior Specification , author=. 2024 , eprint=

    2024

  28. [28]

    Statistical Methods in Medical Research , volume =

    Nan Chen and J Jack Lee , title =. Statistical Methods in Medical Research , volume =. 2020 , doi =

    2020

  29. [29]

    Biostatistics , volume =

    Zheng, Haiyan and Wason, James M S , title = ". Biostatistics , volume =. 2022 , month =. doi:10.1093/biostatistics/kxaa019 , url =

    work page doi:10.1093/biostatistics/kxaa019 2022

  30. [30]

    Biostatistics , year =

    Lin, Ruitao and Yin, Guosheng and Shi, Haolun , title =. Biostatistics , year =

  31. [31]

    and Mozgunov, Pavel , title =

    Chen, Weishi and Liu, Li and Wages, Nolan A. and Mozgunov, Pavel , title =. Statistics in Medicine , volume =. doi:10.1002/sim.70345 , url =. https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.70345 , abstract =

    work page doi:10.1002/sim.70345

  32. [32]

    Clinical Trials , year =

    Daniells, Libby and Jaki, Thomas and Dayimu, Alimu and Demiris, Nikos and Bristi, Basu and Symeonides, Stefan and Mozgunov, Pavel , title =. Clinical Trials , year =

  33. [33]

    , title =

    Thall, Peter F. , title =. 2024 , doi =

    2024

  34. [34]

    Expansion Cohorts: Use in First-in-Human Clinical Trials to Expedite Development of Oncology Drugs and Biologics , year =