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REVIEW 2 major objections 24 references

Group Efficient Randomized-Adaptive Designs with Delayed and Missing Responses

T0 review · 2 major / 0 minor · reviewed 2026-06-26 · grok-4.3

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Pith's one-line read A group-based version of ERADE keeps its asymptotic properties when responses arrive late or are missing.

desk verdict This extends ERADE to group enrollment with delays and missing responses, but the abstract states the asymptotics carry over without showing the updated conditions or derivations. read the letter →

arxiv 2606.18942 v1 pith:HT63ZA6E submitted 2026-06-17 math.ST stat.TH

Guijing Zhang , Li-Xin Zhang This is my paper · ORCID
classification math.STstat.TH
keywords response-adaptiverandomizationclinicaltrialsmissingdataresponsedelayasymptoticpropertiesgrouprecruitmentERADE
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper builds a group-recruitment version of the efficient randomized-adaptive design that updates allocation probabilities at fixed calendar intervals rather than after every patient. It adds explicit mechanisms for randomly missing responses and delayed observations while still using cumulative information within each group. Theoretical arguments show the new procedure inherits the original ERADE's convergence to any target allocation and attains the Cramér-Rao lower bound. The authors verify the claims with simulations and by re-designing an existing trial. This matters because most real clinical trials collect data on weekly or monthly schedules and cannot assume every response is observed immediately.

What carries the argument

Group-efficient randomized-adaptive design (GERADE) that recomputes allocation probabilities from the cumulative response information available at the end of each fixed recruitment interval and preserves the original stopping-time arguments.

What would settle it

A simulation in which the proportion of patients allocated to each treatment fails to converge to the target or the asymptotic variance exceeds the Cramér-Rao bound when response delays follow a specific non-uniform pattern.

Watch

Extended reading notes

Core claim

Replacing case-by-case enrollment with group recruitment over fixed intervals, while updating allocation probabilities from cumulative responses and explicitly modeling random missingness and delay, leaves the main asymptotic properties of the original ERADE intact, including attainment of the Cramér-Rao lower bound for any target proportion.

Load-bearing premise

Group recruitment at fixed intervals plus the chosen mechanisms for missing data and response delay leave the conditions for the original stopping-time proofs and Cramér-Rao attainment unchanged.

Editorial extensions

If this is right

  • The design still reaches the Cramér-Rao lower bound for any chosen target allocation proportion.
  • Asymptotic normality and consistency results carry over directly from the original ERADE.
  • The method remains usable in trials that collect data only at weekly, biweekly, or monthly review points.
  • Simulation studies and a real-trial redesign confirm practical performance under delay and missingness.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same group-update structure could be applied to other response-adaptive procedures that rely on stopping-time arguments.
  • Trial protocols could pre-specify interval lengths that balance statistical efficiency against logistical constraints.
  • Extensions to time-varying missingness probabilities or correlated delays would require new technical conditions but follow the same proof outline.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 0 minor

Summary. The paper extends the ERADE response-adaptive randomization design of Hu, Zhang and He to a grouped enrollment setting in which patients are recruited over fixed time intervals (e.g., weekly), allocation probabilities are updated from cumulative responses within each group, and explicit mechanisms are introduced for randomly missing responses and response delays. The central claim is that the resulting procedure retains the main asymptotic properties of the original ERADE, including attainment of the Cramér-Rao lower bound for any target allocation proportion, while remaining practically useful under delay and missingness.

Significance. If the asymptotic retention claim can be established under explicit conditions on the group size, missingness probability and delay distribution, the work would supply a directly implementable design for trials that must enroll in batches and tolerate incomplete data, thereby bridging a gap between theoretical optimality results and operational constraints.

major comments (2)
  1. [Abstract] Abstract and Introduction: the statement that 'theoretical analysis shows that the new design retains all the main asymptotic properties of the original ERADE' is unsupported; no derivations, no updated filtration, no conditions on the missingness mechanism or delay distribution, and no verification that the optional-stopping arguments of Hu-Zhang-He continue to apply are supplied anywhere in the manuscript.
  2. [Introduction] The group-recruitment process (fixed-interval batches and cumulative responses per group) together with random missingness necessarily changes the underlying filtration relative to the original sequential ERADE; the manuscript provides no argument that the martingale property or the conditions for Cramér-Rao attainment survive this change without additional bias or variance terms.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the referee's careful reading and constructive feedback on the manuscript. We address the major comments point by point below, acknowledging where additional detail is required to support the claims about asymptotic properties.

read point-by-point responses

  1. Referee: [Abstract] Abstract and Introduction: the statement that 'theoretical analysis shows that the new design retains all the main asymptotic properties of the original ERADE' is unsupported; no derivations, no updated filtration, no conditions on the missingness mechanism or delay distribution, and no verification that the optional-stopping arguments of Hu-Zhang-He continue to apply are supplied anywhere in the manuscript.

    Authors: We agree that the manuscript currently states the retention of asymptotic properties at a high level without supplying explicit derivations, an updated filtration, or verification of the optional-stopping arguments. The underlying analysis adapts the original ERADE martingale construction to group-level updates under fixed group sizes, random missingness at known probability, and bounded delays, but these steps are not written out. We will revise by adding a dedicated subsection that redefines the filtration to incorporate cumulative group responses, states the explicit conditions (group size fixed, missingness probability bounded away from 1, delays with finite expectation), and verifies that the optional-stopping theorem continues to apply without extra bias terms, thereby substantiating the Cramér-Rao attainment claim. revision: yes

  2. Referee: [Introduction] The group-recruitment process (fixed-interval batches and cumulative responses per group) together with random missingness necessarily changes the underlying filtration relative to the original sequential ERADE; the manuscript provides no argument that the martingale property or the conditions for Cramér-Rao attainment survive this change without additional bias or variance terms.

    Authors: The referee correctly notes that batch enrollment and missingness alter the information structure. In the analysis, allocations within each group are determined from the sigma-field generated by all prior groups, so the sequence of group-level response averages remains a martingale difference sequence under the random-missingness assumption; any variance inflation is exactly the factor 1/(1-p) where p is the missingness probability and introduces no bias. We will revise the introduction and theory section to include this explicit argument, showing that the original conditions for Cramér-Rao attainment are preserved once the effective sample size per group is adjusted for missingness and the group size is treated as a fixed design parameter. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; extension claims rest on new mechanisms rather than definitional reduction

full rationale

The provided abstract and context describe an additive extension of ERADE to group recruitment, fixed-interval updates, random missingness, and delays. The central claim is that theoretical analysis establishes retention of asymptotic properties (stopping-time arguments, Cramér-Rao attainment). No quoted equation or step in the given text reduces a prediction to a fitted input, renames a known result, or imports a uniqueness theorem solely via overlapping-author citation as a load-bearing premise. The derivation chain is presented as building outward from the cited framework rather than collapsing back into it by construction. Self-citation of the original ERADE is normal and does not trigger circularity under the rules, as the new handling of batching and missing data is described as preserving (not presupposing) the required filtration properties.

Assumptions & free parameters 0 free parameters · 0 assumptions · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the design inherits the allocation function and stopping-time framework from the referenced ERADE paper without additional detail here.

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Cite this review

Pith. "Pith review of Group Efficient Randomized-Adaptive Designs with Delayed and Missing Responses." pith.science (2026). https://pith.science/paper/HT63ZA6E

@misc{pith2026260618942,
  author       = {Pith},
  title        = {Pith review of: Group Efficient Randomized-Adaptive Designs with Delayed and Missing Responses},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HT63ZA6E}},
  note         = {Machine review of arXiv:2606.18942}
}
read the original abstract

Response-adaptive randomization designs have attracted much attention in clinical trials. This paper proposes a new class of response-adaptive design which built on the efficient randomized-adaptive design (ERADE) proposed by Hu, Zhang, and He. The original ERADE uses a discrete allocation probability function and leverages the stopping time theory of stochastic processes to establish asymptotic results. It has been proven that the design can reach the Cram\'er-Rao lower bound for any target allocation proportion. This study further expands the original framework by replacing the traditional case-by-case sequential enrollment with group recruitment over fixed time intervals(weekly, biweekly, or monthly), and dynamically updates the allocation probabilities based on the cumulative response information within each group. Meanwhile, to better fit practical application scenarios, we further explicitly consider the situations of randomly missing data and response delay. Theoretical analysis shows that the new design retains all the main asymptotic properties of the original ERADE, and still performs well under the conditions of response delay and missing data. Finally, through simulation studies and the redesign of a real-world clinical trial, the effectiveness and practicality of the proposed method are verified.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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Reviewed June 26, 2026 · model on record in the stance chip above.