{"id":"a15e5aee-7198-45f3-86f0-6b4ce7f849e8","arxiv_id":"2606.18942","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":4.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Group version of ERADE proposed that incorporates delayed and missing responses while retaining asymptotic properties of the original design.","lead":"This paper extends the efficient randomized-adaptive design (ERADE) to group-based enrollment with explicit handling of response delays and missing data. The extension targets practical clinical trial settings while claiming to keep the original asymptotic guarantees.","discovery_kind":"unclear","skeptic_critique":{"model":"grok-4.3","headline":"Group-wise fixed-interval updates and missing-data mechanisms may alter the filtration needed for original ERADE stopping-time arguments","rationale":"The reader's weakest_assumption directly identifies the same structural premise that must be verified for the retention claim to hold; the full-text examination would need to confirm the filtration argument, but the load-bearing point remains unchanged from the abstract-level inference.","tokens_in":1716,"tokens_out":290,"duration_ms":14346,"concrete_test":"Re-derive the key asymptotic normality result (presumably Theorem 3.x or equivalent) from the original ERADE stopping-time argument applied to the new group filtration; check whether the normalized allocation error still converges to the same normal limit with variance attaining the Cramér-Rao bound, or whether an extra term appears from the fixed-interval grouping.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that the new group-recruitment process (fixed time intervals, cumulative responses per group) together with random missingness and delays generates a filtration under which the original stopping-time arguments and Cramér-Rao attainment still hold verbatim. The abstract states that theoretical analysis shows retention of all main asymptotic properties, yet the weakest link is whether the discrete group structure preserves the martingale property and optional-stopping conditions used in Hu-Zhang-He without extra bias or variance terms induced by the batching and missingness mechanism.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","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.","tokens_in":1813,"tokens_out":376,"duration_ms":18466,"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":[{"comment":"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.","section":"Abstract"},{"comment":"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.","section":"Introduction"}],"minor_comments":[],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"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.","responses":[{"response":"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_made":"yes","referee_comment":"[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."},{"response":"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_made":"yes","referee_comment":"[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."}],"tokens_in":1330,"tokens_out":491,"duration_ms":21094,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The new element here is replacing one-by-one enrollment with fixed-interval group recruitment while updating allocation probabilities from cumulative responses per group, plus explicit rules for random missingness and response delays. That matches a real logistical issue in trials where patients arrive in batches. The paper carries over the ERADE allocation function and claims the same asymptotic properties hold, including Cramér-Rao attainment, plus simulation checks and a re-analysis of an existing trial.\n\nWhat stands out is the practical framing: the authors identify that standard sequential designs do not fit weekly or monthly enrollment cycles and add missing-data handling without changing the core target proportions. That is a straightforward extension rather than a new theoretical framework.\n\nThe soft spot is the theoretical claim. The abstract asserts that analysis confirms retention of the original stopping-time and martingale arguments, yet supplies no explicit conditions on the missingness probability, no updated filtration, and no sketch of how the discrete group structure avoids extra bias terms. The stress-test note correctly flags that batching plus delays could alter the optional-stopping conditions used in the Hu-Zhang-He work; without the derivations visible, it is impossible to judge whether those conditions still hold verbatim or require new bounds. If the full paper contains the proofs, this concern may be minor; on the supplied text it remains the main gap.\n\nThis is aimed at specialists in response-adaptive designs who already know ERADE and need to handle batch logistics. A reader outside that niche will find the motivation clear but the technical advance incremental. The work is coherent on its own terms and engages the right literature, so it deserves a serious referee to check the missing-data conditions and the group-wise martingale arguments.","headline":"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.","tokens_in":2299,"tokens_out":413,"would_cite":false,"duration_ms":13315,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A group-based version of ERADE keeps its asymptotic properties when responses arrive late or are missing.","keywords":["response-adaptive randomization","clinical trials","missing data","response delay","asymptotic properties","group recruitment","ERADE"],"falsifier":"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.","tokens_in":2586,"feed_emoji":"📊","tokens_out":615,"duration_ms":17708,"temperature":0.7,"pith_summary":"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.","feed_headline":"Group ERADE keeps asymptotic properties with delays and missing data","feed_subtitle":"Allocation updates at fixed intervals still reach the Cramér-Rao bound for any target proportion.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["Group ERADE retains asymptotics with delayed and missing responses","Fixed group intervals preserve ERADE Cramér-Rao bound","Group ERADE achieves target allocations under response delays","Asymptotics of group ERADE hold with missing and delayed data","Group ERADE holds properties amid delays and random missingness"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Group ERADE retains asymptotics with delayed and missing responses","Fixed group intervals preserve ERADE Cramér-Rao bound","Group ERADE achieves target allocations under response delays","Asymptotics of group ERADE hold with missing and delayed data","Group ERADE holds properties amid delays and random missingness"]},"model":"grok-4.3","cost_usd":0.005319,"raw_usage":{"total_tokens":2545,"prompt_tokens":620,"num_sources_used":0,"completion_tokens":71,"cost_in_usd_ticks":53187000,"prompt_tokens_details":{"text_tokens":620,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1854,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":620,"tokens_out":71,"duration_ms":14818,"temperature":1.0,"reasoning_tokens":1854,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T19:04:58.685831+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"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.","supporting_citations":[],"review_version":1}