{"id":"7c017447-58de-41e3-84dd-f49765749c3f","arxiv_id":"2606.22016","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Derives recoverability results for mediator and non-mediator auxiliary variables in MI for ACE estimation across m-DAG missingness mechanisms and supplies simulation-based practical guidance favoring compatible flexible MI.","lead":"The paper examines auxiliary variables in multiple imputation for recovering the average causal effect under missing data, using m-DAGs to derive recoverability and simulations to compare MI strategies versus complete-case analysis. A smart generalist might read it to learn when and how to include mediator versus non-mediator auxiliaries without introducing bias in causal estimates from incomplete observational data.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Representativeness of the paper's m-DAGs for real-world missingness mechanisms when estimating ACE remains unverified","rationale":"The reader's weakest assumption directly identifies the load-bearing point. Because the full text supplies the m-DAG figures and simulation designs but cannot itself demonstrate external representativeness, the concern stands and keeps the verdict at UNVERDICTED pending either broader mechanism coverage or explicit sensitivity checks.","tokens_in":1751,"tokens_out":386,"duration_ms":11492,"concrete_test":"Extract the exact m-DAG structures used (including all arrows involving missingness indicators) from Sections 3–4; independently code a convenience sample of 15 recent ACE estimation papers that report missing data; map each paper's implied missingness mechanism onto the closest m-DAG or note mismatches; if >30% of papers require structures absent from the paper's set, re-run the key simulation scenarios under one such additional m-DAG and check whether the bias patterns for mediator vs. non-mediator auxiliaries reverse.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that distinguishing mediator vs. non-mediator auxiliary variables avoids bias and that compatible non-parametric MI is required—rests on recoverability results and simulation findings derived exclusively under the specific univariable and multivariable m-DAGs considered. These m-DAGs encode particular patterns of missingness dependence on observed variables, treatment, outcome, and auxiliaries. If typical applied settings involve missingness structures outside this set (e.g., missingness depending on unmeasured common causes of missingness indicators, or time-varying mechanisms in longitudinal data), the derived bias-avoidance rules and the recommendation to incorporate auxiliaries in a particular way may fail to prevent bias or may be unnecessary. The paper provides no external validation that its m-DAG collection spans the mechanisms arising in practice.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript claims that distinguishing between mediator and non-mediator auxiliary variables is crucial to avoid bias when using multiple imputation (MI) to estimate the average causal effect (ACE) with missing data, and that compatible and flexible non-parametric MI methods incorporating these variables are necessary. It derives recoverability results for a range of univariable and multivariable missingness mechanisms using m-DAGs and evaluates them through simulation studies comparing MI-based and complete-case methods with g-computation.","tokens_in":1915,"tokens_out":447,"duration_ms":19828,"significance":"If the results hold, the paper provides important practical guidance on the use of auxiliary variables in MI for causal inference, filling a gap in the literature regarding auxiliaries necessary for identifiability of the ACE. Strengths include the derivation of recoverability results across multiple m-DAGs and the evaluation of different MI strategies under correctly specified g-computation. This could improve the reliability of ACE estimates in observational data with missingness.","major_comments":[{"comment":"m-DAGs and recoverability section: The recoverability results and bias-avoidance guidance are derived exclusively under the specific set of m-DAGs considered; the manuscript does not provide evidence or discussion that these m-DAGs are representative of typical missingness mechanisms in applied causal inference settings (e.g., those involving unmeasured common causes of missingness indicators or time-varying mechanisms). This is load-bearing for the generalizability of the recommendations.","section":"m-DAGs and recoverability derivations"},{"comment":"Simulation studies section: The simulations rely on the chosen m-DAGs and correctly specified models; no sensitivity analyses are presented for misspecified MI models or deviations from the assumed missingness structures, which could affect the conclusion that non-parametric MI is required to avoid bias.","section":"Simulation studies"}],"minor_comments":[{"comment":"The abstract could more explicitly state the number of m-DAGs considered and summarize the key quantitative findings from the simulations.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their constructive comments on our manuscript. We address the two major comments point by point below, focusing on the scope of our m-DAGs and the design of the simulation studies. We propose targeted revisions to improve clarity on limitations while preserving the core contributions on recoverability and MI compatibility.","responses":[{"response":"We selected the m-DAGs to cover a range of univariable and multivariable mechanisms commonly discussed in the missing data and causal inference literature (e.g., missingness depending on observed covariates or outcomes). The manuscript already frames these as 'typical' based on prior work. We agree that mechanisms with unmeasured common causes of missingness indicators or time-varying structures fall outside this scope and could affect generalizability. We will add a dedicated limitations paragraph in the discussion section explicitly noting the selected m-DAGs, their motivation from existing literature, and the value of future extensions to more complex mechanisms.","revision_made":"partial","referee_comment":"m-DAGs and recoverability section: The recoverability results and bias-avoidance guidance are derived exclusively under the specific set of m-DAGs considered; the manuscript does not provide evidence or discussion that these m-DAGs are representative of typical missingness mechanisms in applied causal inference settings (e.g., those involving unmeasured common causes of missingness indicators or time-varying mechanisms). This is load-bearing for the generalizability of the recommendations."},{"response":"The simulations were intentionally conducted under correctly specified g-computation and the assumed m-DAGs to isolate the impact of MI compatibility and flexibility on bias when recoverability holds. This design directly supports the recoverability derivations. We acknowledge that misspecification of MI models or deviations from the m-DAGs could alter performance and that sensitivity analyses would provide additional practical insight. We will expand the discussion to address this limitation and note that the current results demonstrate bias avoidance under compatible flexible MI when the substantive model is correct.","revision_made":"partial","referee_comment":"Simulation studies section: The simulations rely on the chosen m-DAGs and correctly specified models; no sensitivity analyses are presented for misspecified MI models or deviations from the assumed missingness structures, which could affect the conclusion that non-parametric MI is required to avoid bias."}],"tokens_in":1439,"tokens_out":496,"duration_ms":21839,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main thing is that this paper finds you need to treat mediator and non-mediator auxiliary variables differently in multiple imputation when estimating the average causal effect, or you risk bias, and that the MI model must be compatible and flexible.\n\nIt derives recoverability results for auxiliaries under a set of univariable and multivariable m-DAG missingness mechanisms, then compares MI strategies to complete-case analysis in simulations that use correctly specified g-computation.\n\nThe simulations and derivations give some concrete practical guidance on when and how to include auxiliaries, which fills a gap in the MI-compatibility literature for this setting.\n\nThe soft spot is that everything rests on the chosen m-DAGs being representative. There is no external check that these patterns match the missingness structures that actually arise in applied data, such as dependence on unmeasured common causes or longitudinal complications. If they do not, the bias-avoidance rules may not hold up.\n\nThe approach uses standard tools with no evident circularity or fitting issues.\n\nThis is for statisticians and applied researchers who handle missing data in causal effect estimation. Readers facing similar problems would get usable advice from the guidance section.\n\nIt deserves peer review because it targets a real methodological gap with derivations and targeted simulations.","headline":"Paper shows mediator vs non-mediator auxiliaries matter for bias in MI for ACE but its m-DAGs may not cover typical cases.","tokens_in":2396,"tokens_out":333,"would_cite":false,"duration_ms":22568,"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":"Distinguishing mediator from non-mediator auxiliary variables prevents bias in multiple imputation for average causal effect estimation.","keywords":["multiple imputation","auxiliary variables","average causal effect","missing data","causal inference","missingness DAGs","g-computation","recoverability"],"falsifier":"A simulation or empirical analysis in which mediator auxiliary variables are included in standard MI without compatibility checks produces persistent bias in the ACE estimate relative to a gold-standard complete-data analysis.","tokens_in":2663,"feed_emoji":"","tokens_out":380,"duration_ms":26518,"temperature":0.7,"pith_summary":"The paper examines how auxiliary variables can help recover the average causal effect when data are missing. It uses missingness DAGs to classify univariable and multivariable mechanisms. Simulations compare multiple imputation strategies that incorporate these variables differently. The results show that mediator auxiliary variables and non-mediator ones affect bias differently, and only compatible flexible imputation models succeed across settings.","feed_headline":"Mediator vs non-mediator auxiliaries matter for unbiased MI causal estimates","feed_subtitle":"Simulations show compatible non-parametric MI recovers the ACE while incompatible models and complete-case analysis fail","key_machinery":"Missingness directed acyclic graphs (m-DAGs) that depict the mechanisms, used to derive recoverability results for the ACE with auxiliary variables in MI.","core_discovery":"For a range of missingness mechanisms, the average causal effect is recoverable using multiple imputation only when auxiliary variables are incorporated in a manner compatible with the analysis model, with mediator auxiliary variables requiring particular care to prevent bias in g-computation estimates.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["MI with compatible auxiliaries recovers ACE under various missingness","Mediator vs non-mediator auxiliaries differ in MI causal analysis","Auxiliary inclusion in MI must match analysis model to recover ACE","g-computation bias from incompatible MI when using mediator auxiliaries"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The missingness directed acyclic graphs considered in the paper represent the typical missingness mechanisms encountered when estimating average causal effects.","fun_headline_variants_meta":{"raw":{"variants":["MI with compatible auxiliaries recovers ACE under various missingness","Mediator vs non-mediator auxiliaries differ in MI causal analysis","Auxiliary inclusion in MI must match analysis model to recover ACE","g-computation bias from incompatible MI when using mediator auxiliaries"]},"model":"grok-4.3","cost_usd":0.005196,"raw_usage":{"total_tokens":2526,"prompt_tokens":680,"num_sources_used":0,"completion_tokens":69,"cost_in_usd_ticks":51962000,"prompt_tokens_details":{"text_tokens":680,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1777,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":680,"tokens_out":69,"duration_ms":9053,"temperature":1.0,"reasoning_tokens":1777,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T11:41:44.910540+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A simulation or empirical analysis in which mediator auxiliary variables are included in standard MI without compatibility checks produces persistent bias in the ACE estimate relative to a gold-standard complete-data analysis.","supporting_citations":[],"review_version":1}