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REVIEW 2 major objections 1 minor 46 references

On the use of auxiliary variables in multiple imputation when estimating the average causal effect with missing data

T0 review · 2 major / 1 minor · reviewed 2026-06-26 · grok-4.3

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Pith's one-line read Distinguishing mediator from non-mediator auxiliary variables prevents bias in multiple imputation for average causal effect estimation.

desk verdict Paper shows mediator vs non-mediator auxiliaries matter for bias in MI for ACE but its m-DAGs may not cover typical cases. read the letter →

arxiv 2606.22016 v1 pith:QEHBBXNR submitted 2026-06-20 stat.ME

Jiaxin Zhang , S. Ghazaleh Dashti , John B. Carlin , Katherine J. Lee , Margarita Moreno-Betancur This is my paper · ORCID
classification stat.ME
keywords multipleimputationauxiliaryvariablesaveragecausaleffectmissingdatainferencemissingnessDAGsg-computationrecoverability
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 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.

What carries the argument

Missingness directed acyclic graphs (m-DAGs) that depict the mechanisms, used to derive recoverability results for the ACE with auxiliary variables in MI.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

The missingness directed acyclic graphs considered in the paper represent the typical missingness mechanisms encountered when estimating average causal effects.

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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 / 1 minor

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.

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 (2)
  1. [m-DAGs and recoverability derivations] 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.
  2. [Simulation studies] 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.
minor comments (1)
  1. [Abstract] The abstract could more explicitly state the number of m-DAGs considered and summarize the key quantitative findings from the simulations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

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.

read point-by-point responses

  1. Referee: 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.

    Authors: 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: partial

  2. Referee: 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.

    Authors: 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: partial

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: recoverability results and simulations are independent of fitted quantities

full rationale

The paper derives recoverability results from the structure of specified m-DAGs using standard graphical criteria for missing data, then evaluates MI and complete-case estimators via simulation studies that apply correctly specified g-computation on data generated from those same DAGs. No prediction or result reduces by construction to a parameter fitted from the target data; the simulations serve as external benchmarks rather than self-referential fits. No load-bearing self-citation chains or ansatz smuggling are present. The derivation chain remains self-contained against the paper's stated mechanisms.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

The central claims rest on domain assumptions about the m-DAGs representing real missingness processes and on the correctness of the g-computation specification; no free parameters or invented entities are described in the abstract.

assumptions (1)
  • domain assumption The m-DAGs considered correctly represent typical univariable and multivariable missingness mechanisms for ACE estimation.
    Invoked to derive recoverability results across the range of settings examined.

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Cite this review

Pith. "Pith review of On the use of auxiliary variables in multiple imputation when estimating the average causal effect with missing data." pith.science (2026). https://pith.science/paper/QEHBBXNR

@misc{pith2026260622016,
  author       = {Pith},
  title        = {Pith review of: On the use of auxiliary variables in multiple imputation when estimating the average causal effect with missing data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QEHBBXNR}},
  note         = {Machine review of arXiv:2606.22016}
}
read the original abstract

Estimating the average causal effect (ACE) using observational data is a key focus in causal inference for which missing data present an important challenge. Multiple imputation (MI) is a widely used method for handling missing data and can yield unbiased estimates when the imputation is compatible with the substantive analysis. One of the advantages of MI is its scope to include so-called "auxiliary variables", defined as variables associated with incomplete variables that are excluded from the substantive analysis. Although many studies have looked at the use of auxiliary variables in MI for improving precision, the study of auxiliary variables that are necessary for the identifiability (or "recoverability") of the ACE in the presence of missing data has been scant. In this work, we investigate the use of auxiliary variables, both mediators and non-mediators, across a range of typical univariable and multivariable missingness mechanisms depicted by missingness directed acyclic graphs (m-DAGs). For each setting, we derive recoverability results, then evaluate MI-based and complete-case methods for estimating the ACE using correctly specified g-computation, considering different strategies for incorporating auxiliary variables and varying degrees of compatibility for MI models. Based on findings from the simulation studies, we provide practical guidance, highlighting that distinguishing appropriately between mediator and non-mediator auxiliary variables is important to avoid bias as is the use of compatible and flexible (non-parametric) MI methods that incorporate these variables.

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