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arxiv: 2606.07174 · v1 · pith:S7OG7HHJnew · submitted 2026-06-05 · 📊 stat.ME

One-step Outcome Imputation: An Alternative to Multiple Imputation

Andreas Nordland , Klaus K. Holst , David Redek , Christian B. Pipper , Aske T. Iversen This is my paper

Pith reviewed 2026-06-27 21:09 UTC · model grok-4.3

classification 📊 stat.ME
keywords missing outcomesmultiple imputationinfluence functionone-step estimatorrandomized trialsreference-based imputationasymptotic inference
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The pith

A one-step estimator from the influence function of an imputation model yields asymptotically valid inference for the implied treatment effect.

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

The paper targets missing outcomes in randomized trials and replaces multiple imputation plus Rubin's rules with a direct one-step procedure. It first defines the treatment effect that a chosen imputation model implies, then builds an efficient estimator for that parameter from the model's influence function. This construction supplies correct asymptotic standard errors even when Rubin's rules are known to break down, as they do for reference-based imputation. A reader would care because the method removes both the repeated random imputations and the risk of invalid inference while remaining applicable to any imputation model the analyst is willing to assume.

Core claim

The one-step estimator is obtained by targeting the treatment-effect functional implied by a given imputation model and constructing an asymptotically linear estimator from the corresponding influence function; the resulting procedure delivers valid inference without stochastic imputation draws or reliance on Rubin's variance rules.

What carries the argument

One-step estimator constructed directly from the influence function of the treatment-effect parameter defined by the imputation model.

If this is right

  • The procedure applies to any imputation model, including reference-based and intercurrent-event-dependent schemes.
  • No multiple imputed data sets need to be generated, removing both computational cost and Monte Carlo variability.
  • Standard errors are obtained directly from the influence function without separate variance estimation steps.
  • Inference remains asymptotically valid under the same model assumptions that define the target parameter.

Where Pith is reading between the lines

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

  • Implementation could be reduced to a single matrix calculation once the imputation model is fitted.
  • The same influence-function route might be used to compare how different imputation models alter the estimated treatment effect.
  • Extension to missing covariates or to longitudinal settings would follow the same construction provided the target functional is well-defined.

Load-bearing premise

The imputation model is correctly specified so that the influence function recovers the treatment effect the analyst intends to estimate.

What would settle it

A Monte Carlo experiment in which the one-step estimator achieves nominal coverage for a reference-based imputation model while Rubin's rules do not would support the claim; the opposite result would refute it.

read the original abstract

Missing outcomes in randomized controlled trials are often handled by multiple imputation (MI). Rubin's rules are routinely used to estimate standard errors but can fail to provide valid standard error estimates for some commonly used procedures, such as reference-based imputation. We propose a one-step alternative by explicitly targeting the treatment effect implied by a given imputation model and constructing an efficient one-step estimator for that treatment effect via its influence function. Unlike Rubin's rules, this approach yields asymptotically valid inference. Moreover, the proposed method circumvents the stochastic component and computational burden of MI. We illustrate the approach with examples spanning a range of imputation models, including reference-based imputation and intercurrent-event-dependent imputation.

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

0 major / 2 minor

Summary. The manuscript proposes a one-step outcome imputation estimator as an alternative to multiple imputation (MI) for handling missing outcomes in randomized controlled trials. By explicitly targeting the treatment effect implied by a given imputation model and constructing an efficient one-step estimator via its influence function, the approach is claimed to deliver asymptotically valid inference for the treatment effect, unlike Rubin's rules which can fail for reference-based imputation and similar procedures. The method avoids the stochastic component and computational burden of MI and is illustrated across imputation models including reference-based and intercurrent-event-dependent cases.

Significance. If the central construction holds, the work provides a computationally efficient, asymptotically justified alternative for valid inference under specified imputation models in clinical trial settings where Rubin's rules are known to be invalid. The explicit use of influence-function theory to target the imputation-implied parameter is a standard semiparametric strength that directly addresses a practical limitation in reference-based imputation without requiring multiple stochastic imputations.

minor comments (2)
  1. [Abstract] Abstract: the claim of 'asymptotically valid inference' would benefit from a brief parenthetical note on the key regularity conditions (e.g., correct specification of the imputation model and standard Donsker-class conditions on the nuisance estimators) to make the scope of the result immediately clear to readers.
  2. The manuscript should include a short comparison table or paragraph contrasting the proposed one-step estimator's variance with the Rubin's-rules variance in at least one reference-based example, to quantify the practical difference.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No specific major comments are listed in the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The central claim relies on defining a target treatment effect via a given imputation model and then applying standard influence-function theory to construct an efficient one-step estimator. This is a conventional semiparametric construction once the parameter is specified; the abstract and description indicate no reduction of the estimator to a fitted quantity by construction, no self-citation load-bearing the uniqueness or validity result, and no ansatz smuggled via prior work. The derivation chain is self-contained against external benchmarks of semiparametric efficiency theory.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the method rests on the domain assumption that the imputation model is correctly specified and on standard influence-function theory from semiparametrics.

axioms (1)
  • domain assumption The imputation model is correctly specified so that the influence function targets the desired treatment effect parameter.
    Required for the one-step estimator to be valid for the implied treatment effect.

pith-pipeline@v0.9.1-grok · 5651 in / 983 out tokens · 16434 ms · 2026-06-27T21:09:36.316027+00:00 · methodology

discussion (0)

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Reference graph

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