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arxiv: 2605.20615 · v1 · pith:6XR54B6Dnew · submitted 2026-05-20 · 📊 stat.ME

Evaluating causal indirect effects when mediators are left-censored by assay limit of quantification

Cong Jiang , Michael D. Hughes , Nima S. Hejazi This is my paper

Pith reviewed 2026-05-21 03:18 UTC · model grok-4.3

classification 📊 stat.ME
keywords causal mediation analysisleft-censoringMNARsemi-parametric EMfractional imputationnatural direct effectnatural indirect effect
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The pith

Fractional imputation and semi-parametric EM enable estimation of natural direct and indirect effects when mediators are left-censored by assay limits.

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

Causal mediation analysis aims to separate how much a treatment affects an outcome directly versus through a biological mediator such as viral RNA. Left-censoring at an assay's limit of quantification turns the mediator into MNAR data, which breaks standard estimators and produces biased direct and indirect effect estimates. The paper builds a semi-parametric framework that factorizes the observed-data likelihood and uses fractional imputation inside an EM algorithm to recover the needed conditional distributions. This supports both plug-in estimators and asymptotically efficient ones, together with a data-adaptive m-out-of-n bootstrap for inference. Simulations confirm large bias reductions, while the ACTIV-2 trial re-analysis finds that monoclonal antibodies lower hospitalization risk with only modest mediation through measured viral RNA.

Core claim

The natural direct and indirect effects remain identifiable and estimable under deterministic left-censoring of the mediator at the assay limit of quantification by factorizing the data likelihood and recovering its censored components through fractional imputation embedded in a semi-parametric EM algorithm, which yields both plug-in and efficient estimators together with an m-out-of-n bootstrap that accounts for the imputation step.

What carries the argument

Fractional imputation inside a semi-parametric EM algorithm that flexibly estimates the factorized observed-data likelihood components under known deterministic left-censoring.

If this is right

  • Natural direct and indirect effects can be estimated without discarding or naively imputing censored mediator values.
  • Both traditional plug-in and asymptotically efficient estimators become available once the likelihood components are recovered.
  • The m-out-of-n bootstrap supplies valid standard errors that incorporate uncertainty from the imputation procedure.
  • Application to the ACTIV-2 trial indicates that viral RNA mediates only a modest fraction of the monoclonal antibody effect on hospitalization and death.

Where Pith is reading between the lines

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

  • The same factorization-plus-imputation structure could be reused for other deterministic MNAR mechanisms such as right-censoring or detection limits in different assay types.
  • Extending the framework to time-to-event mediators or multiple partially censored mediators would require only modest changes to the likelihood factorization.
  • In surrogate-endpoint validation settings, the method could supply more accurate mediation proportions when the candidate surrogate is subject to assay censoring.

Load-bearing premise

The censoring mechanism is known and deterministic at the assay limit, and the usual causal mediation assumptions of sequential ignorability and positivity hold.

What would settle it

A simulation experiment with known true direct and indirect effects, known censoring threshold, and repeated application of the proposed versus naive estimators; large remaining bias or coverage failure would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.20615 by Cong Jiang, Michael D. Hughes, Nima S. Hejazi.

Figure 1
Figure 1. Figure 1: Performance of G-computation/plug-in (top panel, Study 1) and one-step estimators (bottom panel, Study 2) [PITH_FULL_IMAGE:figures/full_fig_p016_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Mediator data summary for our ACTIV-2 analysis participants. (a) Histogram of Day 3 AN SARS-CoV-2 [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
read the original abstract

Causal mediation analysis is essential for disentangling the mechanisms by which investigational therapeutic and preventive agents impact clinical outcomes. However, the measurement of biological mediators is often subject to left-censoring by technical measurement limitations, most commonly an assay's limit of quantification. This form of censoring can pose severe challenges for both identification and estimation of causal mediation estimands, particularly when the censoring mechanism is deterministic and the resulting missingness is missing not at random (MNAR) or nonignorable. Motivated by the question of assessing the role of viral RNA in the action mechanism of monoclonal antibody therapies for COVID-19 in the Accelerating COVID-19 Therapeutics and Vaccine (ACTIV)-2 platform trial, we develop a semi-parametric framework for estimation of the natural direct and indirect effects when the mediator of interest is partially subject to this form of left-censoring. Our proposed strategy combines fractional imputation with a semi-parametric EM algorithm to flexibly estimate key components of the factorized data likelihood. Applying the proposed strategy to circumvent the left-censoring, we discuss both traditional plug-in and asymptotically efficient estimators of the direct and indirect effect estimands, introducing a data-adaptive $m$-out-of-$n$ bootstrap for robust inference under the imputation procedure. We demonstrate in numerical experiments that our approach significantly reduces bias and allows for reliable inference. An application to data from the ACTIV-2 platform trial confirms that monoclonal antibody therapies reduce the risk of hospitalization and death due to COVID-19, while suggesting that changes in viral RNA mediate only a modest proportion of the overall treatment effect.

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

2 major / 3 minor

Summary. The manuscript develops a semi-parametric framework for estimating natural direct and indirect effects in causal mediation analysis when the mediator is subject to deterministic left-censoring at an assay limit of quantification, inducing MNAR missingness. The proposed strategy combines fractional imputation with a semi-parametric EM algorithm to estimate components of the observed-data likelihood, discusses plug-in and asymptotically efficient estimators, and introduces a data-adaptive m-out-of-n bootstrap for inference. Numerical experiments show bias reduction relative to naive approaches, and the method is applied to ACTIV-2 trial data to evaluate viral RNA as a mediator of monoclonal antibody effects on COVID-19 hospitalization and death.

Significance. If the central estimators are correctly derived under the stated assumptions (sequential ignorability, positivity, and known deterministic censoring), the work provides a practical and flexible tool for mediation analysis in settings common to biomedical trials where mediators like viral loads are frequently left-censored. The integration of fractional imputation and EM, together with the bootstrap procedure for robust inference, represents a methodological advance that could improve reliability of indirect-effect estimates in infectious-disease and therapeutic-mechanism studies. The application to ACTIV-2 data illustrates real-world relevance.

major comments (2)
  1. [§3] §3 (Methods): the identification of the natural indirect effect under MNAR censoring relies on the factorization of the observed-data likelihood; however, the manuscript should explicitly state whether the semi-parametric EM guarantees consistency when the censoring threshold is estimated from the data rather than treated as known, as this affects the central claim of reliable inference.
  2. [§4] §4 (Numerical experiments): the reported bias reduction is shown for specific simulation settings, but the manuscript does not report results under varying censoring proportions (e.g., 30% vs. 70% censored) or under mild violations of positivity; these are load-bearing for assessing whether the approach 'significantly reduces bias' in general.
minor comments (3)
  1. [Abstract, §2] Abstract and §2: the phrase 'data-adaptive m-out-of-n bootstrap' is introduced without a brief definition or reference to how the adaptivity (choice of m) is implemented; this should be clarified for readers unfamiliar with the technique.
  2. [§5] §5 (Application): the proportion of left-censored viral RNA observations in the ACTIV-2 dataset is not reported; including this summary statistic would help readers gauge the practical severity of the censoring problem addressed.
  3. [Throughout] Notation: the manuscript uses M for the mediator but does not consistently distinguish the observed (possibly censored) version from the latent uncensored version in equations; a short notational table or explicit definition would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation and constructive comments on our manuscript. We address the major comments point by point below.

read point-by-point responses

  1. Referee: [§3] §3 (Methods): the identification of the natural indirect effect under MNAR censoring relies on the factorization of the observed-data likelihood; however, the manuscript should explicitly state whether the semi-parametric EM guarantees consistency when the censoring threshold is estimated from the data rather than treated as known, as this affects the central claim of reliable inference.

    Authors: We appreciate this point. Our framework assumes the censoring threshold is known, which is the case for the assay limit of quantification in the ACTIV-2 application and similar settings. The semi-parametric EM algorithm is developed under this known threshold assumption, ensuring consistency of the estimators. We will revise the manuscript to explicitly state this assumption and clarify that the consistency guarantees apply when the threshold is known. If the threshold were to be estimated from the data, further theoretical work would be required to account for the estimation uncertainty, but this is outside the scope of the current work as the threshold is typically fixed and known. revision: partial

  2. Referee: [§4] §4 (Numerical experiments): the reported bias reduction is shown for specific simulation settings, but the manuscript does not report results under varying censoring proportions (e.g., 30% vs. 70% censored) or under mild violations of positivity; these are load-bearing for assessing whether the approach 'significantly reduces bias' in general.

    Authors: We agree that exploring a wider range of simulation settings would provide stronger support for the method's performance. In the revised manuscript, we will include additional numerical experiments varying the censoring proportion (including 30% and 70% censored cases) and incorporating mild violations of the positivity assumption to assess the robustness of bias reduction and inference. revision: yes

Circularity Check

0 steps flagged

No significant circularity; estimation strategy is self-contained

full rationale

The paper develops a new semi-parametric estimation procedure (fractional imputation + EM algorithm) for natural direct and indirect effects under deterministic left-censoring of the mediator. Identification rests on standard sequential ignorability and positivity assumptions that are stated explicitly and are not derived from the fitted quantities themselves. The central claims of bias reduction and reliable inference are supported by numerical experiments and an application to ACTIV-2 data rather than by re-expressing fitted parameters as predictions or by load-bearing self-citations. No equation or step reduces the target estimands to the inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Review based on abstract only; detailed model assumptions, likelihood factorization, and any free parameters in the imputation or EM steps are not specified in the provided text.

axioms (2)
  • domain assumption Standard causal mediation identification assumptions (sequential ignorability, positivity, consistency) hold for the natural direct and indirect effects.
    These are required to define the target estimands and are implicitly invoked when discussing direct and indirect effects in the presence of censoring.
  • domain assumption The left-censoring mechanism is deterministic and known (censoring at the assay limit of quantification).
    Stated in the abstract as the source of MNAR missingness that the method addresses.

pith-pipeline@v0.9.0 · 5824 in / 1519 out tokens · 38559 ms · 2026-05-21T03:18:22.962619+00:00 · methodology

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