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arxiv: 2606.01539 · v1 · pith:BRXGSBGRnew · submitted 2026-06-01 · 📊 stat.ME · cs.LG

Scalable Counterfactual Risk Estimation for Rare Events in Longitudinal Data

Xiaohui Yin , Avijit Mitra , Ying Zhou , Kun Chen , Hong Yu This is my paper

Pith reviewed 2026-06-28 13:48 UTC · model grok-4.3

classification 📊 stat.ME cs.LG
keywords causal inferencelongitudinal datarare eventsg-formulaiterative conditional expectationsubsamplingreweightingsurvival outcomes
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The pith

A subsampling and reweighting strategy scales ICE estimators for causal effects on rare survival outcomes in longitudinal data while preserving consistency.

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

This paper develops a subsampling and reweighting procedure that can be layered onto g-formula estimators such as iterative conditional expectation for time-varying treatments and survival outcomes. The approach targets the twin problems of high computational cost from bootstrap variance estimation and model instability from severe class imbalance when events are rare at each time point. By reducing the data volume processed while adjusting weights to maintain the original estimator properties, the method aims to keep statistical consistency intact. Simulations and an electronic health record analysis of social determinants and suicide risk are used to check performance. If the procedure works as described, large observational cohorts become tractable for counterfactual risk estimation without loss of reliability.

Core claim

The central claim is that a principled subsampling and reweighting strategy for longitudinal survival data can be applied to existing causal effect estimators including the ICE estimator, substantially reducing computational burden while preserving consistency and improving estimation stability in rare-outcome settings.

What carries the argument

A subsampling and reweighting strategy applied to g-formula estimators such as iterative conditional expectation under longitudinal data structure and rare-event regime.

If this is right

  • The method applies to a range of g-formula estimators beyond ICE for time-varying treatments on survival outcomes.
  • Bootstrap-based variance estimation becomes feasible on large cohorts because the computational load drops.
  • Class imbalance at each time point is mitigated, reducing instability and convergence failures in logistic models.
  • Analysis of large-scale EHR data for rare events such as suicide risk becomes practical while retaining the original estimator's theoretical guarantees.

Where Pith is reading between the lines

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

  • The same subsampling logic could be tested on other longitudinal causal methods that rely on sequential regression or weighting.
  • If the reweighting preserves asymptotic properties, the approach might support sequential updating of estimates as new data arrive in streaming health records.
  • Extensions to non-survival longitudinal outcomes with rare binary events would be a direct next check.

Load-bearing premise

That a subsampling and reweighting procedure can be applied to ICE and similar g-formula estimators while preserving their consistency properties under the longitudinal data structure and rare-event regime.

What would settle it

If bootstrap variance estimates or point estimates from the subsampled reweighted ICE diverge from those obtained on the full dataset as sample size grows in a simulated longitudinal rare-event setting, the preservation of consistency would be falsified.

Figures

Figures reproduced from arXiv: 2606.01539 by Avijit Mitra, Hong Yu, Kun Chen, Xiaohui Yin, Ying Zhou.

Figure 1
Figure 1. Figure 1: Simulation: Risk estimates for always or never ex [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Simulation: Risk estimates for always or never ex [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Simulation: Risk estimates for always or never ex [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
read the original abstract

Estimating the causal effect of time-varying treatments on survival outcomes in large observational studies is computationally demanding, particularly when outcomes are rare. While g-formula-based methods such as the iterative conditional expectation (ICE) estimator provide a principled framework for longitudinal causal inference, they become computationally expensive, especially when bootstrap-based variance estimation is required. In addition, outcome rarity at each time point induces severe class imbalance, leading to instability and convergence issues in logistic regression and related models. To address these challenges, we propose a principled subsampling and reweighting strategy for longitudinal survival data that can be applied to a range of existing causal effect estimators in this setting, including the ICE estimator. The proposed method substantially reduces computational burden while preserving consistency and improving estimation stability in rare-outcome settings. We evaluate the method through simulations and validate it using a large-scale EHR cohort study on social and behavioral determinants of health (SBDH) and suicide risk, demonstrating its effectiveness for modeling rare outcomes in longitudinal data.

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 / 1 minor

Summary. The manuscript proposes a subsampling and reweighting strategy for longitudinal survival data that can be applied to ICE and similar g-formula estimators. The approach is intended to reduce computational burden for bootstrap variance estimation and mitigate instability from class imbalance in rare-outcome settings while preserving consistency of the causal effect estimates. The claims are supported by simulation studies and a real-data application to a large EHR cohort examining social and behavioral determinants of health and suicide risk.

Significance. If the consistency preservation holds under the stated longitudinal and rare-event conditions, the method would address a genuine practical barrier to applying g-formula estimators at scale, enabling more routine use of these methods in large observational datasets with rare survival outcomes. The combination of simulation evidence and real-data validation on suicide risk strengthens the practical relevance.

major comments (2)
  1. [Abstract] Abstract: the central claim that the subsampling-reweighting strategy preserves consistency for ICE-type g-formula estimators is asserted without an explicit statement of the sampling probabilities, the reweighting formula, or a proof sketch showing that the estimator converges to the same limit as the full-data ICE under the longitudinal data structure.
  2. [Methods] Methods (assumed location of the estimator definition): the manuscript does not derive or state the conditions (e.g., requirements on the sampling probabilities or the form of the reweighting) under which the subsampled ICE estimator remains consistent in the rare-event regime; without this, the weakest assumption identified by the reader cannot be evaluated.
minor comments (1)
  1. [Abstract] The abstract refers to 'a range of existing causal effect estimators' but does not list which additional estimators beyond ICE were tested or how the strategy generalizes.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback highlighting the need for greater explicitness regarding the consistency properties of the proposed subsampling-reweighting strategy. We address each major comment below and have revised the manuscript to incorporate the requested details.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the subsampling-reweighting strategy preserves consistency for ICE-type g-formula estimators is asserted without an explicit statement of the sampling probabilities, the reweighting formula, or a proof sketch showing that the estimator converges to the same limit as the full-data ICE under the longitudinal data structure.

    Authors: We agree that the abstract would benefit from additional specificity on these points. In the revised manuscript we have added a concise statement of the sampling probabilities (inclusion probabilities inversely proportional to the observed outcome frequency at each time point) and the corresponding inverse-probability reweighting formula directly into the abstract. We have also inserted a brief proof sketch in the Methods section establishing that the subsampled and reweighted ICE estimator converges in probability to the same limit as the full-data ICE estimator under the stated longitudinal data structure. revision: yes

  2. Referee: [Methods] Methods (assumed location of the estimator definition): the manuscript does not derive or state the conditions (e.g., requirements on the sampling probabilities or the form of the reweighting) under which the subsampled ICE estimator remains consistent in the rare-event regime; without this, the weakest assumption identified by the reader cannot be evaluated.

    Authors: We acknowledge that the original submission did not provide an explicit derivation of the consistency conditions. The revised manuscript now contains a new subsection in Methods that (i) states the precise form of the reweighting, (ii) specifies the requirements on the sampling probabilities (bounded away from zero and one, with the rare-event adjustment ensuring the effective sample size remains sufficient), and (iii) derives the conditions under which the subsampled estimator remains consistent for the g-formula functional in the rare-event longitudinal setting. These additions allow the weakest assumptions to be directly evaluated. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper introduces a subsampling-reweighting procedure for ICE/g-formula estimators under longitudinal rare-event regimes and asserts that the procedure preserves consistency while reducing computation. This claim is framed as a property of the new method, validated externally via simulation studies and real-data application rather than being tautological or defined by construction from the inputs. No load-bearing derivation step reduces to a self-citation chain, a fitted parameter renamed as a prediction, or an ansatz smuggled via prior work by the same authors. The central consistency result is presented as independently verifiable against external benchmarks (simulations, EHR cohort), making the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; all details rest on the unelaborated claim that the strategy preserves consistency.

pith-pipeline@v0.9.1-grok · 5706 in / 938 out tokens · 28751 ms · 2026-06-28T13:48:10.291108+00:00 · methodology

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Reference graph

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