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arxiv: 2604.09898 · v1 · submitted 2026-04-10 · 📊 stat.AP

Evaluating the impact of longitudinal treatment strategies in the presence of informative monitoring and time-dependent confounding

Leah Pirondini , Karla Diaz-Ordaz , Edward Palmer , Ruth H. Keogh This is my paper

Pith reviewed 2026-05-10 15:55 UTC · model grok-4.3

classification 📊 stat.AP
keywords causal inferenceinformative monitoringlongitudinal treatmentstime-to-event outcomeselectronic health recordsinverse probability weightingG-computationtargeted maximum likelihood estimation
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The pith

Incorporating monitoring indicators as time-dependent confounders removes bias from estimates of longitudinal treatment effects on time-to-event outcomes in electronic health records.

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

This paper addresses the problem that in routinely collected health data, how often covariates are measured can depend on a patient's health status and treatment, violating the usual assumption of regular observation times. It demonstrates that treating binary indicators for whether monitoring occurred at each time as additional time-dependent confounders allows inverse probability weighting, G-computation, and longitudinal targeted maximum likelihood estimation to produce unbiased estimates of causal effects for both fixed and flexible treatment strategies. A simulation study shows clear bias when these indicators are ignored and unbiased results when they are included. The methods are applied to compare early versus delayed mechanical ventilation on mortality using intensive care data. This matters for real-world studies because electronic health records are widely available yet their irregular monitoring has previously been ignored in many causal analyses.

Core claim

The central claim is that the causal effects of longitudinal treatment strategies on survival outcomes can be consistently estimated by adapting inverse probability weighting, G-computation, and longitudinal targeted maximum likelihood estimation to include monitoring indicator variables as additional time-dependent confounders. This adaptation handles both static strategies such as always treat or never treat and more general strategies that allow variation in treatment initiation and duration, provided the monitoring process is captured by these indicators and the usual causal assumptions continue to hold after their inclusion.

What carries the argument

Monitoring indicator variables, included as time-dependent confounders that affect both the treatment process and the outcome.

If this is right

  • Ignoring monitoring indicators produces biased estimates of treatment effects on survival.
  • The three adapted methods recover unbiased estimates when monitoring indicators are treated as time-dependent confounders.
  • The approach works for both static treatment rules and rules that allow flexible timing of treatment start and stop.
  • In the intensive care example, the methods support comparison of early and delayed ventilation strategies on mortality risk.
  • Simulation evidence confirms that bias from informative monitoring is removed by the adaptation.

Where Pith is reading between the lines

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

  • The same monitoring-indicator adjustment may apply to other irregularly observed data sources such as insurance claims or wearable sensor records.
  • Future studies using electronic health records could routinely record or model monitoring patterns to enable this correction.
  • Researchers should verify that positivity holds for the combined set of treatment and monitoring variables after inclusion.

Load-bearing premise

That including the monitoring indicators fully accounts for the dependence between monitoring frequency and health status, with no remaining unmeasured factors linking monitoring to treatment or outcome.

What would settle it

A simulation in which the true treatment effect is known but the adapted methods still show bias after adding the monitoring indicators, or a dataset where positivity fails for certain monitoring patterns leading to unstable estimates.

Figures

Figures reproduced from arXiv: 2604.09898 by Edward Palmer, Karla Diaz-Ordaz, Leah Pirondini, Ruth H. Keogh.

Figure 1
Figure 1. Figure 1: Causal DAG illustrating relationships between time-dependent treatment [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Portion of the causal DAG in figure 1 for a single time-point [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Data generating mechanism: steps to generate longitudinal data according to the DAG in figure [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Ventilation status under treatment strategies [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Bias (shown as a percentage of true survival probability) of the estimated survival probabilities for [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Ventilation status under treatment strategies [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Proportion of individuals initiating IMV by day since ICU admission (bar plot) and the cumulative [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Estimated daily cumulative incidences of death up to 30 days (and 95% confidence interval) under [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
read the original abstract

Routinely collected data from electronic health records (EHR) provide opportunities to study effects of longitudinal treatment strategies in real-world clinical settings. A challenge presented by EHR data is that frequency of covariate monitoring differs by patient, covariate type and over time, and may be informative about a patient's health status. Many causal inference methods assume measurements of covariates are observed at a common set of regular time points. In this paper we describe and evaluate methods for estimating causal effects of longitudinal treatments on time-to-event outcomes in the presence of informative monitoring of time-dependent confounders. We show how methods based on inverse probability weighting, G-computation and longitudinal targeted maximum likelihood estimation (TMLE) can be adapted to allow for informative monitoring by incorporating monitoring indicator variables as additional time-dependent confounders. We evaluate these methods using a simulation study, comparing against more simple approaches that ignore monitoring variables. We demonstrate that ignoring monitoring can result in biased estimates of treatment effects. The methods are illustrated through an investigation into the effect of early versus delayed initiation of invasive mechanical ventilation on mortality of intensive care patients using routinely-collected data from an intensive care unit. We consider static treatment strategies such as `always treat' and `never treat' but also generalise to treatment strategies that allow for flexibility in the exact initiation time and duration of treatment.

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 / 2 minor

Summary. The manuscript proposes adapting inverse probability weighting, G-computation, and longitudinal targeted maximum likelihood estimation to estimate causal effects of longitudinal treatment strategies on time-to-event outcomes when time-dependent confounders are subject to informative monitoring in electronic health record data. By treating binary monitoring indicators as additional time-dependent confounders, the adapted methods aim to correct for dependence between monitoring frequency and patient health status. Simulations demonstrate bias in naive approaches that ignore monitoring and recovery of unbiased estimates when indicators are included; the methods are illustrated with an application to early versus delayed mechanical ventilation in ICU data, considering both static and flexible treatment strategies.

Significance. If the adaptation correctly identifies the target causal parameter under the stated assumptions, the work would be significant for applied causal inference in routinely collected clinical data, where informative monitoring is ubiquitous. The simulation provides a direct external check against known truth, and the generalization to flexible treatment strategies broadens applicability. This could improve reliability of observational studies on treatment timing and duration in critical care and similar settings.

major comments (2)
  1. [Methods] Methods section (description of adapted g-formula/IPW/TMLE): Treating the monitoring indicator M_t as an ordinary time-dependent confounder to be conditioned on does not automatically identify the causal effect when L_t is only observed conditional on M_t=1. The manuscript does not specify the handling of missing L_t values (e.g., last-observation-carried-forward, imputation, or complete-case), leaving open the possibility that E[L_t | history, M_t=0] remains unidentified and that residual bias persists after weighting or G-computation on M alone. This assumption is load-bearing for the central claim that the adapted estimators recover the truth.
  2. [Simulation study] Simulation study (data-generating process and results tables): The reported recovery of unbiased estimates when including M_t assumes the simulation's missingness mechanism matches the real-data process exactly. If the simulation generates L_t unconditionally and then sets M_t, rather than generating L_t only when M_t=1, the simulation may understate bias from the missing-not-at-random structure typical in EHR data, weakening the evidence that the adaptation fully corrects for informative monitoring.
minor comments (2)
  1. [Notation and data structure] The notation for the observed data structure (history of A, L, M, Y) could be clarified with an explicit diagram or table showing which variables are observed at each time point under different M_t values.
  2. [Application] In the ICU application, the definition of the 'flexible' treatment strategies (allowing variation in initiation time and duration) should include explicit rules for how monitoring affects eligibility or censoring.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have helped us improve the clarity and rigor of the manuscript. We address each major comment point by point below.

read point-by-point responses

  1. Referee: [Methods] Methods section (description of adapted g-formula/IPW/TMLE): Treating the monitoring indicator M_t as an ordinary time-dependent confounder to be conditioned on does not automatically identify the causal effect when L_t is only observed conditional on M_t=1. The manuscript does not specify the handling of missing L_t values (e.g., last-observation-carried-forward, imputation, or complete-case), leaving open the possibility that E[L_t | history, M_t=0] remains unidentified and that residual bias persists after weighting or G-computation on M alone. This assumption is load-bearing for the central claim that the adapted estimators recover the truth.

    Authors: We appreciate the referee highlighting the need for explicit clarification on this point. In the adapted estimators, M_t is incorporated into the observed history for all models (treatment, monitoring, covariate, and outcome). For g-computation and TMLE, the conditional distributions are estimated from the observed data (i.e., L_t is modeled only on instances where M_t=1), and predictions for L_t at times with M_t=0 are obtained by evaluating the fitted model at the observed history including M_t=0. This approach assumes that, conditional on the full observed history and M_t, the monitoring mechanism accounts for the dependence, with no additional unmeasured factors linking monitoring to the outcome. We have revised the Methods section to explicitly describe this handling of unobserved L_t values and to state the identifying assumptions more clearly, including a note that the framework relies on correct specification of the monitoring process. revision: yes

  2. Referee: [Simulation study] Simulation study (data-generating process and results tables): The reported recovery of unbiased estimates when including M_t assumes the simulation's missingness mechanism matches the real-data process exactly. If the simulation generates L_t unconditionally and then sets M_t, rather than generating L_t only when M_t=1, the simulation may understate bias from the missing-not-at-random structure typical in EHR data, weakening the evidence that the adaptation fully corrects for informative monitoring.

    Authors: We agree that the simulation must faithfully represent the informative monitoring process. Our data-generating mechanism generates the full underlying covariate trajectory L_t at every time point (reflecting that patient health status evolves continuously), then draws M_t conditionally on current and past L_t values (inducing MNAR missingness for the observed data), and applies the estimators to the resulting partially observed dataset while including M_t in all models. This is the standard and appropriate way to simulate MNAR monitoring in longitudinal settings, as the latent health process exists regardless of whether it is measured. We have expanded the simulation description and supplementary material with the exact DGP equations to make this structure explicit and to emphasize how it mirrors EHR data. revision: partial

Circularity Check

0 steps flagged

No significant circularity; simulation provides external validation

full rationale

The paper adapts IPW, G-computation and longitudinal TMLE by treating monitoring indicators M_t as additional time-dependent confounders in the adjustment set. This is a modeling choice justified by the data-generating process description rather than by definition or self-citation. The central claim is evaluated via simulation against known ground truth and via real-data illustration; neither step reduces to a fitted quantity renamed as prediction nor to a load-bearing self-citation chain. No equations or derivations are shown to be tautological with their inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on standard causal assumptions (consistency, positivity, no unmeasured confounding) plus the additional modeling assumption that monitoring indicators can be treated as observed time-dependent confounders.

axioms (1)
  • domain assumption Standard identifiability assumptions for longitudinal causal inference hold after including monitoring indicators.
    Invoked when adapting the three methods to the informative monitoring setting.

pith-pipeline@v0.9.0 · 5541 in / 1144 out tokens · 30082 ms · 2026-05-10T15:55:39.829164+00:00 · methodology

discussion (0)

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Reference graph

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