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arxiv: 2507.04567 · v1 · submitted 2025-07-06 · 📊 stat.ME · stat.AP

Inverse Probability Weighting for Recurrent Event Models

Jiren Sun , Tobias Mutze , Richard Cook , Tianmeng Lyu This is my paper

Pith reviewed 2026-05-19 05:18 UTC · model grok-4.3

classification 📊 stat.ME stat.AP
keywords recurrent eventsinverse probability weightingintercurrent eventshypothetical estimandsclinical trialsLWYY modelnegative binomial model
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The pith

Inverse probability weighting applied to standard recurrent event models estimates hypothetical treatment effects by adjusting for intercurrent events.

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

The paper develops estimators for hypothetical treatment effects in recurrent event data when intercurrent events are present. It applies inverse probability weighting to the Lin-Wei-Yang-Ying and negative binomial models, incorporating adjustments for baseline and time-varying covariates. This targets the treatment effect in the scenario where the intercurrent event would not occur. Simulations demonstrate lower bias and higher power than alternative approaches. A reader would care because many clinical trials use recurrent events as endpoints and intercurrent events are common, making proper hypothetical estimands valuable for interpretation.

Core claim

The authors propose inverse probability weighted versions of the LWYY and NB models that properly account for all confounders of both the recurrent event process and the intercurrent event, thereby providing consistent estimation of the parameters corresponding to the hypothetical estimand in which the intercurrent event does not occur.

What carries the argument

Inverse probability weighting (IPW) applied to the Lin-Wei-Yang-Ying (LWYY) and negative binomial (NB) recurrent event models to adjust for the occurrence of intercurrent events.

If this is right

  • The weighted estimators target the hypothetical estimand of interest.
  • Both baseline and internal time-varying covariates are adjusted for in the weighting step.
  • Simulation studies show the IPW approach has less bias and more power than unadjusted methods.
  • The method works with commonly used models in recurrent event analysis.

Where Pith is reading between the lines

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

  • If the weighting model is correctly specified, the approach could generalize to other recurrent event models.
  • Real-world trial data with measured confounders could be reanalyzed to compare results with standard methods.
  • Extensions might include sensitivity analyses for unmeasured confounding.

Load-bearing premise

All confounders of both the recurrent event process and the intercurrent event are observed and correctly modeled in the weighting step.

What would settle it

A dataset or simulation where a relevant confounder is omitted from the IPW model, resulting in biased estimates of the treatment effect.

Figures

Figures reproduced from arXiv: 2507.04567 by Jiren Sun, Richard Cook, Tianmeng Lyu, Tobias Mutze.

Figure 1
Figure 1. Figure 1: The trajectory of the time-varying covariate at the population level (left) and subject level (right). [PITH_FULL_IMAGE:figures/full_fig_p016_1.png] view at source ↗
read the original abstract

Recurrent events are common and important clinical trial endpoints in many disease areas, e.g., cardiovascular hospitalizations in heart failure, relapses in multiple sclerosis, or exacerbations in asthma. During a trial, patients may experience intercurrent events, that is, events after treatment assignment which affect the interpretation or existence of the outcome of interest. In many settings, a treatment effect in the scenario in which the intercurrent event would not occur is of clinical interest. A proper estimation method of such a hypothetical treatment effect has to account for all confounders of the recurrent event process and the intercurrent event. In this paper, we propose estimators targeting hypothetical estimands in recurrent events with proper adjustments of baseline and internal time-varying covariates. Specifically, we apply inverse probability weighting (IPW) to the commonly used Lin-Wei-Yang-Ying (LWYY) and negative binomial (NB) models in recurrent event analysis. Simulation studies demonstrate that our approach outperforms alternative analytical methods in terms of bias and power.

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 inverse probability weighting (IPW) estimators for hypothetical treatment effects on recurrent events in the presence of intercurrent events. It applies IPW to the Lin-Wei-Yang-Ying (LWYY) and negative binomial (NB) estimating equations, incorporating adjustments for baseline and internal time-varying covariates that confound both the recurrent event process and the intercurrent event. Simulation studies are reported to demonstrate that the IPW-adjusted estimators outperform alternative analytical methods in terms of bias and power.

Significance. If the central claims hold under the required assumptions, the work would provide a useful extension of standard recurrent-event models to handle hypothetical estimands in clinical trials. This is relevant for endpoints such as hospitalizations in heart failure or exacerbations in asthma, where intercurrent events are common. The approach leverages familiar LWYY and NB frameworks rather than introducing entirely new models, which could facilitate adoption if the weighting step is shown to be robust.

major comments (2)
  1. [Simulation studies] Simulation studies: The reported simulation results showing reduced bias and improved power are generated under data-generating processes that satisfy the no-unmeasured-confounding assumption for the intercurrent event by construction, with all relevant baseline and time-varying covariates included in the propensity model. This setup does not evaluate estimator performance when the propensity score is misspecified or when time-varying confounders are omitted, which is load-bearing for the claim that IPW removes bias for the hypothetical estimand.
  2. [Methods] Methods section on IPW implementation: The description of how internal time-varying covariates and their joint dependence structure over time are modeled in the propensity score for the intercurrent event is not sufficiently detailed to allow assessment of whether the weighting correctly targets the hypothetical estimand under realistic longitudinal confounding.
minor comments (2)
  1. [Abstract] Abstract: The statement that the approach 'outperforms alternative analytical methods' would benefit from naming the specific alternatives compared in the simulations.
  2. [Notation] Notation: Ensure consistent use of symbols for the propensity score model and the weighted estimating equations across sections to improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and constructive comments. We address each major comment below, indicating where we agree and plan to revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Simulation studies] Simulation studies: The reported simulation results showing reduced bias and improved power are generated under data-generating processes that satisfy the no-unmeasured-confounding assumption for the intercurrent event by construction, with all relevant baseline and time-varying covariates included in the propensity model. This setup does not evaluate estimator performance when the propensity score is misspecified or when time-varying confounders are omitted, which is load-bearing for the claim that IPW removes bias for the hypothetical estimand.

    Authors: We agree that the current simulations assume correct specification of the propensity score and inclusion of all relevant confounders by design. To address this, we will add new simulation scenarios in the revised manuscript that incorporate propensity score misspecification and omission of key time-varying confounders. These additions will better illustrate the robustness (or sensitivity) of the IPW estimators and clarify the conditions under which they target the hypothetical estimand. revision: yes

  2. Referee: [Methods] Methods section on IPW implementation: The description of how internal time-varying covariates and their joint dependence structure over time are modeled in the propensity score for the intercurrent event is not sufficiently detailed to allow assessment of whether the weighting correctly targets the hypothetical estimand under realistic longitudinal confounding.

    Authors: We acknowledge that the current description of the longitudinal propensity score model lacks sufficient detail on handling internal time-varying covariates and their temporal dependence structure. In the revised manuscript, we will expand the Methods section with additional equations and explicit steps for constructing the time-varying propensity weights, including how the joint distribution over time is accounted for in the weighting procedure. revision: yes

Circularity Check

0 steps flagged

No circularity: estimators defined from standard IPW on LWYY/NB equations; simulations are external benchmarks

full rationale

The paper defines IPW-adjusted estimators by applying inverse probability weights (derived from a propensity model for the intercurrent event) directly to the existing LWYY and negative binomial estimating equations. This is a standard construction under the stated assumption of correct specification of all baseline and time-varying confounders; it does not reduce to a fitted quantity renamed as a prediction. No self-citations are invoked as load-bearing uniqueness theorems, no ansatz is smuggled, and the simulation results are presented as performance checks against alternative methods under data-generating processes that satisfy the modeling assumptions by design. The derivation chain therefore remains self-contained against external statistical benchmarks rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on standard IPW assumptions plus correct specification of the recurrent event models; no new entities or free parameters are described in the abstract.

axioms (1)
  • domain assumption All confounders of the recurrent event process and the intercurrent event are measured and included in the weighting model.
    Required for IPW to produce unbiased estimates of the hypothetical treatment effect.

pith-pipeline@v0.9.0 · 5701 in / 1084 out tokens · 36099 ms · 2026-05-19T05:18:07.442676+00:00 · methodology

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Reference graph

Works this paper leans on

28 extracted references · 28 canonical work pages

  1. [1]

    Akacha, F

    M. Akacha, F. Bretz, D. Ohlssen, G. Rosenkranz, and H. Schmidli. Estimands and their role in clinical trials. Statistics in Biopharmaceutical Research, 9 0 (3): 0 268--271, 2017

    work page 2017

  2. [2]

    L. D. Amorim and J. Cai. Modelling recurrent events: A tutorial for analysis in epidemiology. International Journal of Epidemiology, 44 0 (1): 0 324--333, 2015

    work page 2015

  3. [3]

    P. K. Andersen and R. D. Gill. Cox's regression model for counting processes: A large sample study. The Annals of Statistics, 10 0 (4): 0 1100--1120, 1982

    work page 1982

  4. [4]

    P. C. Austin. Variance estimation when using inverse probability of treatment weighting with survival analysis. Statistics in Medicine, 35 0 (30): 0 5642--5655, 2016

    work page 2016

  5. [5]

    T. P. Clark, B. C. Kahan, A. Phillips, I. White, and J. R. Carpenter. Estimands: bringing clarity and focus to research questions in clinical trials. BMJ Open, 12 0 (1): 0 e052953, 2022

    work page 2022

  6. [6]

    J. A. Cohen and R. A. Rudick. Multiple sclerosis therapeutics. Cambridge University Press, 2011

    work page 2011

  7. [7]

    S. R. Cole and M. A. Hern \'a n. Constructing inverse probability weights for marginal structural models. American Journal of Epidemiology, 168 0 (6): 0 656--664, 2008

    work page 2008

  8. [8]

    R. J. Cook and J. F. Lawless. The statistical analysis of recurrent events. Springer, 2007

    work page 2007

  9. [9]

    R. B. D'Agostino, M.-L. Lee, A. J. Belanger, L. A. Cupples, K. Anderson, and W. B. Kannel. Relation of pooled logistic regression to time dependent cox regression analysis: the framingham heart study. Statistics in Medicine, 9 0 (12): 0 1501--1515, 1990

    work page 1990

  10. [10]

    B. Efron. The jackknife, the bootstrap and other resampling plans. SIAM, 1982

    work page 1982

  11. [11]

    Graffeo, A

    N. Graffeo, A. Latouche, C. Le Tourneau, and S. Chevret. ipcwswitch: an r package for inverse probability of censoring weighting with an application to switches in clinical trials. Computers in Biology and Medicine, 111: 0 103339, 2019

    work page 2019

  12. [12]

    M. \'A . Hern \'a n, B. Brumback, and J. M. Robins. Marginal structural models to estimate the causal effect of zidovudine on the survival of hiv-positive men. Epidemiology, 11 0 (5): 0 561--570, 2000

    work page 2000

  13. [13]

    E9(R1) Statistical Principles for Clinical Trials: Addendum on Estimands and Sensitivity Analysis in Clinical Trials

    ICH . E9(R1) Statistical Principles for Clinical Trials: Addendum on Estimands and Sensitivity Analysis in Clinical Trials . Available online at https://database.ich.org/sites/default/files/E9-R1_Step4_Guideline_2019_1203.pdf, 2019. Accessed: 2024-12-16

    work page 2019

  14. [14]

    Kappos, A

    L. Kappos, A. Bar-Or, B. A. Cree, R. J. Fox, G. Giovannoni, R. Gold, P. Vermersch, D. L. Arnold, S. Arnould, T. Scherz, et al. Siponimod versus placebo in secondary progressive multiple sclerosis ( EXPAND ): a double-blind, randomised, phase 3 study. The Lancet, 391 0 (10127): 0 1263--1273, 2018

    work page 2018

  15. [15]

    O. N. Keene, M. R. Jones, P. W. Lane, and J. Anderson. Analysis of exacerbation rates in asthma and chronic obstructive pulmonary disease: example from the tristan study. Pharmaceutical Statistics: The Journal of Applied Statistics in the Pharmaceutical Industry, 6 0 (2): 0 89--97, 2007

    work page 2007

  16. [16]

    O. N. Keene, H. Lynggaard, S. Englert, V. Lanius, and D. Wright. Why estimands are needed to define treatment effects in clinical trials. BMC Medicine, 21 0 (1): 0 276, 2023

    work page 2023

  17. [17]

    Lasch, L

    F. Lasch, L. Guizzaro, F. P \'e tavy, and C. Gallo. A simulation study on the estimation of the effect in the hypothetical scenario of no use of symptomatic treatment in trials for disease-modifying agents for alzheimer’s disease. Statistics in Biopharmaceutical Research, 15 0 (2): 0 386--399, 2023

    work page 2023

  18. [18]

    N. R. Latimer, C. Henshall, U. Siebert, and H. Bell. Treatment switching: statistical and decision-making challenges and approaches. International Journal of Technology Assessment in Health Care, 32 0 (3): 0 160--166, 2016

    work page 2016

  19. [19]

    N. R. Latimer, K. R. Abrams, P. C. Lambert, J. P. Morden, and M. J. Crowther. Assessing methods for dealing with treatment switching in clinical trials: a follow-up simulation study. Statistical Methods in Medical Research, 27 0 (3): 0 765--784, 2018

    work page 2018

  20. [20]

    J. F. Lawless. Negative binomial and mixed poisson regression. The Canadian Journal of Statistics/La Revue Canadienne de Statistique, 15: 0 209--225, 1987

    work page 1987

  21. [21]

    D. Y. Lin, L.-J. Wei, I. Yang, and Z. Ying. Semiparametric regression for the mean and rate functions of recurrent events. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 62 0 (4): 0 711--730, 2000

    work page 2000

  22. [22]

    R. J. Little and D. B. Rubin. Statistical analysis with missing data. John Wiley & Sons, 2019

    work page 2019

  23. [23]

    Metcalfe and S

    C. Metcalfe and S. G. Thompson. The importance of varying the event generation process in simulation studies of statistical methods for recurrent events. Statistics in Medicine, 25 0 (1): 0 165--179, 2006

    work page 2006

  24. [24]

    Olarte Parra, R

    C. Olarte Parra, R. M. Daniel, and J. W. Bartlett. Hypothetical estimands in clinical trials: a unification of causal inference and missing data methods. Statistics in Biopharmaceutical Research, 15 0 (2): 0 421--432, 2023

    work page 2023

  25. [25]

    J. S. Preisser, K. K. Lohman, and P. J. Rathouz. Performance of weighted estimating equations for longitudinal binary data with drop-outs missing at random. Statistics in Medicine, 21 0 (20): 0 3035--3054, 2002

    work page 2002

  26. [26]

    J. M. Robins, M. A. Hernan, and B. Brumback. Marginal structural models and causal inference in epidemiology. Epidemiology, 11 0 (5): 0 550--560, 2000

    work page 2000

  27. [27]

    J. K. Rogers, S. J. Pocock, J. J. McMurray, C. B. Granger, E. L. Michelson, J. \"O stergren, M. A. Pfeffer, S. D. Solomon, K. Swedberg, and S. Yusuf. Analysing recurrent hospitalizations in heart failure: a review of statistical methodology, with application to charm-preserved. European Journal of Heart Failure, 16 0 (1): 0 33--40, 2014

    work page 2014

  28. [28]

    R. J. Tibshirani and B. Efron. An introduction to the bootstrap. Monographs on Statistics and Applied Probability, 57 0 (1): 0 1--436, 1993

    work page 1993