Estimation of Time-Varying Treatment Effects in a Joint Model for Longitudinal and Recurrent Event Outcomes in Mobile Health Data

Cho Y Lam; David W Wetter; Inbal Nahum-Shani; Jeremy M G Taylor; Lindsey N Potter; Madeline R Abbott; Walter Dempsey

arxiv: 2604.23006 · v1 · submitted 2026-04-24 · 📊 stat.ME

Estimation of Time-Varying Treatment Effects in a Joint Model for Longitudinal and Recurrent Event Outcomes in Mobile Health Data

Madeline R Abbott , Jeremy M G Taylor , Inbal Nahum-Shani , Lindsey N Potter , David W Wetter , Cho Y Lam , Walter Dempsey This is my paper

Pith reviewed 2026-05-08 10:47 UTC · model grok-4.3

classification 📊 stat.ME

keywords micro-randomized trialsjoint longitudinal-survival modelsrecurrent eventslongitudinal outcomesmobile healthBayesian inferencetime-varying treatment effects

0 comments

The pith

An extension of joint longitudinal-survival models estimates time-varying effects of repeated treatments delivered in mobile health trials.

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

The paper develops a statistical approach to estimate how treatments given repeatedly over time affect both continuously measured health outcomes and the occurrence of recurring events. It extends standard joint models by offering several ways to include these treatment effects, each tied to a different assumption about the mechanism of impact. A Bayesian framework handles inference while accounting for the links among the treatments, the longitudinal data, and the events. The method supplies tools for choosing among the specifications and for checking how well the event part of the model fits the data. Simulations and an analysis of substance-use trial data illustrate how the approach recovers treatment effects under realistic conditions.

Core claim

We present a model-based approach for estimating the effect of repeatedly delivered treatments in a micro-randomized trial via an extension of a joint longitudinal-survival model. Different model specifications correspond to different mechanisms by which treatment is assumed to impact the longitudinal and event processes. Taking a Bayesian approach to inference, we model the association between repeated treatments, multiple longitudinally measured outcomes, and recurrent events, and we show how to calculate information criteria for model selection together with goodness-of-fit plots for the survival submodel.

What carries the argument

Extension of the joint longitudinal-survival model that incorporates repeated treatment effects through alternative specifications, each corresponding to a distinct assumed mechanism of action on the longitudinal and recurrent-event processes.

Load-bearing premise

The chosen specification must correctly represent the actual mechanisms by which the repeated treatments affect the longitudinal outcomes and the recurrent events.

What would settle it

In a controlled micro-randomized trial with known treatment delivery times and known true effect mechanisms, the estimated time-varying effects would recover the known values only when the model uses the matching specification and would show clear bias or poor calibration otherwise.

Figures

Figures reproduced from arXiv: 2604.23006 by Cho Y Lam, David W Wetter, Inbal Nahum-Shani, Jeremy M G Taylor, Lindsey N Potter, Madeline R Abbott, Walter Dempsey.

**Figure 1.** Figure 1: Simplified diagram of the MRT. Each day, a participant is randomized up to six times view at source ↗

**Figure 2.** Figure 2: Treatment models for the longitudinal process. The plots show the difference between view at source ↗

**Figure 3.** Figure 3: Box plots summarize the distribution of the view at source ↗

**Figure 4.** Figure 4: For data generated under settings 1 and 2 with different hazards and treatment ef view at source ↗

**Figure 5.** Figure 5: Median and (5, 95)th percentiles of the mean cumulative function (MCF) for posterior predicted events (red line with shaded ribbon) based on conditional posterior predictions from the joint model when the model for treatment effect on the latent process assumed the drift form and the hazard had two treatment-related coefficients. The black lines show the MCF for observed events. WAIC Impact of treatment … view at source ↗

**Figure 6.** Figure 6: Posterior means and 95% credible intervals for parameters in the joint models fit to view at source ↗

**Figure 19.** Figure 19: If our approximation works well, then we expect the value of the marginal log view at source ↗

read the original abstract

Not only does mobile health technology enable researchers to track changes in multiple longitudinal outcomes of interest and to record the occurrence of health-related events over time, but it also allows for the delivery of repeated low-cost treatments directly to individuals in real time. We present a model-based approach for estimating the effect of repeatedly delivered treatments in a micro-randomized trial (MRT) via an extension of a joint longitudinal-survival model. We discuss different ways that these repeated treatment effects can be incorporated into the joint model; these different model specifications correspond to different mechanisms by which treatment is assumed to impact the longitudinal and event processes. Taking a Bayesian approach to inference, we model the association between repeated treatments, multiple longitudinally measured outcomes, and recurrent events. We also demonstrate how to calculate information criteria for model selection and present goodness-of-fit plots for assessing survival submodel calibration. We then illustrate the performance of our method via simulations and analysis of data collected in an MRT of substance use.

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.

Desk Editor's Note private letter to a colleague

This paper gives a Bayesian joint model extension for estimating repeated treatment effects on longitudinal and recurrent outcomes in MRTs, with built-in selection tools.

read the letter

The core contribution is a practical way to model how repeated treatments in micro-randomized trials influence both continuous longitudinal outcomes and recurrent events, using different assumed mechanisms for the treatment impact and Bayesian inference to handle the joint structure. They add information criteria for picking among those mechanisms and calibration plots for the survival part, then back it with simulations and a substance-use MRT dataset. That combination moves beyond off-the-shelf joint models by directly addressing the repeated randomization and multiple outcome types common in mobile health studies. The simulations recover parameters when the mechanism is correctly specified, and the real-data example shows the workflow in action. Credit to the authors for including model comparison rather than assuming one mechanism fits all. The main limitation is that performance still depends on the true treatment pathway being close to one of the options they consider; misspecification there would bias the time-varying effects even if the selection criteria favor a model. They do not run extensive sensitivity checks outside the listed specifications, so readers will need to judge whether their own data align with the mechanisms. This is aimed at statisticians and behavioral researchers who already work with MRTs and have both longitudinal and event data. If that matches your setting, the framework and the accompanying code would be worth pulling in for your own analyses. It deserves peer review because the extension is targeted and the validation steps are present, even if the paper will likely need more detail on prior sensitivity and robustness to mechanism choice.

Referee Report

0 major / 2 minor

Summary. The manuscript presents a model-based approach for estimating time-varying effects of repeatedly delivered treatments in micro-randomized trials (MRTs) by extending joint longitudinal-survival models to accommodate multiple longitudinal outcomes and recurrent events in mobile health data. It explores alternative specifications for how treatments affect the processes (corresponding to different assumed mechanisms), employs Bayesian inference, demonstrates information criteria for model selection and goodness-of-fit plots for survival calibration, and validates via simulations plus a real-data analysis from a substance-use MRT.

Significance. If the derivations hold and the mechanism-specific models are correctly specified, the work provides a flexible, unified framework for causal estimation in MRTs that jointly handles longitudinal trajectories, recurrent events, and time-varying treatments. The explicit discussion of multiple treatment-effect mechanisms, combined with Bayesian tools, information criteria, and calibration checks, addresses a practical need in digital health research and could improve the reliability of analyses involving complex, repeatedly measured mHealth data.

minor comments (2)

Abstract: The high-level description does not include any model equations, parameter definitions, or quantitative summaries of the simulation or real-data results; adding one or two key equations (e.g., the form of the treatment-effect term in the longitudinal or hazard submodel) would improve accessibility without lengthening the abstract excessively.
The manuscript would benefit from a dedicated subsection or table that explicitly contrasts the different treatment-mechanism specifications (e.g., direct effect on longitudinal mean vs. effect on event intensity) with their implied identifiability conditions and expected bias under misspecification.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript, accurate summary of its contributions, and recommendation for minor revision. We appreciate the recognition that our extension of joint longitudinal-survival models provides a flexible framework for causal estimation in micro-randomized trials.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper extends existing joint longitudinal-survival models to accommodate repeated treatments in MRTs by enumerating multiple explicit mechanisms for how treatments affect the processes, then applies standard Bayesian inference, information criteria for selection, and calibration diagnostics. Simulations and real-data analysis serve as independent validation steps separate from any fitted quantities. No equations or claims reduce by construction to inputs, self-citations, or renamed empirical patterns; the central contribution is the availability of this flexible modeling framework under stated assumptions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard joint modeling assumptions and the validity of alternative treatment incorporation mechanisms; limited abstract detail prevents exhaustive listing.

free parameters (1)

Treatment effect parameters
Time-varying effects of repeated treatments are estimated from data under each model specification.

axioms (1)

domain assumption Joint distribution of longitudinal outcomes and recurrent events can be modeled via shared random effects or equivalent linking structures.
Core to the joint model extension described.

pith-pipeline@v0.9.0 · 5492 in / 1143 out tokens · 94052 ms · 2026-05-08T10:47:21.683495+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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write newline

" write newline "" before.all 'output.state := FUNCTION format.url url empty "" url if FUNCTION article output.bibitem format.authors "author" output.check author format.key output output.year.check new.block format.title "title" output.check new.block crossref missing format.jour.vol output format.article.crossref output.nonnull format.pages output if ne...

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[2] [2]

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work page 2025

[3] [3]

barticle [author] Abbott , M R M. R. , Dempsey , W H W. H. , Nahum-Shani , I I. , Lam , C Y C. Y. , Wetter , D W D. W. Taylor , J M G J. M. G. ( 2025 b). A Continuous-Time Dynamic Factor Model for Intensive Longitudinal Data Arising from Mobile Health Studies . Psychometrika 90 1-22 . barticle

work page 2025

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, Almirall , D D

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work page 2018

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Mercurio , F F

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, Gelman , A A

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barticle [author] Klasnja , P P. , Hekler , E B E. B. , Shiffman , S S. , Boruvka , A A. , Almirall , D D. , Tewari , A A. Murphy , S A S. A. ( 2015 ). Microrandomized trials: An experimental design for developing just-in-time adaptive interventions . Health Psychology 0 1220-8 . 10.1037/hea0000305 barticle

work page doi:10.1037/hea0000305 2015

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, Smith , S S

barticle [author] Klasnja , P P. , Smith , S S. , Seewald , N J N. J. , Lee , A A. , Hall , K K. , Luers , B B. , Hekler , E B E. B. Murphy , S A S. A. ( 2019 ). Efficacy of Contextually Tailored Suggestions for Physical Activity: A Micro-randomized Optimization Trial of HeartSteps . Annals of Behavioral Medicine 53 573-582 . barticle

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barticle [author] Nahum-Shani , I I. , Potter , L N L. N. , Lam , C Y C. Y. , Yap , J J. , Moreno , A A. , Stoffel , R R. , Wu , Z Z. , Wan , N N. , Dempsey , W W. , Kumar , S S. , Ertin , E E. , Murphy , S A S. A. , Rehg , J M J. M. Wetter , D W D. W. ( 2021 ). The mobile assistance for regulating smoking ( MARS ) micro-randomized trial design protocol ....

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barticle [author] Qian , T T. , Yoo , H H. , Klasnja , P P. , Almirall , D D. Murphy , S A S. A. ( 2021 ). Estimating time-varying causal excursion effect in mobile health with binary outcomes . Biometrika 108 507-527 . barticle

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( 2023 )

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