A joint longitudinal-survival framework for dynamic treatment regimen evaluation in sequential multiple assignment randomized trials

Holly Hartman; Zhengxi Chen

arxiv: 2605.03319 · v1 · submitted 2026-05-05 · 📊 stat.ME

A joint longitudinal-survival framework for dynamic treatment regimen evaluation in sequential multiple assignment randomized trials

Zhengxi Chen , Holly Hartman This is my paper

Pith reviewed 2026-05-07 14:38 UTC · model grok-4.3

classification 📊 stat.ME

keywords joint longitudinal-survival modeldynamic treatment regimensSMART trialscausal inferencesurvival analysislongitudinal biomarkersg-formulaoptimal DTR identification

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The pith

A joint longitudinal-survival model produces unbiased and more efficient estimates of dynamic treatment regimen survival outcomes in SMART trials.

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

This paper develops a framework that combines longitudinal biomarker data with survival analysis to evaluate dynamic treatment regimens in sequential multiple assignment randomized trials. It specifies a linear mixed model for how biomarkers change over time and connects this to a survival model where the current biomarker level influences the hazard of the event. By estimating these jointly and using a parametric g-formula, the approach accounts for the time-varying nature of treatments in two-stage trials. A reader would care because it allows incorporating routine monitoring data to get more precise and less biased assessments of which adaptive treatment strategies work best for patients.

Core claim

The authors establish that within a two-stage SMART, a joint model with a linear mixed model for biomarker trajectories and a relative risk model for survival linked to the latent biomarker value, incorporating piecewise cumulative exposure for treatments, yields unbiased DTR-specific marginal survival outcomes via the plug-in parametric g-formula. This leads to substantial efficiency gains over inverse probability of treatment weighted Kaplan-Meier estimators and improved accuracy when identifying the optimal DTR using multiple comparisons with the best method, as demonstrated in simulations and prostate cancer data under correct model specification and standard causal assumptions.

What carries the argument

The joint longitudinal-survival model that links a linear mixed model for biomarker evolution to a relative risk survival model through the current latent biomarker value, with treatment effects modeled as piecewise cumulative exposure.

If this is right

Estimates of DTR-specific survival curves remain unbiased when the models are correctly specified.
Substantial efficiency gains are achieved compared to standard inverse probability weighted methods.
Accuracy in selecting the optimal DTR is higher when using the joint model with multiplicity-adjusted comparisons.
The framework can be applied to other SMART studies to develop evidence-based adaptive treatment strategies using biomarker information.

Where Pith is reading between the lines

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

Future trials could use this approach to reduce the number of participants needed by leveraging biomarker data for greater precision.
The method might generalize to multi-stage SMARTs or other adaptive designs beyond two stages.
Integrating this with real-time decision support could lead to more responsive personalized medicine protocols.

Load-bearing premise

The biomarker trajectory follows a linear mixed model and the survival process follows the specified relative risk model linked to the latent biomarker, while standard causal assumptions for identification hold.

What would settle it

A simulation study in which the joint model is misspecified, such as by omitting a key random effect in the biomarker model, would produce biased DTR survival estimates that deviate from the known truth.

Figures

Figures reproduced from arXiv: 2605.03319 by Holly Hartman, Zhengxi Chen.

**Figure 1.** Figure 1: Schematic of the two-stage tailoring-variable sequential multiple assignment randomized trial design, longitudinal biomarker measurement schedule, and survival follow-up through administrative censoring. A, B, C and D represent the four available treatments; RD indicates a decision point for randomization; R and NR represent response and nonresponse; the expressions along the lines indicate treatment rando… view at source ↗

**Figure 3.** Figure 3: Diagnostic plots for the fitted joint model using the androgen-independent prostate cancer trial data: (A) observed and linear mixed model fitted mean log(PSA) trajectories by firststage treatment; (B) standardized conditional residuals versus fitted values; (C) normal Q–Q plot of standardized conditional residuals; (D) empirical Bayes estimates of the subject-specific random intercepts from the fitted jo… view at source ↗

read the original abstract

Sequential multiple assignment randomized trials (SMARTs) provide a systematic framework for constructing and evaluating dynamic treatment regimens (DTRs). In clinical studies, longitudinal biomarkers are routinely collected to monitor disease progression and define treatment response. However, the integration of longitudinal biomarker data into survival analysis for DTR evaluation within a SMART remains unexplored. We propose a joint longitudinal-survival framework to estimate DTR-specific survival outcomes within a two-stage SMART. A linear mixed model specifies the biomarker trajectory, and a relative risk model links the survival process to the current latent biomarker value. To accommodate the time-varying treatment assignment, treatment effects are parameterized through piecewise cumulative exposure terms with a structural change at the decision point. Joint-model parameters are estimated by maximum likelihood using pseudo-adaptive Gauss-Hermite quadrature for random-effect integration. Under standard causal identification assumptions, DTR-specific marginal survival outcomes are obtained through a plug-in parametric g-formula. We compare the joint-model framework to the inverse probability of treatment weighted Kaplan-Meier estimator and implement the multiple comparisons with the best method to identify the optimal DTR with multiplicity control. Through a simulation study and an application to a SMART for androgen-independent prostate cancer, we demonstrate that the joint-model framework produces unbiased estimates under correct model specification, with substantial efficiency gains and higher accuracy in optimal DTR identification. This framework exploits prognostic information from longitudinal biomarkers, enables valid causal inference for DTR-specific survival outcomes, and provides a generalizable analytic tool for developing evidence-based adaptive treatment strategies.

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 sets up a joint longitudinal-survival model for DTR evaluation in two-stage SMARTs that folds in biomarker trajectories via piecewise exposure terms and a plug-in g-formula, delivering efficiency gains over IPW-KM when the models are correct.

read the letter

The core contribution is a joint model that tracks a longitudinal biomarker with a linear mixed model, links its current value to a relative-risk survival process, and parameterizes the sequential treatments through cumulative exposure pieces that change at the decision point. Marginal DTR-specific survival curves then come from the parametric g-formula under standard causal assumptions. This combination for SMART survival analysis with biomarkers has not been laid out before, and the simulation confirms unbiased point estimates plus narrower intervals than inverse-probability-weighted Kaplan-Meier when specification is right. The prostate-cancer application shows the method running on real SMART data, and the multiple-comparisons-with-the-best step for optimal-regimen selection adds a practical control for error rates. The framework is internally consistent and the assumptions are stated plainly. The main limitation is the usual one for these models: unbiasedness and efficiency hold only under correct specification of both the biomarker trajectory and the survival link. Misspecification can produce bias, and while the paper conditions on correct models, real-data use will require diagnostics that are not always easy with the random effects. No hidden circularity or unstated identifiability problem appears. This is aimed at biostatisticians and trialists who work with adaptive designs and routinely collected biomarkers. Readers who need a tool to bring longitudinal prognostic information into causal survival estimates for DTRs will find it directly usable. The technical setup is coherent enough and fills a stated gap without load-bearing flaws, so it deserves a serious referee. I would send it out for peer review.

Referee Report

1 major / 3 minor

Summary. The manuscript proposes a joint longitudinal-survival modeling framework for estimating DTR-specific marginal survival outcomes in two-stage SMARTs. Biomarker trajectories are modeled via a linear mixed model, survival via a relative-risk model linked to the current latent biomarker value, and time-varying treatment effects via piecewise cumulative exposure terms with a structural break at the decision point. Joint parameters are estimated by maximum likelihood with pseudo-adaptive Gauss-Hermite quadrature; DTR-specific marginal survival curves are then obtained by a plug-in parametric g-formula under standard causal assumptions (consistency, positivity, no unmeasured confounding). The method is compared with IPW-KM, uses multiple-comparisons-with-the-best for optimal-DTR selection, and is illustrated in simulations (unbiasedness and efficiency gains under correct specification) and a prostate-cancer SMART application.

Significance. If the modeling assumptions hold, the framework offers a principled way to incorporate routinely collected longitudinal biomarker data into causal DTR evaluation for survival endpoints in SMARTs. This can yield efficiency gains relative to IPW-KM and improved accuracy in optimal-regimen identification, which is relevant for developing evidence-based adaptive treatment strategies in oncology and other fields where biomarkers are prognostic. The approach is transparent in its use of standard joint-modeling and g-formula machinery, and the explicit conditioning on correct specification is appropriately stated.

major comments (1)

[Simulation study] Simulation study section: the reported unbiasedness and efficiency gains are conditioned on correct model specification, yet the manuscript provides no explicit description of the data-generating process, chosen parameter values, sample sizes, number of Monte Carlo replications, or any sensitivity checks when the linear mixed model or relative-risk link is misspecified. Because the central claim of finite-sample performance rests on these simulations, the absence of these details makes it difficult to assess how robust the efficiency advantage is.

minor comments (3)

[Methods] Methods section: the piecewise cumulative exposure parameterization for treatment effects (structural change at the decision point) would benefit from an explicit equation or diagram showing how the cumulative exposure is constructed for each possible DTR path.
[Application] Application section: a table reporting the estimated joint-model parameters, predicted marginal survival probabilities at key time points, and standard errors for each DTR would make the prostate-cancer results easier to interpret and compare with the IPW-KM benchmark.
[Methods] Notation: the random-effect integration and the plug-in g-formula steps should be written with consistent indexing (e.g., explicit summation or integration limits over the random effects for each counterfactual treatment sequence).

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment and the overall positive evaluation of the manuscript. We address the major comment below.

read point-by-point responses

Referee: [Simulation study] Simulation study section: the reported unbiasedness and efficiency gains are conditioned on correct model specification, yet the manuscript provides no explicit description of the data-generating process, chosen parameter values, sample sizes, number of Monte Carlo replications, or any sensitivity checks when the linear mixed model or relative-risk link is misspecified. Because the central claim of finite-sample performance rests on these simulations, the absence of these details makes it difficult to assess how robust the efficiency advantage is.

Authors: We agree that the Simulation Study section requires additional detail for reproducibility and to allow readers to assess the reported performance. In the revised manuscript we will expand this section to provide a complete description of the data-generating process (including how longitudinal biomarker trajectories and survival times are generated under the joint model), the specific parameter values used for the linear mixed model, relative-risk model, and piecewise treatment effects, the sample sizes examined, the number of Monte Carlo replications, and new sensitivity analyses under misspecification of the linear mixed model (e.g., nonlinear biomarker trajectories) and the relative-risk link. These additions will directly address the concern about evaluating the robustness of the efficiency gains. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's derivation chain consists of fitting a standard joint longitudinal-survival model (linear mixed model for biomarker trajectories linked to a relative-risk survival model) via maximum likelihood, followed by a plug-in parametric g-formula to obtain marginal DTR-specific survival curves under the usual causal assumptions (consistency, positivity, no unmeasured confounding). This is the conventional two-step procedure for such models and does not reduce any target quantity to its fitted inputs by construction; the g-formula step is an explicit marginalization that requires the model to be correctly specified, which is stated as a precondition rather than smuggled in. No self-definitional loops, fitted parameters renamed as predictions, load-bearing self-citations, uniqueness theorems, or ansatz smuggling appear in the described framework. The simulation and application results are presented as finite-sample checks rather than as the source of the central claims.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on standard causal identification assumptions for the g-formula step and correct parametric specification of the linear mixed and relative risk models; no new entities are postulated and free parameters are the usual random effects and regression coefficients implicit in joint modeling.

axioms (1)

domain assumption standard causal identification assumptions
Invoked to justify obtaining DTR-specific marginal survival outcomes through the plug-in parametric g-formula.

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Works this paper leans on

3 extracted references · 3 canonical work pages

[1]

Petites Cellules

Fisher B, Dignam J, Bryant J, Wolmark N. Five versus more than five years of tamoxifen for lymph node-negative breast cancer: updated findings from the National Surgical Adjuvant Breast and Bowel Project B-14 randomized trial. J Natl Cancer Inst. May 2 2001;93(9):684-90. doi:10.1093/jnci/93.9.684 18. Hammel P, Huguet F, van Laethem JL, et al. Effect of Ch...

work page doi:10.1093/jnci/93.9.684 2001
[2]

Estimating the Cumulative Incidence Function of Dynamic Treatment Regimes

Yavuz I, Chng Y, Wahed AS. Estimating the Cumulative Incidence Function of Dynamic Treatment Regimes. Journal of the Royal Statistical Society Series A: Statistics in Society. 2018;181(1):85-106. 34. Lokhnygina Y, Helterbrand JD. Cox regression methods for two-stage randomization designs. Biometrics. Jun 2007;63(2):422-8. doi:10.1111/j.1541-0420.2007.0070...

work page doi:10.1111/j.1541-0420.2007.00707.x 2018
[3]

Adaptive therapy for androgen-independent prostate cancer: a randomized selection trial of four regimens

Thall PF, Logothetis C, Pagliaro LC, et al. Adaptive therapy for androgen-independent prostate cancer: a randomized selection trial of four regimens. J Natl Cancer Inst. Nov 7 2007;99(21):1613-22. doi:10.1093/jnci/djm189 52. Wang L, Rotnitzky A, Lin X, Millikan RE, Thall PF. Evaluation of Viable Dynamic Treatment Regimes in a Sequentially Randomized Trial...

work page doi:10.1093/jnci/djm189 2007

[1] [1]

Petites Cellules

Fisher B, Dignam J, Bryant J, Wolmark N. Five versus more than five years of tamoxifen for lymph node-negative breast cancer: updated findings from the National Surgical Adjuvant Breast and Bowel Project B-14 randomized trial. J Natl Cancer Inst. May 2 2001;93(9):684-90. doi:10.1093/jnci/93.9.684 18. Hammel P, Huguet F, van Laethem JL, et al. Effect of Ch...

work page doi:10.1093/jnci/93.9.684 2001

[2] [2]

Estimating the Cumulative Incidence Function of Dynamic Treatment Regimes

Yavuz I, Chng Y, Wahed AS. Estimating the Cumulative Incidence Function of Dynamic Treatment Regimes. Journal of the Royal Statistical Society Series A: Statistics in Society. 2018;181(1):85-106. 34. Lokhnygina Y, Helterbrand JD. Cox regression methods for two-stage randomization designs. Biometrics. Jun 2007;63(2):422-8. doi:10.1111/j.1541-0420.2007.0070...

work page doi:10.1111/j.1541-0420.2007.00707.x 2018

[3] [3]

Adaptive therapy for androgen-independent prostate cancer: a randomized selection trial of four regimens

Thall PF, Logothetis C, Pagliaro LC, et al. Adaptive therapy for androgen-independent prostate cancer: a randomized selection trial of four regimens. J Natl Cancer Inst. Nov 7 2007;99(21):1613-22. doi:10.1093/jnci/djm189 52. Wang L, Rotnitzky A, Lin X, Millikan RE, Thall PF. Evaluation of Viable Dynamic Treatment Regimes in a Sequentially Randomized Trial...

work page doi:10.1093/jnci/djm189 2007