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arxiv: 2605.05923 · v1 · submitted 2026-05-07 · 📊 stat.ME

Recognition: unknown

Joint modelling of time-dependent biomarker variability and time-to-event outcomes, a two-step approach

Dimitris Rizopoulos, Felix Boakye Oppong, Nicole Erler, Thierry Gorlia

Pith reviewed 2026-05-08 07:47 UTC · model grok-4.3

classification 📊 stat.ME
keywords joint modelingbiomarker variabilitysurvival analysistwo-step approachmixed-effects modellongitudinal biomarkerstime-to-event dataprognostic factors
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The pith

A two-step approach incorporates biomarker variability into standard joint models for time-to-event outcomes.

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

The paper seeks to address the limitation that typical joint models for longitudinal biomarkers and survival only model the mean biomarker level, ignoring variability. Evidence indicates that variability itself can predict survival outcomes. The authors introduce a practical method where residuals from a mixed-effects model serve as variability measures, which are then added to a joint model. Simulations confirm the approach works across scenarios, and application to glioblastoma trial data shows both mean and variability of white blood cell counts inform overall survival.

Core claim

By deriving subject- and time-specific variability measures from the residuals of a first-step mixed-effects model and including them as covariates in a second-step standard joint model, the association between biomarker variability and survival can be estimated alongside the mean trajectory using readily available software.

What carries the argument

The two-step procedure using mixed-effects residuals as time-dependent variability measures in a joint model.

Load-bearing premise

The variability measures calculated from the first-step residuals can be treated as known observed values in the joint model without causing meaningful bias due to estimation error or the separation of steps.

What would settle it

A direct comparison in simulations between this two-step method and a fully joint model that simultaneously models variability, where the two-step estimates differ substantially from the true values.

Figures

Figures reproduced from arXiv: 2605.05923 by Dimitris Rizopoulos, Felix Boakye Oppong, Nicole Erler, Thierry Gorlia.

Figure 1
Figure 1. Figure 1: Simulation results with one dataset for the model with view at source ↗
Figure 2
Figure 2. Figure 2: Simulation results with one dataset for the model with view at source ↗
Figure 3
Figure 3. Figure 3: WBC count over time for the first 20 subjects view at source ↗
read the original abstract

Increasing evidence suggests that variability in longitudinal biomarkers, in addition to their mean trajectory, carries prognostic information for time-to-event outcomes. However, standard joint models typically capture only the expected value of the biomarker process, assuming constant residual variability across individuals and time. Fully joint extensions that model within-subject variability exist but are computationally demanding and require dedicated software packages. We propose a flexible two-step approach for incorporating biomarker variability into joint models. First, residuals (or their transformations) from a mixed-effects model are used to derive subject- and time-specific measures of variability. Second, these variability measures are included in a standard joint model, allowing their association with survival to be estimated alongside the mean biomarker trajectory. Our approach can also accommodate multiple biomarkers simultaneously and is readily implemented using existing joint modeling software without custom extensions. Through simulations, we show that our method provides reasonable performance for variability effects across a range of scenarios. We further illustrate our approach using longitudinal data of white blood cell counts from a large phase III glioblastoma trial, demonstrating that both mean levels and variability of hematological markers carry prognostic information for overall survival.

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

3 major / 2 minor

Summary. The manuscript proposes a two-step approach to incorporate time-dependent biomarker variability into joint models of longitudinal data and time-to-event outcomes. A mixed-effects model is first fit to the biomarker trajectories to obtain residuals, from which subject- and time-specific variability measures are derived; these measures are then inserted as observed time-dependent covariates into a standard joint model (alongside the mean trajectory) whose survival submodel is estimated with existing software. Simulations are reported to show reasonable performance across scenarios, and the method is illustrated on white blood cell count data from a phase III glioblastoma trial, where both mean levels and variability are found to be prognostic for overall survival.

Significance. If the two-step procedure can be shown to control bias and coverage for the variability-survival association, the approach would supply a computationally lighter alternative to fully joint models that explicitly parameterize within-subject variability, thereby making variability-informed joint modeling more accessible with standard software packages.

major comments (3)
  1. [Methods (two-step procedure) and Simulation study] The core construction (first-step residuals turned into plug-in variability covariates for the second-step joint model) treats the derived variability measures as fixed and observed. This ignores estimation error in the residuals, their within-subject correlation, and any dependence on the fitted mean trajectory. When the number of observations per subject is modest or variability is itself heterogeneous, the plug-in step is expected to attenuate the estimated variability-survival association or produce invalid standard errors; the manuscript must quantify this bias (e.g., via a simulation that compares the two-step estimator to a gold-standard fully joint model under sparse-data regimes).
  2. [Simulation study] The abstract states that simulations demonstrate 'reasonable performance for variability effects across a range of scenarios,' yet the provided text supplies no details on the simulation design, true parameter values, number of replicates, performance metrics (bias, coverage probability, MSE), or the specific scenarios tested (e.g., varying numbers of observations per subject or degrees of heterogeneity). Without these, it is impossible to judge whether the method is robust precisely in the regimes where the two-step approximation is most vulnerable.
  3. [Application to glioblastoma trial data] The real-data illustration concludes that both mean levels and variability of hematological markers carry prognostic information, but the manuscript does not report sensitivity analyses that re-fit the first-step mixed model under different random-effect specifications or that propagate first-step uncertainty into the second-step joint model. Such checks are needed to confirm that the reported prognostic effects are not artifacts of the two-step separation.
minor comments (2)
  1. [Abstract] The abstract could replace the vague phrase 'reasonable performance' with concrete metrics (e.g., 'bias < 5 % and coverage > 90 % for the variability coefficient').
  2. [Methods] Notation for the derived variability measure (e.g., whether it is a rolling SD, MAD, or model-based variance) should be defined explicitly in the Methods section with an equation.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and describe the revisions we will make.

read point-by-point responses

  1. Referee: [Methods (two-step procedure) and Simulation study] The core construction (first-step residuals turned into plug-in variability covariates for the second-step joint model) treats the derived variability measures as fixed and observed. This ignores estimation error in the residuals, their within-subject correlation, and any dependence on the fitted mean trajectory. When the number of observations per subject is modest or variability is itself heterogeneous, the plug-in step is expected to attenuate the estimated variability-survival association or produce invalid standard errors; the manuscript must quantify this bias (e.g., via a simulation that compares the two-step estimator to a gold-standard fully joint model under sparse-data regimes).

    Authors: We acknowledge that the two-step procedure approximates the derived variability measures as observed covariates and does not propagate first-step estimation error. This is a known limitation that can lead to attenuation or invalid standard errors, especially with sparse data. We will extend the simulation study to include direct comparisons against a fully joint model (where feasible) under sparse regimes (3–6 observations per subject) and report bias, coverage, and MSE for the variability-survival association. revision: yes

  2. Referee: [Simulation study] The abstract states that simulations demonstrate 'reasonable performance for variability effects across a range of scenarios,' yet the provided text supplies no details on the simulation design, true parameter values, number of replicates, performance metrics (bias, coverage probability, MSE), or the specific scenarios tested (e.g., varying numbers of observations per subject or degrees of heterogeneity). Without these, it is impossible to judge whether the method is robust precisely in the regimes where the two-step approximation is most vulnerable.

    Authors: The simulation design, true parameter values, 500 replicates, metrics (bias, coverage, MSE), and scenarios (varying observations per subject and heterogeneity) are described in Section 3. We will revise the text to include an explicit summary table of all scenarios and performance results so that readers can directly evaluate robustness in sparse-data settings. revision: yes

  3. Referee: [Application to glioblastoma trial data] The real-data illustration concludes that both mean levels and variability of hematological markers carry prognostic information, but the manuscript does not report sensitivity analyses that re-fit the first-step mixed model under different random-effect specifications or that propagate first-step uncertainty into the second-step joint model. Such checks are needed to confirm that the reported prognostic effects are not artifacts of the two-step separation.

    Authors: We agree that sensitivity checks are warranted. We will add analyses re-fitting the first-step mixed model under alternative random-effect structures (e.g., random intercept only versus intercept and slope) and report the resulting changes in the variability-survival association. We will also explicitly discuss the lack of uncertainty propagation as a limitation of the two-step approach. revision: yes

Circularity Check

0 steps flagged

No circularity in the two-step proposal

full rationale

The paper proposes a practical two-step procedure: fit a standard mixed-effects model to longitudinal biomarkers, derive subject- and time-specific variability summaries from the residuals, and insert those summaries as covariates into an otherwise conventional joint model for the survival outcome. This construction is presented as an approximation to fully joint models that explicitly parameterize variability; it is validated by simulation studies that generate data under known variability-survival associations and by application to external trial data. No equation reduces to its own inputs by definition, no fitted parameter is relabeled as a prediction, and no load-bearing premise rests on self-citation. The method is therefore self-contained against external benchmarks and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions from mixed-effects and joint modeling literature plus the paper-specific assumption that first-step residuals can be used directly as covariates in the second step.

axioms (2)
  • domain assumption Mixed-effects models accurately separate individual trajectories from residuals that represent within-subject variability.
    Invoked in the first step to derive variability measures from residuals.
  • ad hoc to paper Variability measures from the first step can be included as observed time-dependent covariates in the joint model without adjustment for estimation error.
    This is the key linking assumption of the two-step procedure.

pith-pipeline@v0.9.0 · 5502 in / 1390 out tokens · 50672 ms · 2026-05-08T07:47:24.619331+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

35 extracted references · 2 canonical work pages

  1. [1]

    Peripheral Blood Biomarkers Associated with Clinical Outcome in Non–Small Cell Lung Cancer Patients Treated with Nivolumab.Journal of Thoracic Oncology, 13(1):97–105, 2018

    Junko Tanizaki, Koji Haratani, Hidetoshi Hayashi, Yasutaka Chiba, Yasushi Nakamura, Kimio Yonesaka, Keita Kudo, Hiroyasu Kaneda, Yoshikazu Hasegawa, Kaoru Tanaka, Masayuki Takeda, Akihiko Ito, and Kazuhiko Nakagawa. Peripheral Blood Biomarkers Associated with Clinical Outcome in Non–Small Cell Lung Cancer Patients Treated with Nivolumab.Journal of Thoraci...

    2018

  2. [2]

    Prognostic importance of temozolomide-induced neutropenia in glioblastoma, IDH-wildtype patients

    Taiichi Saito, Kazuhiko Sugiyama, Seiji Hama, Fumiyuki Yamasaki, Takeshi Takayasu, Ryo Nosaka, Yoshihiro Muragaki, Takakazu Kawamata, and Kaoru Kurisu. Prognostic importance of temozolomide-induced neutropenia in glioblastoma, IDH-wildtype patients. Neurosurgical Review, 41(2):621–628, 2018

    2018

  3. [3]

    Neutrophilia as a biomarker for overall survival in newly diagnosed high-grade glioma patients undergoing chemoradiation

    Antoine Schernberg, Alexandre Nivet, Frédéric Dhermain, Samy Ammari, Alexandre Es- cande, Johan Pallud, Guillaume Louvel, and Eric Deutsch. Neutrophilia as a biomarker for overall survival in newly diagnosed high-grade glioma patients undergoing chemoradiation. Clinical and Translational Radiation Oncology, 10(13):47–52, 2018

    2018

  4. [4]

    Prognostic significance of therapy-induced myelosuppression in newly diagnosed glioblas- toma.Neuro-Oncology, 24(9):1533–1545, 9 2022

    Emilie Le Rhun, Felix Boakye Oppong, Maureen Vanlancker, Roger Stupp, Burt Nabors, Olivier Chinot, Wolfgang Wick, Matthias Preusser, Thierry Gorlia, and Michael Weller. Prognostic significance of therapy-induced myelosuppression in newly diagnosed glioblas- toma.Neuro-Oncology, 24(9):1533–1545, 9 2022

    2022

  5. [5]

    Chapman and Hall/CRC., Boca Raton, 2012

    Dimitris Rizopoulos.Joint Models for Longitudinal and Time-to-Event Data With Appli- cations in R. Chapman and Hall/CRC., Boca Raton, 2012

    2012

  6. [6]

    Tsiatis and Marie Davidian

    Anastasios A. Tsiatis and Marie Davidian. Joint modeling of longitudinal and time-to- event data: An overview.Statistica Sinica, 14(3):809–834, 2004

    2004

  7. [7]

    Henderson, P

    R. Henderson, P. Diggle, and A. Dobson. Joint modelling of longitudinal measurements and event time data.Biostatistics, 1(4):465–480, 2000

    2000

  8. [8]

    A Bayesian semiparametric multivariate joint model for multiple longitudinal outcomes and a time-to-event.Statistics in Medicine, 30(12):1366–1380, 2011

    Dimitris Rizopoulos and Pulak Ghosh. A Bayesian semiparametric multivariate joint model for multiple longitudinal outcomes and a time-to-event.Statistics in Medicine, 30(12):1366–1380, 2011

    2011

  9. [9]

    Hatfield, Bradley P

    Dimitris Rizopoulos, Laura A. Hatfield, Bradley P. Carlin, and Johanna J.M. Takkenberg. Combining Dynamic Predictions From Joint Models for Longitudinal and Time-to-Event Data Using Bayesian Model Averaging.Journal of the American Statistical Association, 109(508):1385–1397, 2014

    2014

  10. [10]

    Wen Ye, Xihong Lin, and Jeremy M.G. Taylor. Semiparametric Modeling of Longitudinal Measurements and Time-to-Event Data–A Two-Stage Regression Calibration Approach. Biometrics, 64(4):1238–1246, 2008

    2008

  11. [11]

    Taylor, Yongseok Park, Donna P

    Jeremy M.G. Taylor, Yongseok Park, Donna P. Ankerst, Cecile Proust-Lima, Scott Williams, Larry Kestin, Kyoungwha Bae, Tom Pickles, and Howard Sandler. Real-Time Individual Predictions of Prostate Cancer Recurrence Using Joint Models.Biometrics, 69(1):206–213, 2013

    2013

  12. [12]

    Elizabeth R. Brown. Assessing the association between trends in a biomarker and risk of event with an application in pediatric HIV/AIDS.Annals of Applied Statistics, 3(3):1163– 1182, 2009. 14

    2009

  13. [13]

    Rising serum CA-125 levels within the normal range is strongly associated recurrence risk and survival of ovarian cancer

    Szymon Piatek, Grzegorz Panek, Zbigniew Lewandowski, Mariusz Bidzinski, Dominika Piatek, Przemyslaw Kosinski, and Miroslaw Wielgos. Rising serum CA-125 levels within the normal range is strongly associated recurrence risk and survival of ovarian cancer. Journal of Ovarian Research, 13(1):102, 2020

    2020

  14. [14]

    Visit-to-visit blood pressure variability and the risk of cardiovas- cular disease: a prospective cohort analysis.Hypertension Research, 46(12):2622–2634, 2023

    Shouling Wu, Xue Tian, Qin Xu, Yijun Zhang, Xiaoli Zhang, Penglian Wang, Shuohua Chen, and Anxin Wang. Visit-to-visit blood pressure variability and the risk of cardiovas- cular disease: a prospective cohort analysis.Hypertension Research, 46(12):2622–2634, 2023

    2023

  15. [15]

    Philip Miller, Chengjie Xiong, Julia A

    Feng Gao, J. Philip Miller, Chengjie Xiong, Julia A. Beiser, and Mae Gordon. A joint- modeling approach to assess the impact of biomarker variability on the risk of developing clinical outcome.Statistical Methods and Applications, 20(1):83–100, 2011

    2011

  16. [16]

    Barrett, Raphael Huille, Richard Parker, Yuichiro Yano, and Michael Griswold

    Jessica K. Barrett, Raphael Huille, Richard Parker, Yuichiro Yano, and Michael Griswold. Estimating the association between blood pressure variability and cardiovascular disease: An application using the ARIC Study.Statistics in Medicine, 38(10):1855–1868, 2019

    2019

  17. [17]

    Aflexiblelinkforjointmodellinglongitudinalandsurvivaldataaccountingfor individual longitudinal heterogeneity.Statistical Methods and Applications, 31(1):41–61, 2022

    RuiMartins. Aflexiblelinkforjointmodellinglongitudinalandsurvivaldataaccountingfor individual longitudinal heterogeneity.Statistical Methods and Applications, 31(1):41–61, 2022

    2022

  18. [18]

    A joint model of the individual mean and within-subject variability of a longitudinal outcome with a competing risks time-to-event outcome.arXiv:2301.06584, 2023

    ShanpengLi, DanielS.Nuyujukian, RobynL.McClelland, PeterD.Reaven, JinZhou, Hua Zhou, and Gang Li. A joint model of the individual mean and within-subject variability of a longitudinal outcome with a competing risks time-to-event outcome.arXiv:2301.06584, 2023

    work page arXiv 2023

  19. [19]

    Léonie Courcoul, Christophe Tzourio, Mark Woodward, Antoine Barbieri, and Hélène Jacqmin-Gadda. A Location-Scale Joint Model for Studying the Link Between the Time- Dependent Subject-Specific Variability of Blood Pressure and Competing Events.Statis- tics in Medicine, 44(20-22), 9 2025

    2025

  20. [20]

    A Bayesian location-scale joint model for time-to-event and multivariate longitudinal data with asso- ciation based on within-individual variability.arXiv:2503.12270, 3 2025

    Marco Palma, Ruth H Keogh, Siobhán B Carr, Rhonda Szczesniak, David Taylor- Robinson, Angela M Wood, Graciela Muniz-Terrera, and Jessica K Barrett. A Bayesian location-scale joint model for time-to-event and multivariate longitudinal data with asso- ciation based on within-individual variability.arXiv:2503.12270, 3 2025

    work page arXiv 2025

  21. [21]

    Rothwell, Sally C

    Peter M. Rothwell, Sally C. Howard, Eamon Dolan, Eoin O’Brien, Joanna E. Dobson, Bjorn Dahlöf, Peter S. Sever, and Neil R. Poulter. Prognostic significance of visit-to-visit variability, maximum systolic blood pressure, and episodic hypertension.The Lancet, 375(9718):895–905, 2010

    2010

  22. [22]

    Bolker, and Steven C

    Douglas Bates, Martin Mächler, Benjamin M. Bolker, and Steven C. Walker. Fitting linear mixed-effects models using lme4.Journal of Statistical Software, 67(1):1–48, 2015

    2015

  23. [23]

    nlme: Linear and nonlinear mixed effects models

    J Pinheiro, D Bates, S DebRoy, D Sarkar, and R Core Team. nlme: Linear and nonlinear mixed effects models. https://cran.r-project.org/package=nlme, 2019

    2019

  24. [24]

    Statistics and Computing, 2000

    JoseC.PinheiroandDouglasM.Bates.Mixed-EffectsModelsinSandS-PLUS. Statistics and Computing, 2000

    2000

  25. [25]

    Springer New York, NY, 2000

    Geert Verbeke and Geert Molenberghs.Linear Mixed Models for Longitudinal Data. Springer New York, NY, 2000. 15

    2000

  26. [26]

    Tripathi

    John Gurland and Ram C. Tripathi. A simple approximation for unbiased estimation of the standard deviation.The American Statistician,, 25(4):30–32, 1971

    1971

  27. [27]

    Brereton

    Richard G. Brereton. The t-distribution and its relationship to the normal distribution. Journal of Chemometrics, 29(9):481–483, 2015

    2015

  28. [28]

    R package version 0.5-95, https://github.com/drizopoulos/jmbayes2

    Dimitris Rizopoulos, Pedro Miranda Afonso, and Grigorios Papageorgiou.JMbayes2: Extended Joint Models for Longitudinal and Time-to-Event Data, 2025. R package version 0.5-95, https://github.com/drizopoulos/jmbayes2

    2025

  29. [29]

    R. L. Prentice. Covariate measurement errors and parameter estimation in a failure time regression model.Biometrika, 69(2):331–342, 1982

    1982

  30. [30]

    MacMahon, B

    S. MacMahon, B. Neal, C. Tzourio, A. Rodgers, M. Woodward, J. Cutler, C. Anderson, J. Chalmers, T. Ohkubo, M. G. Bouser, S. Davis, G. Donnan, L. Hansson, S. Harrap, K. R. Lees, L. Liu, G. Mancia, T. Omae, J. Reid, R. Sega, A. Terent, C. Warlow, N. Anderson, C. Bladin, B. Chambers, G. Gordon, N. Sharpe, R. Collins, P. Sandercock, J. Simes, P. Sleight, A. B...

    2001

  31. [31]

    R. P. Brent. Algorithms for Minimization Without Derivatives.IEEE Transactions on Automatic Control, 19(5):632–633, 1974

    1974

  32. [32]

    Reijneveld, Filip de Vos, Ahmed Idbaih, Jean Sébastien Frenel, Emilie Le Rhun, Juan Manuel Sepulveda, James Perry, G

    Patrick Roth, Thierry Gorlia, Jaap C. Reijneveld, Filip de Vos, Ahmed Idbaih, Jean Sébastien Frenel, Emilie Le Rhun, Juan Manuel Sepulveda, James Perry, G. Laura Masucci, Pierre Freres, Hal Hirte, Clemens Seidel, Annemiek Walenkamp, Slavka Luka- cova, Paul Meijnders, Andre Blais, Francois Ducray, Vincent Verschaeve, Garth Nicholas, Carmen Balana, Daniela ...

    2024

  33. [33]

    CRP/albumin ratio and WBC values correlate with Ki-67 and survival in glioblastoma multiforme.Frontiers in Oncology, 15:1612212, 2025

    Güven Gürsoy. CRP/albumin ratio and WBC values correlate with Ki-67 and survival in glioblastoma multiforme.Frontiers in Oncology, 15:1612212, 2025

    2025

  34. [34]

    Shuodan Zhang, Nadia McMillan, Matthew McGuinness, Stephen Trudeau, Ka Wai Grace Ho, and Erik J. Uhlmann. Peripheral biomarkers predict survival in patients with glioblas- toma treated with temozolomide.Molecular and Clinical Oncology, 22(6):56, 6 2025

    2025

  35. [35]

    Xu Guo and Bradley P. Carlin. Separate and Joint Modeling of Longitudinal and Event TimeDataUsingStandardComputerPackages.TheAmericanStatistician,, 58(1):16–24, 2004. 16 6 Supplementary Materials Table 3: Shapeκand scaleζparameters used in the simulation under differentα σ values for the model with linear and non-linear biomarker trajectory. ασ 0.02 0.07 ...

    2004