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A trajectory-based random forest predicts entire HbA1c response curves from baseline covariates, even under severe missingness, instead of reducing each patient to a single endpoint change.

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2026-08-01 06:35 UTC pith:OATGQRTT

load-bearing objection A plausible but not-yet-established framework: the general LRF algorithm loses its strongest empirical support once the hand-patched LRF-PACE-2 is set aside. the 5 major comments →

arxiv 2607.21817 v1 pith:OATGQRTT submitted 2026-07-23 stat.ME cs.LGstat.ML

Longitudinal Random Forests for Sparse and Irregular Response Trajectories

Yangsheng Wang , Xiaotian Dai , Haoda Fu , Guifang Fu This is my paper
classification stat.ME cs.LGstat.ML
keywords longitudinal data analysisrandom forestssparse and irregular observationstrajectory predictionvariable importanceinteraction detectionHbA1c durabilityclinical trials
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper tries to establish that the full shape of a patient's response over time—not just a single endpoint change—can be learned and predicted from baseline covariates, even when measurements are sparse, irregular, and full of long gaps. To do this it builds a random forest in which each tree node carries its own estimated longitudinal trajectory, and a split is chosen by how far the two resulting child trajectories are from each other, with a size-based penalty against unbalanced splits. The authors argue this joint scheme outperforms existing longitudinal tree methods and standard mixed models in simulations and on a large diabetes trial, where it predicts whole HbA1c curves for new patients and forecasts future values for existing ones. If the claim holds, clinical analyses of treatment durability could move off scalar endpoints and onto individualized trajectory prediction.

Core claim

The central claim is that longitudinal response trajectories can be modeled and predicted by embedding trajectory estimation inside the random-forest splitting process, rather than as a separate first step. At every node, subject trajectories are reconstructed with a node-specific smoother—nonparametric PACE or a semiparametric adaptive linear mixed model—and a candidate split is scored by the size-weighted integrated squared difference between the representative trajectories of the two child nodes. The forest then outputs an entire predicted trajectory for a new subject using only baseline covariates, and a forecast for an existing subject using covariates plus observed history. Simulations

What carries the argument

The load-bearing mechanism is the trajectory-based splitting criterion S(Xk,c) = (n_L n_R/(n_L+n_R)) ∫ (f̂_L(t) − f̂_R(t))² dt, which scores a split by the integrated squared difference between the representative trajectories of the resulting child nodes, penalizing unbalanced splits that could be driven by a few noisy subjects. The representative trajectory f̂_I(t) is the average of subject-specific smoothed trajectories within a node, estimated either by PACE (functional principal components via conditional expectation, a nonparametric method for sparse irregular data) or by an adaptive linear mixed-effects model whose fixed effects are chosen by the variables that split along the path to

Load-bearing premise

The whole procedure assumes that within small nodes (as few as 20 subjects) and with up to 70% of measurements missing, the node-level PACE or LMM estimates of subject trajectories are accurate enough that the integrated difference in Equation (4) separates true signal from noise; the paper itself shows this failed in realistic Simulation 2 until a piecewise fix, LRF-PACE–2, was introduced.

What would settle it

A controlled simulation in which the true child trajectories are identical but node-level smoothers produce large estimation errors—for example, nmin = 20 with 70% missingness and a long empty window—would show the splitting criterion selecting splits on noise. Equivalently, if full-window PACE were replaced by the piecewise LRF-PACE–2 strategy and predictive error on the near-empty Weeks 15–22 remained competitive, the paper's claim that the empty gap necessitates the adaptive fix would be falsified.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • For a new patient, the full expected response trajectory over the study period can be predicted from baseline covariates alone, before treatment begins, replacing endpoint-only projections.
  • For an existing patient with partial observations, future unobserved responses can be forecast, demonstrated by fitting Weeks 1–10 and predicting Weeks 11–14.
  • Permutation variable importance ranks covariates by their contribution to trajectory prediction, and a path co-occurrence count identifies two-, three-, and four-way interactions in one procedure without joint permutation.
  • In the diabetes application, the framework organizes covariates into clinically coherent importance groups—baseline HbA1c first, then glucose-related measures, then anthropometric and hemodynamic variables—and finds that therapy assignment has low importance, consistent with the small trial-level treatment difference.
  • A piecewise variant, LRF-PACE–2, is needed to handle near-empty observation windows like Weeks 15–22, showing that the framework's nonparametric variant is sensitive to large gaps and that adaptive local estimation restores performance.

Where Pith is reading between the lines

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

  • The splitting criterion maximizes between-node trajectory separation but is not shown to minimize any explicit prediction-error objective; a natural extension is to prove consistency or to compare it against a loss-based splitting rule under misspecified smoother models.
  • New-subject predictions from LRF-PACE use only node-level representative trajectories, so predicted curves may understate between-patient variability; interval estimates or quantile extensions would be a testable way to quantify this.
  • The frequency-based interaction count weights covariates near the root more heavily because they appear in more paths; normalizing by depth or by number of subjects traversing the split would give a fairer interaction importance measure.
  • The same machinery should transfer to other sparse longitudinal biomarkers where durability matters—renal function, blood pressure, or weight trajectories—but the simulation suggests a piecewise or parametric smoother will be required whenever the observation window contains a large empty gap.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper proposes a Longitudinal Random Forest (LRF) framework for modeling sparse, irregular, and unequally spaced longitudinal response trajectories as functions of baseline covariates. Two variants are introduced: LRF–PACE, which uses PACE as a node-wise nonparametric smoother, and LRF–adaptiveLMM, which embeds a linear mixed-effects model at each node with an adaptively selected fixed-effects structure. A trajectory-based splitting criterion (Eq. 4) maximizes the size-weighted integrated squared difference between child-node representative trajectories. The framework also provides a permutation variable importance measure and a frequency-based multi-way interaction detection procedure. Performance is evaluated in two simulations—one with dense observations under increasing missingness and one mimicking the INSULIN trial’s empirical missingness pattern—plus a real-data analysis of the INSULIN trial. The central claims are superior predictive performance even under severe sparsity and the ability to address five clinical questions, including prediction of entire trajectories for new subjects and forecasting future values for existing subjects.

Significance. If the results are reliable, the LRF framework is a valuable addition to the longitudinal and functional data literature: it integrates tree-based ensemble learning with flexible node-wise trajectory estimation, offers a novel split criterion, and addresses practical clinical questions. The manuscript is ambitious and includes an explicit algorithm, two estimation variants, and a real-data application. However, the claimed 'superior performance even under severe sparsity' is not convincingly established. The best-performing variant in Simulation 2, LRF–PACE–2, is a manual, data-set-specific modification introduced after the original LRF–PACE failed; no general selection mechanism is provided. Moreover, simulation results are reported only as averages with no uncertainty quantification, and the frequency-based interaction detector is never validated in simulation. These issues are load-bearing for the paper’s main claims, but they are addressable in a revision.

major comments (5)
  1. [§4.3, Table 4] The Abstract and Discussion state that 'LRF achieves superior performance over several competing methods, even under severe sparsity.' In Simulation 2, however, the variant achieving the lowest prediction error is LRF–PACE–2, which is not the algorithm defined in §3.1–§3.3. The paper admits (Sec. 4.3) that the original LRF–PACE 'did not perform well' under the full 24-week schedule. LRF–PACE–2 is created by applying PACE only to Weeks 1–14, extrapolating through the empty Weeks 15–22, and replacing Weeks 23–24 with simple averages. Because the simulation’s missingness pattern is itself estimated from the INSULIN trial, the patch exploits detailed knowledge of the evaluation regime. No principled adaptive procedure for choosing such a segmentation is described. Consequently, the 'superior performance under severe sparsity' claim is supported only by a data-set-specific adjustment, not by
  2. [§3.2, Eq. (4); §4.3] The split criterion in Eq. (4) uses node-specific trajectory estimates bY_{i,I}(t) from Eqs. (1)–(2). With nmin=20 and up to 70% missingness (Simulation 1) or near-empty intervals (Simulation 2), these estimates at small nodes are likely unstable. The manuscript never isolates whether the integrated squared difference in Eq. (4) separates true signal from noise at nodes of size 20. The admitted failure of LRF–PACE in Simulation 2 is direct evidence that this assumption can fail in the realistic setting the paper targets. No diagnostic, simulation experiment, or remedy is provided for the general algorithm, which weakens the claim that the splitting rule itself is sound.
  3. [§3.3, Eq. (6)] For LRF–PACE, the forecast for an existing subject at a future time is bf_I(tnew)—the node-average representative trajectory—not a subject-specific trajectory. The subject's own observed responses do not appear in Eq. (6), and routing to a terminal node is based on covariates only. This directly contradicts the Abstract’s claim of 'individualized response trajectories' and the Discussion’s emphasis on personalized medicine. The predictive distinction between LRF–PACE and LRF–adaptiveLMM should be stated clearly, and the personalized-forecasting claim should be qualified accordingly.
  4. [§3.5, Table 7] The frequency-based interaction detection is presented as a major methodological contribution, but no simulation evidence is provided that co-occurrence frequencies along root-to-terminal paths correspond to true statistical interactions. The real-data results in Table 7 are interpreted substantively (e.g., 'SBP's contribution is driven primarily by interaction effects'), yet there is no calibration of the frequency threshold, no comparison to known interaction structures, and no false-discovery analysis. Without a simulation study or theoretical justification, the interaction findings remain unvalidated and the claimed advantage over permutation-based interaction detection is not demonstrated.
  5. [Tables 1–5 and Tables 8–9] All simulation results are reported as averages over 100 replications, but no standard errors, confidence intervals, or paired comparisons are given. In several cases the differences are small (e.g., Table 2, 70% missingness: LRF–PACE 1.81 vs. SREEMF 2.02; Table 4: LRF–PACE–2 3.06 vs. SPLF 3.24). Without uncertainty quantification it is impossible to assess whether the claimed 'superior performance' is statistically meaningful. The real-data results in Table 8 similarly report single cross-validated averages with no variability measures, and Table 9 reports only Spearman correlations, which may mask systematic prediction errors.
minor comments (5)
  1. [§3.1 introduction] There is a typographical error: 'tir' should presumably be 'tij' in the definition of the observed data.
  2. [Abstract/Introduction] The phrasing 'representing a revolutionary advance over traditional endpoint efficacy analysis' is editorializing. Suggest replacing with a neutral statement about the proposed framework's scope.
  3. [§4.2] The example tree described as 'a tree consisting of only two decision nodes' actually induces three terminal nodes; the wording is confusing.
  4. [Table 9] The sentence 'Both Panels demonstrate only Week 12' is unclear; presumably it means that only Week 12 results are shown.
  5. [Figure 2 caption] The caption refers to 'representative trajectory' but does not define it; linking to Eq. (3) in the caption would aid the reader.

Circularity Check

0 steps flagged

No significant circularity: predictions and simulation comparisons are computed from data and external baselines, not from the claims themselves.

full rationale

The paper proposes an algorithm rather than deriving a mathematical result, so the relevant circularity checks are whether reported predictions are constructed from their own targets. They are not. New-subject trajectories are predicted from covariates via node membership and node-level trajectory averages (Eqs. 3, 5, 7); future forecasts for existing subjects use past-data node representatives (Eq. 6); both are evaluated on held-out observations (Eqs. 10, 13). The trajectory-based splitting criterion (Eq. 4) measures integrated squared differences of node-average trajectories, an operational objective, not a quantity later reported as an independent prediction. PVIM (Eq. 9) is a standard permutation importance computed from OOB error. The frequency-based interaction counts are defined directly as covariate co-occurrences along tree paths, so Table 7 is a descriptive summary of the fitted ensemble rather than a circular claim. References [14] and [59] share a coauthor (H. Fu) and are cited to motivate the scalar-endpoint limitation and for real-data comparison, but neither is load-bearing for the LRF algorithm or its simulation performance; the simulation evidence is generated against independent comparators (SPLF, SREEMF, LongCART, LMM, GEE). The introduction of LRF-PACE-2 after the original LRF-PACE struggled in Simulation 2 is a disclosed model-selection issue that may affect the generality of the sparsity claim, but it is not circular: the reported errors are still measured on test subjects. No step reduces by construction to its own input.

Axiom & Free-Parameter Ledger

7 free parameters · 5 axioms · 0 invented entities

The method introduces no new scientific entities. The central claim rests on several hand-set tuning choices (nmin, mtry, B, dmax, L, bandwidths), a hand-adapted LRF-PACE-2 segmentation, and unvalidated structural assumptions about the accuracy of small-node PACE and the meaning of tree-path co-occurrence frequencies.

free parameters (7)
  • nmin (minimum node size) = 20
    Chosen by hand in §3.6; controls stability of node-level smoothers that the splitting rule depends on.
  • mtry (candidate covariates per split) = p/3
    Set by common practice in §3.6; affects variable selection and tree diversity.
  • B (number of trees) = 50
    Set in §3.6; the paper states this is sufficient for stable performance without a formal criterion.
  • dmax (maximum tree depth) = selected by 5-fold CV
    Tuning parameter in §3.6; selected values are not reported for simulations or real data.
  • L (number of PACE components) = explain ≥90% variance per node
    Adaptive node-specific bandwidth/component choice in §3.1.1 and §3.6; affects trajectory reconstruction quality.
  • PACE bandwidth h_I = GCV-selected
    Node-specific Gaussian kernel bandwidths selected by GCV (§3.1.1); values not reported.
  • LRF-PACE-2 segmentation = PACE weeks 1-14; extrapolate 15-22; simple average at weeks 23-24
    Hand-crafted modification introduced because original LRF-PACE failed under the realistic missingness pattern (§4.3); this variant carries the main prediction results.
axioms (5)
  • domain assumption PACE local-linear and 2D kernel smoothing recover the node mean, covariance, eigenfunctions, and FPC scores accurately at node sizes as small as nmin=20 and at 70% missingness.
    Used throughout §3.1.1 and §3.2; no diagnostic in the paper isolates this assumption.
  • domain assumption The average trajectory bf_I(t) is an adequate summary of a node for comparing split quality in Eq. (4).
    The splitting rule trusts within-node averaged trajectories; it is sensitive to outliers and small sample sizes.
  • standard math Bootstrap OOB predictions and averaging across B=50 trees are unbiased and stable.
    Standard random-forest heuristic invoked in §3.3 and §3.6.
  • domain assumption Random intercept and random slope capture within-subject correlation in LRF-adaptiveLMM.
    Used in Eq. (2); the linear trajectory assumption is explicitly acknowledged as restrictive in §6.
  • ad hoc to paper Co-occurrence of covariates along root-to-terminal paths tracks true statistical interactions.
    Proposed in §3.5 and presented in Table 7; no null baseline, no simulation validation, and counts are confounded by tree depth, collinearity, and split order.

pith-pipeline@v1.3.0-alltime-deepseek · 22939 in / 16215 out tokens · 166613 ms · 2026-08-01T06:35:26.125147+00:00 · methodology

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read the original abstract

Longitudinal studies often collect data at sparse, irregular, and unequally spaced time points. Such heterogeneity is often driven by subject-specific covariates, yet existing methods have been restricted to a scalar endpoint value, completely neglecting the underlying response trajectories. We propose a novel Longitudinal Random Forest (LRF) framework that leverages tree-based ensemble machine learning with adaptive node-wise longitudinal trajectory estimation. The LRF framework makes five methodological contributions. it captures each subject's individual response trajectory while simultaneously accommodating within-node correlation, between-node heterogeneity, and nonlinear and interactive covariate effects. It introduces a novel trajectory-based splitting criterion that maximizes trajectory separation while incorporating a size-weighted penalty; it provides two variants, Principal Analysis by Conditional Expectation (LRF-PACE) and adaptive linear mixed-effects models (LRF-adaptiveLMM), which employ nonparametric and semiparametric node-wise smoothers, respectively, while learning covariate effects in a data-driven manner. It provides a comprehensive interpretation of covariates using both the classical trajectory-based permutation variable importance measure (PVIM) and a newly proposed finite-way interaction frequency count, and it not only predicts entire trajectories for new subjects but also forecasts future trajectories for existing subjects. Extensive simulation studies demonstrate that LRF achieves superior performance over several competing methods, even under severe sparsity. The practical significance of the LRF framework lies in its ability to address five important clinical questions.

Figures

Figures reproduced from arXiv: 2607.21817 by Guifang Fu, Haoda Fu, Xiaotian Dai, Yangsheng Wang.

Figure 1
Figure 1. Figure 1: The original discretely and repeatedly measured HbA1c values for nine representative [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: A representative tree obtained by fitting LRF–PACE to the INSULIN trial data. The [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Predicted trajectories for three randomly selected test subjects from the INSULIN trial [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Forecasted trajectories for three randomly selected training subjects from the INSULIN trial [PITH_FULL_IMAGE:figures/full_fig_p022_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Scatterplots of the ranks of the predicted/forecasted HbA1c response values versus the [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗

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Reference graph

Works this paper leans on

69 extracted references · 38 canonical work pages

  1. [1]

    A semi-parametric mixed models for longitudinally measured fasting blood sugar level of adult diabetic patients.BMC Medical Research Methodology, 19(1): 13, 2019

    Tafere Tilahun Aniley, Legesse Kassa Debusho, Zelalem Mehari Nigusie, Wondwosen Kassahun Yimer, and Belay Birlie Yimer. A semi-parametric mixed models for longitudinally measured fasting blood sugar level of adult diabetic patients.BMC Medical Research Methodology, 19(1): 13, 2019. doi: 10.1186/s12874-018-0648-x

    work page doi:10.1186/s12874-018-0648-x 2019

  2. [2]

    Beverley Balkau, Françoise Calvi-Gries, Nick Freemantle, Maya Vincent, Valérie Pilorget, and Philip D. Home. Predictors of hba1c over 4 years in people with type 2 diabetes starting insulin therapies: The credit study.Diabetes Research and Clinical Practice, 108(3):432–440,

  3. [3]

    Buse, Bruce H.R

    John B. Buse, Bruce H.R. Wolffenbuttel, William H. Herman, Natalie K. Shemonsky, Honghua H. Jiang, Jessie L. Fahrbach, Jamie L. Scism-Bacon, and Sherry A. Martin. Durability of basal versus lispro mix 75/25 insulin efficacy (durable) trial 24-week results: Safety and efficacy of insulin lispro mix 75/25 versus insulin glargine added to oral antihyperglyce...

    work page doi:10.2337/dc08-2117 2009

  4. [4]

    Buse, Bruce H

    John B. Buse, Bruce H. R. Wolffenbuttel, William H. Herman, Stephen Hippler, Sherry A. Martin, Honghua H. Jiang, Sylvia K. Shenouda, and Jessie L. Fahrbach. Durability of basal versus lispro mix 75/25 insulin efficacy (durable) trial: comparing the durability of lispro mix 75/25 and glargine.Diabetes Care, 34(2):249–255, February 2011. doi: 10.2337/dc10-1701

    work page doi:10.2337/dc10-1701 2011

  5. [5]

    URLhttps://cran

    Loïc Capitaine.LongituRF: Random forests for longitudinal data, 2020. URLhttps://cran. r-project.org/package=LongituRF. R package version 0.9

    2020

  6. [6]

    Random forests for high-dimensional longitudinal data.Statistical Methods in Medical Research, 30(1):166–184, 2021

    Loïc Capitaine, Robin Genuer, and Rodolphe Thiébaut. Random forests for high-dimensional longitudinal data.Statistical Methods in Medical Research, 30(1):166–184, 2021

    2021

  7. [7]

    E. J. Caruana, M. Roman, J. Hernández-Sánchez, and P. Solli. Longitudinal studies.Journal of Thoracic Disease, 7(11):E537–E540, 2015. doi: 10.3978/j.issn.2072-1439.2015.10.63. 25

    arXiv 2015

  8. [8]

    Gaurav Chandra, Petteri Lavikainen, Pekka Siirtola, Sanna Tamminen, Anuradha Ihalap- athirana, Tiina Laatikainen, and Juha Röning. Explainable prediction of long-term glycated hemoglobin response change in finnish patients with type 2 diabetes following drug initiation using evidence-based machine learning approaches.Clinical Epidemiology, 17:225–240, 202...

    work page doi:10.2147/clep.s505966 2025

  9. [9]

    Regression analysis of longitudinal data with irregular and informative observation times.Biostatistics, 16(4):727–739, 2015

    Yong Chen, Jing Ning, and Chunyan Cai. Regression analysis of longitudinal data with irregular and informative observation times.Biostatistics, 16(4):727–739, 2015. doi: 10.1093/biostatis- tics/kxv008. URLhttps://doi.org/10.1093/biostatistics/kxv008

    work page doi:10.1093/biostatis- 2015

  10. [10]

    Delporte, M

    M. Delporte, M. Aerts, G. Verbeke, and G. Molenberghs. Analysing matched continuous longitudinal data: A review.Statistical Methods in Medical Research, 34(1):170–179, 2024. doi: 10.1177/09622802241300823. URLhttps://doi.org/10.1177/09622802241300823

    work page doi:10.1177/09622802241300823 2024

  11. [11]

    L. Deng, L. Jia, X. L. Wu, and M. Cheng. Association between body mass index and glycemic control in type 2 diabetes mellitus: A cross-sectional study.Diabetes, Metabolic Syndrome and Obesity: Targets and Therapy, 18:555–563, February 2025. doi: 10.2147/DMSO.S508365. URL https://doi.org/10.2147/DMSO.S508365

    work page doi:10.2147/dmso.s508365 2025

  12. [12]

    Biostatistics of generalized estimating equations in developmental medicine and child neurology.Developmental Medicine & Child Neurology, 68 (6):767–773, 2026

    Camille Eugénie Dieu and Giovanni Briganti. Biostatistics of generalized estimating equations in developmental medicine and child neurology.Developmental Medicine & Child Neurology, 68 (6):767–773, 2026. doi: 10.1111/dmcn.70060

    work page doi:10.1111/dmcn.70060 2026

  13. [13]

    Diggle, Patrick Heagerty, Kung-Yee Liang, and Scott L

    Peter J. Diggle, Patrick Heagerty, Kung-Yee Liang, and Scott L. Zeger.Analysis of Longitudinal Data. Oxford University Press, 2 edition, 2002

    2002

  14. [14]

    Analgorithmforgeneratingindividualized treatment decision trees and random forests.Journal of Computational and Graphical Statistics, 27(4):849–860, 2018

    KevinDoubleday, HuaZhou, HaodaFu, andJinZhou. Analgorithmforgeneratingindividualized treatment decision trees and random forests.Journal of Computational and Graphical Statistics, 27(4):849–860, 2018. doi: 10.1080/10618600.2018.1451337. PMCID: PMC7274035

    arXiv 2018

  15. [15]

    Dungan, Silvio Torro Povedano, Thomas Forst, et al

    Kathleen M. Dungan, Silvio Torro Povedano, Thomas Forst, et al. Once-weekly dulaglutide versus once-daily liraglutide in type 2 diabetes (award-6).Lancet, 384(9951):1349–1357, 2014. doi: 10.1016/S0140-6736(14)60976-4

    work page doi:10.1016/s0140-6736(14)60976-4 2014

  16. [16]

    Katherine Esposito, Paolo Chiodini, Annalisa Capuano, Maria Ida Maiorino, Giuseppe Bel- lastella, and Dario Giugliano. Baseline glycemic parameters predict the hemoglobin A1c response to DPP-4 inhibitors: meta-regression analysis of 78 randomized controlled trials with 20,053 patients.Endocrine, 46(1):43–51, 2014. doi: 10.1007/s12020-013-0090-0

    work page doi:10.1007/s12020-013-0090-0 2014

  17. [17]

    Nomogram to estimate the hba1c response to different dpp-4 inhibitors in type 2 diabetes: a systematic review and meta-analysis of 98 trials with 24,163 patients

    Katherine Esposito et al. Nomogram to estimate the hba1c response to different dpp-4 inhibitors in type 2 diabetes: a systematic review and meta-analysis of 98 trials with 24,163 patients. BMJ Open, 5(2):e005892, 2015. doi: 10.1136/bmjopen-2014-005892. URLhttps://bmjopen. bmj.com/content/5/2/e005892

    work page doi:10.1136/bmjopen-2014-005892 2015

  18. [18]

    URLhttps://www.ema.europa.eu/en/documents/scientific-guideline/ guideline-adjustment-baseline-covariates-clinical-trials_en.pdf

    European Medicines Agency.Guideline on Adjustment for Baseline Covariates in Clini- cal Trials, 2015. URLhttps://www.ema.europa.eu/en/documents/scientific-guideline/ guideline-adjustment-baseline-covariates-clinical-trials_en.pdf

    2015

  19. [19]

    E. Eyth, M. Zubair, and R. Naik. Hemoglobin a1c. InStatPearls [Internet]. StatPearls Publishing, Treasure Island, FL, 2025. [Updated 2025 Jun 2]. Available from:https://www. ncbi.nlm.nih.gov/books/NBK549816/. 26

    2025

  20. [20]

    Analysis of longitudinal data with semiparametric estimation of covariance function.Journal of the American Statistical Association, 102(478): 632–641, 2007

    Jianqing Fan, Tao Huang, and Runze Li. Analysis of longitudinal data with semiparametric estimation of covariance function.Journal of the American Statistical Association, 102(478): 632–641, 2007. doi: 10.1198/016214507000000095

    work page doi:10.1198/016214507000000095 2007

  21. [21]

    Fitzmaurice, Nan M

    Garrett M. Fitzmaurice, Nan M. Laird, and James H. Ware.Applied Longitudinal Analysis. John Wiley & Sons, Hoboken, NJ, 2nd edition, 2011. ISBN 978-0-470-38027-7

    2011

  22. [22]

    Frías, Melanie J

    Juan P. Frías, Melanie J. Davies, Julio Rosenstock, et al. Tirzepatide versus semaglutide once weekly in patients with type 2 diabetes.New England Journal of Medicine, 385(6):503–515,

  23. [23]

    Hajjem, F

    A. Hajjem, F. Bellavance, and D. Larocque. Mixed effects regression trees for clustered data. Statistics and Probability Letters, 81(4):451–459, 2011

    2011

  24. [24]

    Hajjem, F

    A. Hajjem, F. Bellavance, and D. Larocque. Mixed effects random forest for clustered data. Journal of Statistical Computation and Simulation, 84(6):1313–1328, 2014

    2014

  25. [25]

    Gillett, Rahul Bala, John Tyrrell, and Cathryn M

    Daniel Handley, Alexander C. Gillett, Rahul Bala, John Tyrrell, and Cathryn M. Lewis. Latent class growth mixture modeling of hba1c trajectories identifies individuals at high risk of developing complications of type 2 diabetes mellitus in the UK Biobank.BMJ Open Diabetes Research & Care, 13(5):e004826, 2025. doi: 10.1136/bmjdrc-2024-004826

    work page doi:10.1136/bmjdrc-2024-004826 2025

  26. [26]

    Missing data analysis using multiple imputation: getting to the heart of the matter

    Yang He. Missing data analysis using multiple imputation: getting to the heart of the matter. Circulation: Cardiovascular Quality and Outcomes, 3(1):98–105, 2010. doi: 10.1161/CIRCOUT- COMES.109.875658

    work page doi:10.1161/circout- 2010

  27. [27]

    Horton and Ken P

    Nicholas J. Horton and Ken P. Kleinman. Much ado about nothing: A comparison of missing data methods and software to fit incomplete data regression models.The American Statistician, 61(1):79–90, 2007. doi: 10.1198/000313007X172556

    work page doi:10.1198/000313007x172556 2007

  28. [28]

    The relationship between bmi and glycated albumin to glycated hemoglobin (ga/a1c) ratio according to glucose tolerance status.PLoS ONE, 9(2):e89478, 2014

    Jae Hyun Huh, Kyu Jeung Kim, Byung-Wan Lee, Dae-Won Kim, Eun Seok Kang, Bong Soo Cha, and Hyeong Cheol Lee. The relationship between bmi and glycated albumin to glycated hemoglobin (ga/a1c) ratio according to glucose tolerance status.PLoS ONE, 9(2):e89478, 2014. doi: 10.1371/journal.pone.0089478. URL https://doi.org/10.1371/journal.pone.0089478

    work page doi:10.1371/journal.pone.0089478 2014

  29. [29]

    K. Kim, S. Unni, D. I. Brixner, S. M. Thomas, C. J. Olsen, K. L. Sterling, M. Mitchell, and C. McAdam-Marx. Longitudinal changes in glycated haemoglobin following treatment intensification after inadequate response to two oral antidiabetic agents in patients with type 2 diabetes.Diabetes, Obesity and Metabolism, 21(7):1725–1733, 2019. doi: 10.1111/dom.13694

    work page doi:10.1111/dom.13694 2019

  30. [30]

    Regression trees for longitudinal data with baseline covariates.Biostatistics & Epidemiology, 3(1):1–22, 2019

    Malay Ghosh Kundu and Jaroslaw Harezlak. Regression trees for longitudinal data with baseline covariates.Biostatistics & Epidemiology, 3(1):1–22, 2019. doi: 10.1080/24709360.2018.1557797

    arXiv 2019

  31. [31]

    Laird and James H

    Nan M. Laird and James H. Ware. Random-effects models for longitudinal data.Biometrics, 38(4):963–974, December 1982. ISSN 0006-341X

    1982

  32. [32]

    Kung-Yee Liang and Scott L. Zeger. Longitudinal data analysis using generalized linear models. Biometrika, 73(1):13–22, 1986. doi: 10.1093/biomet/73.1.13

    doi:10.1093/biomet/73.1.13 1986

  33. [33]

    Birong Liao, Yun Chen, Farai Chigutsa, and Carolina Piras de Oliveira. Fasting and postprandial plasma glucose contribution to glycated haemoglobin and time in range in people with type 2 diabetes on basal and bolus insulin therapy: Results from a pooled analysis of insulin lispro clinical trials.Diabetes, Obesity and Metabolism, 23(7):1571–1579, 2021. do...

    work page doi:10.1111/dom.14370 2021

  34. [34]

    Mehrotra

    Kaifeng Lu and Devan V. Mehrotra. Specification of covariance structure in longitudinal data analysis for randomized clinical trials.Statistics in Medicine, 29(4):474–488, 2010. doi: 10.1002/sim.3820

    work page doi:10.1002/sim.3820 2010

  35. [35]

    Ming Luo, Kenneth H. X. Tan, Chuen Seng Tan, Wei Yen Lim, E. Shyong Tai, and Kavita Venkataraman. Longitudinal trends in hba1c patterns and association with outcomes: A systematic review.Diabetes & Metabolism Research and Reviews, 34(6):e3015, 2018. doi: 10.1002/dmrr.3015

    work page doi:10.1002/dmrr.3015 2018

  36. [36]

    Mallinckrodt, Peter W

    Craig H. Mallinckrodt, Peter W. Lane, David Schnell, Yi Peng, and John P. Mancuso. Recommen- dationsfortheprimaryanalysisofcontinuousendpointsinlongitudinalclinicaltrials.Therapeutic Innovation & Regulatory Science, 42(4):303–319, 2008. doi: 10.1177/009286150804200402

    work page doi:10.1177/009286150804200402 2008

  37. [37]

    Mancl and Timothy A

    Lloyd A. Mancl and Timothy A. DeRouen. A covariance estimator for gee with improved small-sample properties.Biometrics, 57(1):126–134, 2001

    2001

  38. [38]

    McCarthy

    Mark I. McCarthy. Painting a new picture of personalised medicine for diabetes.Diabetologia, 60(5):793–799, 2017. doi: 10.1007/s00125-017-4210-x

    work page doi:10.1007/s00125-017-4210-x 2017

  39. [39]

    McCoy, Lisa Faust, Heather C

    Renee G. McCoy, Lisa Faust, Heather C. Heien, Shilpa Patel, Brian Caffo, and Che Ngufor. Longitudinal trajectories of glycemic control among u.s. adults with newly diagnosed diabetes. Diabetes Research and Clinical Practice, 205:110989, 2023. doi: 10.1016/j.diabres.2023.110989

    arXiv 2023

  40. [40]

    Anna Neufeld and Brianna Heggeseth.splinetree: Longitudinal Regression Trees and Forests,

  41. [41]

    Ewan R. Pearson. Type 2 diabetes: a multifaceted disease.Diabetologia, 62(6):1107–1112, 2019. doi: 10.1007/s00125-019-4909-y

    work page doi:10.1007/s00125-019-4909-y 2019

  42. [42]

    Franco, An Pan, Maigeng Zhou, Kai Huang, and Gang Liu

    Zixin Qiu, Frank Qian, Jun Liu, Rui Li, Hancheng Yu, Yue Wang, Xiao Zhang, Tingting Geng, Xuefeng Yu, Oscar H. Franco, An Pan, Maigeng Zhou, Kai Huang, and Gang Liu. Phenotypic heterogeneity of type 2 diabetes and risks of all-cause and cause-specific mortality.Cell Reports Medicine, page 102367, 2025. ISSN 2666-3791. doi: https://doi.org/10.1016/j.xcrm.2...

    arXiv 2025

  43. [43]

    Regulatory experiences with the use of multiple imputation for missing data in a phase 3 confirmatory trial.Therapeutic Innovation & Regulatory Science, 60(1):8–14, 2026

    Mouna Sassi-Sayadi, Pierre Verweij, and Peter Cornelisse. Regulatory experiences with the use of multiple imputation for missing data in a phase 3 confirmatory trial.Therapeutic Innovation & Regulatory Science, 60(1):8–14, 2026. doi: 10.1007/s43441-025-00872-1

    work page doi:10.1007/s43441-025-00872-1 2026

  44. [44]

    Model-based meta-analysis of hba1c reduction across sglt2 inhibitors using dose adjusted by urinary glucose excretion.Scientific Reports, 14:24695, 2024

    Hiroshi Sato, Akira Ishikawa, Hiroyuki Yoshioka, et al. Model-based meta-analysis of hba1c reduction across sglt2 inhibitors using dose adjusted by urinary glucose excretion.Scientific Reports, 14:24695, 2024. doi: 10.1038/s41598-024-76256-6. URLhttps://doi.org/10.1038/ s41598-024-76256-6

    work page doi:10.1038/s41598-024-76256-6 2024

  45. [45]

    Savieri, L

    P. Savieri, L. Stas, and K. Barbé. Limmcov: An interactive research tool for efficiently selecting covariance structures in linear mixed models using insights from time series analysis.PLOS ONE, 20(6):e0325834, 2025. doi: 10.1371/journal.pone.0325834

    work page doi:10.1371/journal.pone.0325834 2025

  46. [46]

    Sela and Jeffrey S

    Rebecca J. Sela and Jeffrey S. Simonoff. Re-em trees: A data mining approach for longitudinal and clustered data.Machine Learning, 86(2):169–207, 2012. 28

    2012

  47. [47]

    Sela, Jeffrey S

    Rebecca J. Sela, Jeffrey S. Simonoff, and Weixin Jing.REEMtree: Regression trees with random effects for longitudinal (panel) data, 2021. URL https://cran.r-project.org/package= REEMtree. R package version 0.90.4

    2021

  48. [48]

    S. I. Sherwani, H. A. Khan, A. Ekhzaimy, A. Masood, and M. K. Sakharkar. Significance of hba1c test in diagnosis and prognosis of diabetic patients.Biomarker Insights, 11:95–104, 2016. doi: 10.4137/BMI.S38440

    work page doi:10.4137/bmi.s38440 2016

  49. [49]

    Klimontov, Sanjay Kalra, Suzanne Peterson, et al

    Carolina Sorli, Shin Harashima, Marek Tsoukas, Jochen Unger, Takashi Kadowaki, Eiji Araki, Martin Trautmann, Vadim V. Klimontov, Sanjay Kalra, Suzanne Peterson, et al. Efficacy and safety of once-weekly semaglutide vs exenatide er in type 2 diabetes (sustain 3).Lancet Diabetes & Endocrinology, 5(4):251–260, 2017. doi: 10.1016/S2213-8587(17)30013-X

    work page doi:10.1016/s2213-8587(17)30013-x 2017

  50. [50]

    H. Sun, P. Saeedi, S. Karuranga, M. Pinkepank, K. Ogurtsova, B. B. Duncan, C. Stein, A. Basit, J. C. N. Chan, J. C. Mbanya, M. E. Pavkov, A. Ramachandaran, S. H. Wild, S. James, W. H. Herman, P. Zhang, C. Bommer, S. Kuo, E. J. Boyko, and D. J. Magliano. Idf diabetes atlas: Global, regional and country-level diabetes prevalence estimates for 2021 and proje...

    arXiv 2021

  51. [51]

    A longitudinal examination of blood sugar dynamics in diabetes and non-diabetes using growth curve model: The sabzevar persian cohort study

    Yaser Tabarraei, Abbas Ali Keshtkar, Mir Saeed Yekaninejad, Najme Rahimi, Yousef Dowlatabadi, and Kamal Azam. A longitudinal examination of blood sugar dynamics in diabetes and non-diabetes using growth curve model: The sabzevar persian cohort study. Advanced Biomedical Research, 13(1):30, 2024

    2024

  52. [52]

    Jafar, and Yong Mong Bee

    Clarence Tee, Haiyan Xu, Xiuju Fu, Di Cui, Tazeen H. Jafar, and Yong Mong Bee. Longitudinal hba1c trajectory modelling reveals the association of hba1c and risk of hospitalization for heart failure for patients with type 2 diabetes mellitus.PLOS ONE, 18(1):1–13, 2023. doi: 10.1371/journal.pone.0275610. URLhttps://doi.org/10.1371/journal.pone.0275610

    work page doi:10.1371/journal.pone.0275610 2023

  53. [53]

    Food and Drug Administration.Adjusting for Covariates in Random- ized Clinical Trials for Drugs and Biological Products, 2023

    U.S. Food and Drug Administration.Adjusting for Covariates in Random- ized Clinical Trials for Drugs and Biological Products, 2023. URL https: //www.fda.gov/regulatory-information/search-fda-guidance-documents/ adjusting-covariates-randomized-clinical-trials-drugs-and-biological-products

    2023

  54. [54]

    H. J. van der Horn, E. B. Erhardt, A. B. Dodd, U. Nathaniel, T. V. Wick, J. R. McQuaid, S. G. Ryman, A. A. Vakhtin, T. B. Meier, and A. R. Mayer. A cautionary tale on the effects of different covariance structures in linear mixed effects modeling of fmri data.Human Brain Mapping, 45(7):e26699, 2024. doi: 10.1002/hbm.26699

    work page doi:10.1002/hbm.26699 2024

  55. [55]

    Springer Series in Statistics

    Geert Verbeke and Geert Molenberghs.Linear Mixed Models for Longitudinal Data. Springer Series in Statistics. Springer, New York, 2nd edition, 2009. doi: 10.1007/978-0-387-77218-1

    work page doi:10.1007/978-0-387-77218-1 2009

  56. [56]

    The analysis of multivariate longitudinal data: A review.Statistical Methods in Medical Research, 23(1):42–59,

    Geert Verbeke, Steffen Fieuws, Geert Molenberghs, and Marie Davidian. The analysis of multivariate longitudinal data: A review.Statistical Methods in Medical Research, 23(1):42–59,

  57. [57]

    Vickers and Douglas G

    Andrew J. Vickers and Douglas G. Altman. Statistics notes: Analysing controlled tri- als with baseline and follow up measurements.BMJ, 323(7321):1123–1124, 2001. doi: 10.1136/bmj.323.7321.1123. 29

    arXiv 2001

  58. [58]

    B. G. Vittal, Mahantesh Patil, and D. Abhijith. A comparative study of correlation of random, fasting and postprandial blood glucose with glycated haemoglobin: A multicentre study.Journal of Medical Science and Health, 7(3):26–31, 2021

    2021

  59. [59]

    Lu Wang, Haoda Fu, and Donglin Zeng. Learning optimal personalized treatment rules in consideration of benefit and risk: with an application to treating type 2 diabetes patients with insulin therapies.Journal of the American Statistical Association, 113(521):1–13, 2018. doi: 10.1080/01621459.2017.1330207

    arXiv 2018

  60. [60]

    M. Wang, L. Kong, Z. Li, and L. Zhang. Covariance estimators for generalized estimating equations (gee) in longitudinal analysis with small samples.Statistics in Medicine, 35(10): 1706–1721, 2016. doi: 10.1002/sim.6817

    work page doi:10.1002/sim.6817 2016

  61. [61]

    Woerle, Walter P

    Hans J. Woerle, Walter P. Pimenta, Christian Meyer, et al. Diagnostic and therapeutic impli- cations of relationships between fasting, 2-hour postchallenge plasma glucose and hemoglobin a1c values.Archives of Internal Medicine, 164(15):1627–1632, 2004. doi: 10.1001/arch- inte.164.15.1627

    work page doi:10.1001/arch- 2004

  62. [62]

    Min Yan, Li Zhou, Chao Zhao, Chen Shi, and Chao Ou. Comparison of different approaches in handling missing data in longitudinal multiple-item patient-reported outcomes: a simulation study.Health and Quality of Life Outcomes, 23(1):34, 2025. doi: 10.1186/s12955-025-02364-0

    work page doi:10.1186/s12955-025-02364-0 2025

  63. [63]

    Functional data analysis for sparse longitudinal data.Journal of the American Statistical Association, 100(470):577–590, 2005

    Fang Yao, Hans-Georg Müller, and Jane-Ling Wang. Functional data analysis for sparse longitudinal data.Journal of the American Statistical Association, 100(470):577–590, 2005. doi: 10.1198/016214504000001745

    doi:10.1198/016214504000001745 2005

  64. [64]

    Jiajing Yin, Yi Lin, Mingyu Gu, and Yongde Peng. Quantitative models for evaluating the correlation between baseline HbA1c levels and sitagliptin as monotherapy or dual therapy treatment in type 2 diabetes: A meta-regression analysis.International Journal of Diabetes and Clinical Research, 3(3):051, 2016. doi: 10.23937/2377-3634/1410051

    work page doi:10.23937/2377-3634/1410051 2016

  65. [65]

    Fitting trees to functional data, with an application to time- of-day patterns.Journal of Computational and Graphical Statistics, 8(4):749–762, 1999

    Yan Yu and Diane Lambert. Fitting trees to functional data, with an application to time- of-day patterns.Journal of Computational and Graphical Statistics, 8(4):749–762, 1999. doi: 10.1080/10618600.1999.10474847. 30

    arXiv 1999

  66. [2014]

    doi: 10.1177/0962280212445834

    work page doi:10.1177/0962280212445834

  67. [2015]

    URL https://www.sciencedirect.com/science/ article/pii/S0168822715001357

    doi: 10.1016/j.diabres.2015.02.010. URL https://www.sciencedirect.com/science/ article/pii/S0168822715001357

    work page doi:10.1016/j.diabres.2015.02.010 2015

  68. [2021]

    doi: 10.1056/NEJMoa2107519

    work page doi:10.1056/nejmoa2107519

  69. [2025]

    R package version 0.2.0, https://CRAN.R-project.org/package=splinetree

    URL https://CRAN.R-project.org/package=splinetree. R package version 0.2.0, https://CRAN.R-project.org/package=splinetree