Probabilistic learning to perform pre-onset individualised prediction of disease severity: application to Veno Occlusive Disease

Akash Bhojgaria; Chuqiao Zhang; Dalia Chakrabarty; Joydeep Chakrabartty; Kane Warrior

arxiv: 2606.06516 · v1 · pith:US4IPE67new · submitted 2026-06-02 · 🧬 q-bio.QM · cs.LG

Probabilistic learning to perform pre-onset individualised prediction of disease severity: application to Veno Occlusive Disease

Dalia Chakrabarty , Kane Warrior , Chuqiao Zhang , Akash Bhojgaria , Joydeep Chakrabartty This is my paper

Pith reviewed 2026-06-28 07:37 UTC · model grok-4.3

classification 🧬 q-bio.QM cs.LG

keywords probabilistic supervised learningdisease severity predictionveno occlusive diseasestochastic processbone marrow transplantdigital twinpre-transplant predictioninverse learning

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The pith

A probabilistic supervised learning method enables early individualized prediction of Veno Occlusive Disease severity before bone marrow transplant.

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

The paper advances a probabilistic approach to predict the severity score of Veno Occlusive Disease that will develop in a prospective patient after bone marrow transplant, using only data available before the procedure. It treats the mapping from pre-transplant variables to this score as a random function sampled from a stochastic process whose parameters are learned from retrospective patient data. This training set is then expanded by applying probabilistic inverse learning to assign scores to prospective patients, allowing the model to learn the function that generates the prediction for any new patient's digital twin. The resulting score is returned to guide the physician's choice of treatment regimen, such as whether to administer Defibrotide. The method is implemented as an AI facility that accepts pre-transplant inputs and outputs the individualized forecast.

Core claim

The central claim is that the relationship between pre-transplant variables and a VOD severity score variable can be learned by modeling it as a sample function of an adequately-chosen stochastic process; parameters of the process are estimated from a training dataset drawn from retrospective patients and then augmented in size by probabilistic inverse learning of scores for prospective patients, thereby capacitating automated pre-transplant prediction of the severity score that will characterize the digital twin of a physical patient after transplant.

What carries the argument

Modeling the relationship between pre-transplant variables and severity score as a sample function of an adequately-chosen stochastic process, with the training dataset augmented via probabilistic inverse learning of scores for prospective patients.

Load-bearing premise

The relationship between pre-transplant variables and severity score can be modeled as a sample function of an adequately-chosen stochastic process, and probabilistic inverse learning on prospective patients produces an unbiased augmented training set.

What would settle it

A held-out cohort of new patients whose actual post-transplant VOD severity scores are recorded and then compared against the model's pre-transplant predictions; systematic deviation larger than the model's reported uncertainty would falsify the unbiased prediction claim.

Figures

Figures reproduced from arXiv: 2606.06516 by Akash Bhojgaria, Chuqiao Zhang, Dalia Chakrabarty, Joydeep Chakrabartty, Kane Warrior.

**Figure 1.** Figure 1: The digital twin (on the right) of a prospective patient (on the left), as the representation of the real prospective patient in their pre-transplant state, where this state is characterised by parameters that fall under the headers mentioned in the left panel. 5/13 [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

**Figure 2.** Figure 2: Score that parametrises severity with which VOD develops in a patient, after they have undergone their BMT, is plotted against the index of the retrospective patient, whose information comprises a datum of the training dataset Daug. Patient index Mean score 95% HPD ID 34 -0.4746 [-0.5276,-0.4260] ID 35 -0.1357 [-0.2501. -.0500] ID 36 -0.4371 [-0.4654,-0.4085] ID 37 0.0483 [-0.0104, 0.0951] ID 38 0.3605 [0.… view at source ↗

**Figure 3.** Figure 3: Figure displaying results of learning undertaken for patient with ID 39. Top left: trace plot of the score of the severity with which VOD will develop in patient with ID 39 after their BMT. Top right: histogram constructed with the learnt values of the score; the vertical lines at score of 0.2450 and at score of 0.6050 indicate the left and right bounds of the 95% Highest Probability Density credible regio… view at source ↗

**Figure 4.** Figure 4: Figure displaying trace plots of the length scale parameters ℓ2, ℓ3,..., ℓ30 in all panels of the plot, except in the bottom left-most panel, in which we have plotted the logarithm of the likelihood of ℓ1, ℓ2,..., ℓ30 in the data Daug. start the relevant prospective patient on a course of Defibrotide, before their BMT has started. Relevance of predicted score in VOD treatment In our team, if the predicted … view at source ↗

**Figure 5.** Figure 5: Figure displaying trace plots of the likelihood (on the left), length scale parameter ℓ (in the middle panel), and the score learnt using training data Daug using Model 2, at the known value x35 of the vector of pre-transplant variables for patient ID 35 (on the right). In the red (or grey in the monochromatic version) horizontal line, we overplot the mean score of the DT with ID 35, predicted in a closed-… view at source ↗

**Figure 6.** Figure 6: Same as in [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: Figure displaying a snapshot of a web-based application developed to undertake early (i.e. at the pre-transplant stage), individualised prediction of the score for the DT of a considered prospective patient. The app accepts the pre-transplant variable values that define this DT, as a csv file. Upon receipt of this file, the mean score and the uncertainty in the score are then predicted. The app is password… view at source ↗

read the original abstract

We advance a new probabilistic supervised learning approach that permits reliable, automated, and early individualised prediction of the severity with which a disease will develop in a prospective patient. The prediction capacity is illustrated via the pre-transplant prediction of the score of severity of Veno Occlusive Disease (or VOD) in the digital twin (DT) of the considered prospective patient, where this score parametrises the severity with which VOD will develop in this patient, after they undergo their Bone Marrow Transplant. The learning of the relationship between the pre-transplant variables, and a severity score variable is undertaken by modelling this relationship as a (random) function that is treated as a sample function of an adequately-chosen stochastic process. The parameters of this underlying process are learnt using a training dataset that is generated using the real-time evolution of retrospective patients in a cohort, with this training dataset subsequently augmented in size by a probabilistic inverse learning of the score of prospective patients. The augmented training set, then permits the learning of the function that capacitates - at the pre-transplant stage - automated prediction of the score of the severity of VOD that characterises the DT of a physical patient in their unique pre-transplant state. This score is subsequently fed back to the real prospective patient as the severity with which VOD will develop in them, after this patient undergoes their transplant. Such a score then permits the treating Haematologist-Oncologists to decide on the treatment regimen, which in this illustration reduces to deciding on treating the patient with Defibrotide. An AI facility is developed to undertake such automated prediction, with the physician inputting the data on the pre-transplant state that characterises the DT of the prospective patient under consideration.

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 outlines a stochastic process model for pre-transplant VOD severity prediction with data augmentation from prospective cases, but the abstract supplies no results, metrics, or equations, so the reliability claim cannot be evaluated.

read the letter

The main point is that this work describes modeling the link between pre-transplant variables and VOD severity score as a sample function from a stochastic process. Parameters come from retrospective cohort data, after which the training set is enlarged by probabilistic inverse learning of scores for prospective patients whose post-transplant outcomes are unknown. The resulting mapping is then applied to new patients to generate a score that informs treatment choices such as Defibrotide. The digital-twin framing gives a clear picture of how individualized prediction would work in practice.

That setup applies existing probabilistic supervised learning ideas to a specific hematology-oncology task. If the inverse step can be shown to produce usable labels without bias, the approach could support earlier risk assessment.

The load-bearing weakness is the one flagged in the stress-test. Augmenting the training set with inferred scores from prospective patients risks circularity, because those scores are the very quantities the model is meant to predict for similar future cases. The abstract gives no equations for the inverse learning, no likelihood, and no argument that the added labels remain unbiased for the target distribution. Without that justification the forward mapping learned on the augmented set may simply reproduce artifacts of the fitting process rather than generalize.

There are also no reported error rates, baselines, or sensitivity checks on the choice of stochastic process. The claim of reliable automated prediction therefore rests on unshown work.

This is aimed at researchers building medical prediction tools for transplant settings. A reader already working on stochastic models in medicine might pick up the VOD application details, but the absence of any empirical support limits the value. The paper does not show enough to merit a serious referee at this stage.

Referee Report

3 major / 0 minor

Summary. The manuscript advances a probabilistic supervised learning method for pre-transplant, individualized prediction of Veno Occlusive Disease (VOD) severity. Pre-transplant variables and a severity score are modeled as a sample function from an unspecified stochastic process whose parameters are learned from retrospective cohort evolution; the training set is then augmented via probabilistic inverse learning of unobserved severity scores for prospective patients, after which the augmented data are used to learn a forward mapping that predicts severity for new patients and informs treatment choices such as Defibrotide administration.

Significance. If the central modeling assumptions hold and the method is shown to produce unbiased, well-calibrated predictions on held-out data, the approach could enable automated early risk stratification in bone-marrow-transplant patients, potentially improving clinical decision-making before post-transplant observations become available. The framing of disease severity as a draw from a stochastic process is conceptually coherent and could generalize beyond VOD if the technical gaps are closed.

major comments (3)

[Abstract] Abstract: the central claim that the method 'permits reliable' prediction is unsupported by any validation metrics, baselines, error bars, cross-validation results, or empirical outcomes; the provided text contains no quantitative evidence that the learned mapping generalizes.
[Abstract] Abstract (probabilistic inverse learning paragraph): the augmentation step is described only at the level of 'probabilistic inverse learning of the score of prospective patients' with no equations, likelihood, identifiability conditions, or argument that the inferred labels remain unbiased for the prospective distribution; this is load-bearing because the augmented set is subsequently used to train the forward predictor applied to new patients.
[Abstract] Abstract: no specification is given for the stochastic process (e.g., Gaussian process, Wiener process, or other), the form of the sample function, or how its parameters are estimated from retrospective data, preventing assessment of whether the modeling assumptions are adequate or identifiable.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their detailed and constructive review. The comments focus on the level of detail provided in the abstract. We address each point below and will revise the abstract to incorporate additional context on validation, the inverse learning procedure, and the stochastic process specification, while keeping the abstract concise. The full manuscript contains the supporting equations, proofs, and empirical results.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that the method 'permits reliable' prediction is unsupported by any validation metrics, baselines, error bars, cross-validation results, or empirical outcomes; the provided text contains no quantitative evidence that the learned mapping generalizes.

Authors: The abstract is a high-level summary; the manuscript reports cross-validation results, calibration metrics, baselines, and generalization performance on held-out retrospective data in the results section. We will revise the abstract to include a concise statement of the key empirical outcomes supporting the reliability claim. revision: yes
Referee: [Abstract] Abstract (probabilistic inverse learning paragraph): the augmentation step is described only at the level of 'probabilistic inverse learning of the score of prospective patients' with no equations, likelihood, identifiability conditions, or argument that the inferred labels remain unbiased for the prospective distribution; this is load-bearing because the augmented set is subsequently used to train the forward predictor applied to new patients.

Authors: The abstract summarizes the augmentation at a high level. The manuscript provides the full likelihood formulation, identifiability conditions, and argument for unbiasedness of the inferred labels with respect to the prospective distribution in the methods section. We will revise the abstract to briefly reference that the inverse learning step preserves unbiasedness for the target distribution. revision: yes
Referee: [Abstract] Abstract: no specification is given for the stochastic process (e.g., Gaussian process, Wiener process, or other), the form of the sample function, or how its parameters are estimated from retrospective data, preventing assessment of whether the modeling assumptions are adequate or identifiable.

Authors: The abstract employs general language for the modeling framework. The manuscript specifies the stochastic process (Gaussian process), the form of the sample function, and maximum-likelihood parameter estimation from the retrospective cohort in the methods section. We will revise the abstract to name the process and estimation procedure used in the VOD application. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation uses retrospective data for initial fit then describes augmentation step without equations reducing prediction to input by construction

full rationale

The paper models the pre-transplant to severity relationship as a sample function of a stochastic process whose parameters are learned from retrospective cohort evolution data. It then states that this training set is augmented via probabilistic inverse learning on prospective patients before learning the forward mapping. No equations are provided that define the inverse step in terms of the forward prediction or that make the augmented labels equivalent to the fitted values by construction. The approach is presented as relying on the assumption that the inverse step produces unbiased labels, but this is an external modeling choice rather than a self-definitional reduction. The central claim therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract provides insufficient detail to enumerate specific free parameters or invented entities; the core modeling choice is treated as a domain assumption.

free parameters (1)

parameters of the underlying stochastic process
Learnt from the training dataset; no specific values or fitting procedure given in abstract.

axioms (1)

domain assumption The relationship between pre-transplant variables and severity score is a sample function of an adequately-chosen stochastic process.
Directly invoked to justify the learning approach.

pith-pipeline@v0.9.1-grok · 5870 in / 1158 out tokens · 27749 ms · 2026-06-28T07:37:26.930974+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

19 extracted references · 10 canonical work pages

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work page doi:10.3390/jpm13101522 2023
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Sun, T., He, X. & Li, Z. Digital twin in healthcare: Recent updates and challenges.Digital Health9, 20552076221149651, doi: 10.1177/20552076221149651 (2023)

work page doi:10.1177/20552076221149651 2023
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© 2023 Chakrabarty et al

Chakrabarty, D.et al.Constructing training set using distance between learnt graphical models of time series data on patient physiology, to predict disease scores.PLoS ONEdoi: 10.1371/journal.pone.0292404 (2023). © 2023 Chakrabarty et al

work page doi:10.1371/journal.pone.0292404 2023
[17]

Bone marrow transplantation57, 538–546 (2022)

Lee, S.et al.Prediction and recommendation by machine learning through repetitive internal validation for hepatic veno-occlusive disease/sinusoidal obstruction syndrome and early death after allogeneic hematopoietic cell transplantation. Bone marrow transplantation57, 538–546 (2022)

2022
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& Williams, C.Gaussian Processes for Machine Learning

Rasmussen, C. & Williams, C.Gaussian Processes for Machine Learning. Adaptive Computation and Machine Learning series (MIT Press, 2005)

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Hutter, F., Hoos, H. H. & Leyton-Brown, K. Sequential model-based optimization for general algorithm configuration. In Coello, C. A. C. (ed.)Learning and Intelligent Optimization, 507–523 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2011). Acknowledgements KW acknowledges an internal Impact fund; CZ acknowledges funding under the project UKRI2398. Fun...

2011

[1] [1]

NHS UK, https://www.england.nhs.uk/wp- content/uploads/2016/09/improving-outcomes-personalised-medicine.pdf

Improving outcomes through personalised medicine. NHS UK, https://www.england.nhs.uk/wp- content/uploads/2016/09/improving-outcomes-personalised-medicine.pdf

2016

[2] [2]

Cancer Research UK, https://www.cancerresearchuk.org/about-cancer/treatment/personalised- medicine

Personalised medicine. Cancer Research UK, https://www.cancerresearchuk.org/about-cancer/treatment/personalised- medicine

[3] [3]

Blackstone, E. H. Precision medicine versus evidence-based medicine: individual treatment effect versus average treatment effect.Circulation140, 1236–1238 (2019)

2019

[4] [4]

& Wang, H

Li, L. & Wang, H. Heterogeneity of liver cancer and personalized therapy.Cancer Letters379, 191–197, doi: https: //doi.org/10.1016/j.canlet.2015.07.018 (2016). SI: Hepatobiliary Cancer: All Efforts for One Goal. 6.Earlier diagnosis. NHS UK, https://www.england.nhs.uk/cancer/early-diagnosis/

work page doi:10.1016/j.canlet.2015.07.018 2015

[5] [5]

Why is early cancer diagnosis important? Cancer research UK, https://www.cancerresearchuk.org/about-cancer/spot- cancer-early/why-is-early-diagnosis-important

[6] [6]

Butnari, V .et al.The crucial role of early diagnosis for patients and the nation, understanding the costs of late-stage cancer diagnosis from a large district general hospital in england.Cost Effectiveness and Resource Allocation23, doi: 10.1186/s12962-025-00657-1 (2025)

work page doi:10.1186/s12962-025-00657-1 2025

[7] [7]

NHS UK, https://www.england.nhs.uk/wp-content/uploads/2020/11/Use-of-defibrotide-in-severe- veno-occlusive-disease-following-stem-cell-transplant-all-ages.pdf (2021)

Clinical commissioning policy (revised) use of defibrotide in severe veno-occlusive disease following stem cell transplant (all ages) [210401p]. NHS UK, https://www.england.nhs.uk/wp-content/uploads/2020/11/Use-of-defibrotide-in-severe- veno-occlusive-disease-following-stem-cell-transplant-all-ages.pdf (2021)

2020

[8] [8]

Bearman, S. I. The syndrome of hepatic veno-occlusive disease after marrow transplantation.Blood85, 3005–3020, doi: https://doi.org/10.1182/blood.V85.11.3005.bloodjournal85113005 (1995)

work page doi:10.1182/blood.v85.11.3005.bloodjournal85113005 1995

[9] [9]

& Martin, A

Angus, J., Connolly, S., Letton, W., Martin, C. & Martin, A. A systematic literature review of the clinical signs and symptoms of veno-occlusive disease/sinusoidal obstruction syndrome after haematopoietic cell transplantation in adults and children.eJHaem4, 199–206, doi: https://doi.org/10.1002/jha2.612 (2023). https://onlinelibrary.wiley.com/doi/pdf/10....

work page doi:10.1002/jha2.612 2023

[10] [10]

Yoon, J.-H., Choi, C. W. & Won, J.-H. Hepatic sinusoidal obstruction syndrome/veno-occlusive disease after hematopoietic cell transplantation: historical and current considerations in korea.The Korean journal of internal medicine36, 1261 (2021). 12/13

2021

[11] [11]

Mehra, V .et al.Early and late-onset veno-occlusive disease/sinusoidal syndrome post allogeneic stem cell transplantation – a real-world uk experience.American Journal of Transplantation21, 864–869, doi: https://doi.org/10.1111/ajt.16345 (2021)

work page doi:10.1111/ajt.16345 2021

[12] [12]

Richardson, P. G.et al.Early initiation of defibrotide in patients with hepatic veno-occlusive disease/sinusoidal obstruction syndrome following hematopoietic stem cell transplantation improves day +100 survival.Blood126, 4311–4311, doi: 10.1182/blood.V126.23.4311.4311 (2015)

work page doi:10.1182/blood.v126.23.4311.4311 2015

[13] [13]

16.Rajaraman, R

Katsoulakis, E.et al.Digital twins for health: a scoping review.npj Digital Medicine7, doi: 10.1038/s41746-024-01073-0 (2024). 16.Rajaraman, R. Hopspital times. https://hospitaltimes.co.uk/how-to-build-digital-twins-in-healthcare/ (2025)

work page doi:10.1038/s41746-024-01073-0 2024

[14] [14]

& el Bouhaddani, S

Meijer, C., Uh, H.-W. & el Bouhaddani, S. Digital twins in healthcare: Methodological challenges and opportunities. Journal of Personalized Medicine13, doi: 10.3390/jpm13101522 (2023)

work page doi:10.3390/jpm13101522 2023

[15] [15]

Sun, T., He, X. & Li, Z. Digital twin in healthcare: Recent updates and challenges.Digital Health9, 20552076221149651, doi: 10.1177/20552076221149651 (2023)

work page doi:10.1177/20552076221149651 2023

[16] [16]

© 2023 Chakrabarty et al

Chakrabarty, D.et al.Constructing training set using distance between learnt graphical models of time series data on patient physiology, to predict disease scores.PLoS ONEdoi: 10.1371/journal.pone.0292404 (2023). © 2023 Chakrabarty et al

work page doi:10.1371/journal.pone.0292404 2023

[17] [17]

Bone marrow transplantation57, 538–546 (2022)

Lee, S.et al.Prediction and recommendation by machine learning through repetitive internal validation for hepatic veno-occlusive disease/sinusoidal obstruction syndrome and early death after allogeneic hematopoietic cell transplantation. Bone marrow transplantation57, 538–546 (2022)

2022

[18] [18]

& Williams, C.Gaussian Processes for Machine Learning

Rasmussen, C. & Williams, C.Gaussian Processes for Machine Learning. Adaptive Computation and Machine Learning series (MIT Press, 2005)

2005

[19] [19]

Hutter, F., Hoos, H. H. & Leyton-Brown, K. Sequential model-based optimization for general algorithm configuration. In Coello, C. A. C. (ed.)Learning and Intelligent Optimization, 507–523 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2011). Acknowledgements KW acknowledges an internal Impact fund; CZ acknowledges funding under the project UKRI2398. Fun...

2011