Modelling multi-cancer screening data to infer on natural history of disease: when can valid, identifiable and precise inference be obtained?

AE Ades; J Lange; K Gogebakan; MO Soares; NJ Welton; R Etzioni; S Dias; S Palmer

arxiv: 2606.02076 · v1 · pith:QMPDOH77new · submitted 2026-06-01 · 📊 stat.ME

Modelling multi-cancer screening data to infer on natural history of disease: when can valid, identifiable and precise inference be obtained?

MO Soares , J Lange , K Gogebakan , S Dias , NJ Welton , R Etzioni , AE Ades , S Palmer This is my paper

Pith reviewed 2026-06-28 13:13 UTC · model grok-4.3

classification 📊 stat.ME

keywords multistate modelsmulticancer early detectionnatural history of cancermean sojourn timeidentifiabilityBayesian estimationsimulation studyscreening data

0 comments

The pith

Disaggregating multistate models to individual cancer stages increases reliance on external assumptions when fitting multicancer screening data.

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

The paper tests how well multistate models can recover parameters like mean sojourn time from simulated multicancer early detection screening data as the models are disaggregated into more clinical states. It compares a basic 3-state version, a 5-state version separating early and late stages, and a 9-state version separating stages I-IV, using Bayesian MCMC estimation and checks for chain convergence, profile likelihood identifiability, and estimate precision. The 5-state model performs similarly to the 3-state model, while the 9-state model shows clear drops in convergence, identifiability, and precision. Hierarchical models improve results, but informative priors reduce bias only at the cost of pulling estimates toward the prior values.

Core claim

Based only on MCED trial data, the 5-state model is as robust as the 3-state model, showing slight improvements to convergence and identifiability while maintaining precision for overall MST; in contrast, the 9-state model shows worsened convergence and identifiability, and a significant reduction in the precision of overall MST estimates.

What carries the argument

Multistate models of cancer progression applied to longitudinal screening data, with increasing numbers of states (3, 5, or 9), estimated via Bayesian Markov chain Monte Carlo and assessed via chain convergence, profile likelihood, and estimate precision.

If this is right

Disaggregating natural history models by individual cancer stages increases reliance on external data or assumptions.
Hierarchical models improve convergence, identifiability, and precision across the disaggregated models.
Informative prior models can restore performance but shift estimates toward the chosen prior values.
Explicit identifiability assessments and checks on the influence of external assumptions are needed to support inference for MCED screening evaluations.

Where Pith is reading between the lines

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

Real MCED trial analyses may need to supplement screening data with independent sources such as population incidence rates to support stage-specific natural history estimates.
Policy questions that do not require stage detail could be answered adequately with the simpler 3-state or 5-state models.
Direct application of the same simulation design to published MCED trial data would provide a direct test of whether the identifiability patterns observed here appear in practice.

Load-bearing premise

The simulated longitudinal MCED screening datasets accurately capture the key unobserved onset and progression features of real trial data so that the observed differences in convergence, identifiability, and precision generalize beyond the simulations.

What would settle it

If actual multicancer screening trial data allow 9-state models to converge reliably and produce precise overall MST estimates without external priors or assumptions, while 5-state models fail to do so, the simulation results would not hold.

Figures

Figures reproduced from arXiv: 2606.02076 by AE Ades, J Lange, K Gogebakan, MO Soares, NJ Welton, R Etzioni, S Dias, S Palmer.

read the original abstract

Background: Multistate models (MSMs) applied to screening data can characterise the natural history of cancer and predict "stage-shifts" from screening. However, inferring parameters like mean sojourn time (MST) is challenging as disease onset is inherently unobserved in these data. This is even more challenging when characterising heterogeneity between cancer types in multicancer early detection (MCED) trial data. Methods: We utilised simulated longitudinal MCED screening datasets to evaluate the inferential bounds of MSMs under increasing clinical disaggregation: a 3-state (overall MST), 5-state (early/late stage), and 9-state (stages I-IV) model. Bayesian estimation was performed via Markov chain Monte Carlo. Robustness was assessed through chain convergence, parameter identifiability (via profile likelihood), and precision of estimates. We also explored hierarchical models and the use of informative priors to improve identifiability. Results: Based only on MCED trial data, many cancer types exhibited inferential challenges. Generally, the 5-state model was as robust as the 3-state model, showing slight improvements to convergence and identifiability while maintaining precision for overall MST. In contrast, the 9-state model showed worsened convergence and identifiability, and a significant reduction in the precision of overall MST estimates. Hierarchical models successfully improved performance, as have informative prior models but the latter introduced bias towards the prior values. Conclusions: While disaggregating natural history models by individual cancer stages is desirable for policy, these higher-dimensional models show a greater reliance on external data/assumptions. We recommend explicit identifiability assessments and assessments of the influence of external data/assumptions to support inference for MCED screening evaluations.

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

Simulations indicate 9-state multistate models lose identifiability and precision on MCED data compared to 3- or 5-state versions, with hierarchical structures helping but priors biasing results.

read the letter

The paper's central finding is that moving to a 9-state multistate model for individual cancer stages in multi-cancer screening data leads to poorer MCMC convergence, weaker identifiability via profile likelihood, and less precise estimates of overall mean sojourn time, while 5-state models perform nearly as well as 3-state ones. Hierarchical models help with this, but informative priors pull estimates toward the prior and reduce reliability.

They do this by generating simulated longitudinal MCED datasets and fitting the models under different disaggregations. The work checks robustness through convergence diagnostics and identifiability measures, then tests hierarchical structures and prior sensitivity. This is a useful extension because it focuses on the MCED setting where heterogeneity across cancer types is key, and it gives practical advice on when external data or assumptions become necessary.

The simulations make a clear case that finer disaggregation increases dependence on outside information for policy modeling. That part is straightforward and addresses a real issue in applying these models to screening trials.

The soft spot is the reliance on a single simulation design. The claim that higher-dimensional models inherently need more external assumptions only follows if the generated data reflects the actual unobserved onset times, progression rates, and screening sensitivities in real trials. Without showing that the simulations match empirical patterns from existing studies, like stage distributions or sojourn time bounds, it's possible the identifiability problems are exaggerated or understated. The paper would be stronger with some validation against real observables.

This is for methodologists in cancer screening evaluation who use multistate models. It deserves peer review because it provides evidence on identifiability limits that matter for how we interpret MCED data, even if the simulation setup needs more justification.

I would recommend sending it to referees, with the expectation that they will ask for more on how the data generation process was chosen.

Referee Report

2 major / 1 minor

Summary. The paper conducts a simulation study of multistate models fitted via MCMC to longitudinal MCED screening data, comparing inferential performance across a 3-state model (overall MST), 5-state model (early/late), and 9-state model (stages I-IV). It reports that the 9-state model exhibits poorer chain convergence, weaker profile-likelihood identifiability, and reduced precision for overall MST relative to the lower-dimensional models; hierarchical random-effects structures improve convergence and identifiability while informative priors improve precision at the cost of bias. The central conclusion is that greater clinical disaggregation increases reliance on external data or assumptions.

Significance. If the simulation design reproduces the key unobserved-onset and stage-progression bottlenecks present in real MCED trials, the results supply concrete, quantitative guidance on the identifiability–complexity trade-off that is directly relevant to ongoing MCED evaluations. The explicit use of profile likelihood alongside MCMC diagnostics and the demonstration that hierarchical models can partially restore performance are methodological strengths that could inform future trial analyses.

major comments (2)

[Methods] Methods (simulation design): The data-generating process is not reported as having been calibrated or cross-validated against empirical observables from existing screening studies (e.g., stage-shift distributions or published sojourn-time bounds). Because the central claim—that 9-state models inherently exhibit greater external-data dependence—rests on the simulations reproducing the identifiability bottlenecks of real MCED data, this omission is load-bearing for the generalization.
[Results] Results (profile-likelihood and precision comparisons): The manuscript does not report the exact number of profile points evaluated, the parameter ranges explored, or the quantitative threshold used to declare “non-identifiability” for the 9-state model; without these details it is difficult to judge whether the reported degradation in the 9-state model is robust to reasonable changes in the simulation design.

minor comments (1)

[Abstract] The abstract states that “many cancer types exhibited inferential challenges” but does not indicate how many cancer types were simulated or whether results are pooled or reported per type; adding this information would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight important aspects of simulation design and reporting. We respond to each major comment below and indicate planned revisions.

read point-by-point responses

Referee: [Methods] Methods (simulation design): The data-generating process is not reported as having been calibrated or cross-validated against empirical observables from existing screening studies (e.g., stage-shift distributions or published sojourn-time bounds). Because the central claim—that 9-state models inherently exhibit greater external-data dependence—rests on the simulations reproducing the identifiability bottlenecks of real MCED data, this omission is load-bearing for the generalization.

Authors: We agree that formal calibration against empirical observables from screening studies would strengthen claims about generalization to real MCED trials. Our simulation parameters were selected from ranges reported in the published literature on sojourn times and stage distributions to capture the key structural features of unobserved onset and stage progression; however, no explicit cross-validation step was performed. In revision we will expand the Methods section to document the literature sources and parameter ranges used, and add a dedicated limitations paragraph discussing the implications for external validity. We believe the qualitative finding that higher-dimensional models increase reliance on external information remains robust under the simulated conditions that reproduce the core identifiability bottlenecks, but we accept the referee’s point that calibration would improve the manuscript. revision: partial
Referee: [Results] Results (profile-likelihood and precision comparisons): The manuscript does not report the exact number of profile points evaluated, the parameter ranges explored, or the quantitative threshold used to declare “non-identifiability” for the 9-state model; without these details it is difficult to judge whether the reported degradation in the 9-state model is robust to reasonable changes in the simulation design.

Authors: We thank the referee for noting this reporting gap. The profile-likelihood analyses evaluated the likelihood on a grid while optimizing remaining parameters, but the precise grid size, explored ranges, and numerical criterion for declaring non-identifiability (e.g., flatness within a tolerance) were not stated. In the revised manuscript we will add these details to the Results section and Supplementary Material, including the number of profile points, the parameter ranges, and the threshold applied, together with a brief sensitivity note on grid density. revision: yes

Circularity Check

0 steps flagged

No circularity: simulation-based identifiability assessment is self-contained

full rationale

The paper generates simulated longitudinal MCED datasets and applies Bayesian MCMC estimation to 3/5/9-state multistate models, then evaluates convergence, profile likelihood identifiability, and precision directly on those generated data. No fitted parameter is renamed as a prediction, no equation reduces to another by construction, and no load-bearing premise rests on self-citation chains or imported uniqueness theorems. The conclusion that 9-state models exhibit greater external-data reliance follows from the external simulation metrics rather than from any internal redefinition of inputs as outputs. This is the standard non-circular structure of a simulation study assessing inferential limits.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The analysis rests on standard domain assumptions for multistate models of cancer progression and Bayesian MCMC estimation; simulations are used to probe limits rather than to introduce new entities or free parameters beyond the model states themselves.

free parameters (1)

mean sojourn time
Key target parameter whose identifiability and precision are evaluated across model dimensions.

axioms (1)

domain assumption Multistate model structure accurately represents unobserved cancer onset and progression in screening data
Invoked in the construction of the simulated datasets and the estimation targets.

pith-pipeline@v0.9.1-grok · 5874 in / 1367 out tokens · 36852 ms · 2026-06-28T13:13:00.098674+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

33 extracted references · 19 canonical work pages

[1]

stage-shift

Introduction The modelling of longitudinal cancer screening data using multistate models (MSMs) can characterise the natural history of cancer by describing progression through mutually exclusive states, including ‘no cancer’ (undetectable cancer), preclinical detectable cancer, and clinical diagnosis.1 A primary parameter of interest is the (preclinical)...

2009
[2]

no cancer

Methods 2.1 Generating simulated datasets: Dai’s model To simulate the NHS-Galleri trial data6, we used two published models.12,13 Dai’s microsimulation model12 served as our primary source because it supports the highest level of stage disaggregation (stages I to IV). The alternative model, MCEDsim13, allowing only disaggregation between early- and late-...

2024
[3]

Full results, including of test sensitivity, are in Supp C

Results 3.1 3-, 5- and 9-state MSM models Table 3 presents inference results for MST and stage-MST and the results of explorations of convergence (C), identifiability (I) and precision (P) using a representative dataset (Dai’s model, 50th percentile of predicted primary endpoint). Full results, including of test sensitivity, are in Supp C. Across all mode...
[4]

Discussion Given the inherent heterogeneity in tumor biology, not only in (multi-cancer) test sensitivity but also in preclinical cancer progression, it is essential that analyses of longitudinal cancer screening data reliably estimate mean sojourn time across cancer types and stages to determine the effect of screening on stage shift. In this study, we e...

2021
[5]

Br J Cancer

Cheung LC, Albert PS, Das S, Cook RJ Multistate models for the natural history of cancer progression. Br J Cancer. 2022 Jul 11;127(7):1279–1288. doi: 10.1038/s41416-022-01904-5

work page doi:10.1038/s41416-022-01904-5 2022
[6]

Quantifying the duration of the preclinical detectable phase in cancer screening: a systematic review

Geurts SME, Aarts AMWM, Verbeek ALM, Chen THH, Broeders MJM, Duffy SW. Quantifying the duration of the preclinical detectable phase in cancer screening: a systematic review. Epidemiol Health. 2022;44:e2022008. doi: 10.4178/epih.e2022008

work page doi:10.4178/epih.e2022008 2022
[7]

A Scoping Review on Calibration Methods for Cancer Simulation Models

Zhang Y, Lipa N, Alagoz O. A Scoping Review on Calibration Methods for Cancer Simulation Models. Med Decis Making. 2025 Nov;45(8):965-975. doi: 10.1177/0272989X251353211. 15/26

work page doi:10.1177/0272989x251353211 2025
[8]

Simplified models of screening for chronic disease: Estimation procedures from mass screening programmes

Day NE, Walter SD (1984). Simplified models of screening for chronic disease: Estimation procedures from mass screening programmes. Biometrics, 40(1), 1–14. PMID: 6733223

1984
[9]

Methods Med

Uhry et al., Multi-state Markov models in cancer screening evaluation: a brief review and case study, Stat. Methods Med. Res. 19 (2010) 463–486

2010
[10]

Cell-Free DNA–Based Multi-Cancer Early Detection Test in an Asymptomatic Screening Population (NHS-Galleri): Design of a Pragmatic, Prospective Randomised Controlled Trial

Neal RD, Johnson P, Clarke CA, Hamilton SA, Zhang N, Kumar H, Swanton C, Sasieni P. Cell-Free DNA–Based Multi-Cancer Early Detection Test in an Asymptomatic Screening Population (NHS-Galleri): Design of a Pragmatic, Prospective Randomised Controlled Trial. Cancers 2022, 14(19), 4818; https://doi.org/10.3390/cancers14194818

work page doi:10.3390/cancers14194818 2022
[11]

The National Health Service-Galleri multi-cancer screening trial: explanation and justification of unique and important design issues

Sasieni P, Swanton C, Neal RD. The National Health Service-Galleri multi-cancer screening trial: explanation and justification of unique and important design issues. J Natl Cancer Inst. 2025 Aug 9:djaf218. https://doi.org/10.1093/jnci/djaf218

work page doi:10.1093/jnci/djaf218 2025
[12]

NHS-Galleri trial: Enriched enrolment approaches and sociodemographic characteristics of enrolled participants

Swanton C, Bachtiar V, Mathews C, et al. NHS-Galleri trial: Enriched enrolment approaches and sociodemographic characteristics of enrolled participants. Clinical Trials. 2025;22(2):227-

2025
[13]

https://doi.org/10.1177/174077452413024

work page doi:10.1177/174077452413024
[14]

Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood,

Raue A, Kreutz C, Maiwald T, Bachmann J, Schilling M, Klingmüller U, Timmer J. Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics. 2009 Aug 1;25(15):1923-9. doi: 10.1093/bioinformatics/btp358. Epub 2009 Jun 8. PMID: 19505944

work page doi:10.1093/bioinformatics/btp358 2009
[15]

A confidence building exercise in data and identifiability: Modeling cancer chemotherapy as a case study

Eisenberg MC, Jain HV. A confidence building exercise in data and identifiability: Modeling cancer chemotherapy as a case study. J Theor Biol. 2017 Oct 27;431:63-78. doi: 10.1016/j.jtbi.2017.07.018. Epub 2017 Jul 19. Erratum in: J Theor Biol. 2019 Mar 7;464:179. doi: 10.1016/j.jtbi.2018.12.042

work page doi:10.1016/j.jtbi.2017.07.018 2017
[16]

Nonidentifiability in Model Calibration and Implications for Medical Decision Making

Alarid-Escudero F, MacLehose RF, Peralta Y, Kuntz KM, Enns EA. Nonidentifiability in Model Calibration and Implications for Medical Decision Making. Medical Decision Making. 2018;38(7):810-821. doi:10.1177/0272989X18792283 16/26

work page doi:10.1177/0272989x18792283 2018
[17]

J Med Screen

Dai JY, Zhang J, Braun JV, Simon N, Hubbell E, Zhang N, Clinical performance and utility: A microsimulation model to inform the design of screening trials for a multi-cancer early detection test. J Med Screen. 2024 Feb 2;31(3):140–149. doi: 10.1177/09691413241228041

work page doi:10.1177/09691413241228041 2024
[18]

Projecting the Impact of Multi-Cancer Early Detection on Late-Stage Incidence Using Multi-State Disease Modeling

Lange JM., Gogebakan KC, Gulati R, Etzioni R. Projecting the Impact of Multi-Cancer Early Detection on Late-Stage Incidence Using Multi-State Disease Modeling. Cancer Epidemiol Biomarkers Prev (2024) 33 (6): 830–837. https://doi.org/10.1158/1055-9965.EPI-23-1470

work page doi:10.1158/1055-9965.epi-23-1470 2024
[19]

Klein, E. A., D. Richards, A. Cohn, M. Tummala, R. Lapham, D. Cosgrove, G. Chung, et al
[20]

Annals of Oncology : Official Journal of the European Society for Medical Oncology 32 (9): 1167–77

Clinical Validation of a Targeted Methylation-Based Multi-Cancer Early Detection Test Using an Independent Validation Set. Annals of Oncology : Official Journal of the European Society for Medical Oncology 32 (9): 1167–77. https://doi.org/10.1016/j.annonc.2021.05.806

work page doi:10.1016/j.annonc.2021.05.806 2021
[21]

Estimating stage-specific sensitivity for cancer screening tests

Pinsky P, Lange J, Etzioni R. Estimating stage-specific sensitivity for cancer screening tests. Journal of Medical Screening. 2023;30(2):69-73. doi:10.1177/09691413231154801

work page doi:10.1177/09691413231154801 2023
[22]

A multistate survival model of the natural history of cancer using data from screened and unscreened population

Bhatt R, vanden Hout A, Pashayan N. A multistate survival model of the natural history of cancer using data from screened and unscreened population. Statistics in Medicine. 2021;40:3791–3807. https://doi.org/10.1002/sim.8998

work page doi:10.1002/sim.8998 2021
[23]

Maple2025.0, Maplesoft, Waterloo, Canada
[24]

Moving beyond noninformative priors: why and how to choose weakly informative priors in Bayesian analyses

Lemoine NP. Moving beyond noninformative priors: why and how to choose weakly informative priors in Bayesian analyses. Oikos. 128: 912–928, 2019 doi: 10.1111/oik.05985

work page doi:10.1111/oik.05985 2019
[25]

https://CRAN.R-project.org/package=R2jags
[26]

Rank-Normalization, Folding, and Localization: An Improved R for Assessing Convergence of MCMC (with Discussion)

Vehtari A, Gelman A, Simpson D, Carpenter B, Burkner PC. Rank-Normalization, Folding, and Localization: An Improved R for Assessing Convergence of MCMC (with Discussion). Bayesian Analysis (2021) 16, Number 2, pp. 667–718

2021
[27]

On structural and practical identifiability

Wieland FG, Hauber AL, Rosenblatt M, Tönsing C, Timmer J. On structural and practical identifiability. Current Opinion in Systems Biology, 2021 25:60-69. https://doi.org/10.1016/j.coisb.2021.03.005. 17/26

work page doi:10.1016/j.coisb.2021.03.005 2021
[28]

Bayesian Data Analysis

Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB. Bayesian Data Analysis. 3rd ed. CRC Press; 2013

2013
[29]

J., Best, N

Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & van der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64(4), 583-639

2002
[30]

Gogebakan KC, Lange J, Owens L, Pinderup A, Gulati R, Kessler LG, Lyratzopoulos G, Etzioni R. 2025. Clinical Significance of a Multicancer Screening Trial With Stage-Based End Points. JAMA Network Open 8 (10): e2536247. https://doi.org/10.1001/jamanetworkopen.2025.36247

work page doi:10.1001/jamanetworkopen.2025.36247 2025
[31]

Feasibility of blood testing combined with PET-CT to screen for cancer and guide intervention

Lennon AM, Buchanan AH, Kinde I, Warren A, Honushefsky A, Cohain AT, Ledbetter DH, Sanfilippo F, Sheridan K, Rosica D, Adonizio CS, Hwang HJ, Lahouel K, Cohen JD, Douville C, Patel AA, Hagmann LN, Rolston DD, Malani N, Zhou S, Bettegowda C, Diehl DL, Urban B, Still CD, Kann L, Woods JI, Salvati ZM, Vadakara J, Leeming R, Bhattacharya P, Walter C, Parker A...

work page doi:10.1126/science.abb9601 2020
[32]

https://investors.grail.com/node/8281/pdf, February 2026

2026
[33]

Model Parameter Estimation and Uncertainty: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-6

Briggs AH, Weinstein MC, Fenwick EAL, Karnon J, Sculpher MJ, Paltiel AD, on Behalf of the ISPOR-SMDM Modeling Good Research Practices Task Force “Model Parameter Estimation and Uncertainty: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-6” Value in Health 15 (2012) 835– 842 doi: 10.1016/j.jval.2012.04.014 18/26 Table 1: Exemplar ag...

work page doi:10.1016/j.jval.2012.04.014 2012

[1] [1]

stage-shift

Introduction The modelling of longitudinal cancer screening data using multistate models (MSMs) can characterise the natural history of cancer by describing progression through mutually exclusive states, including ‘no cancer’ (undetectable cancer), preclinical detectable cancer, and clinical diagnosis.1 A primary parameter of interest is the (preclinical)...

2009

[2] [2]

no cancer

Methods 2.1 Generating simulated datasets: Dai’s model To simulate the NHS-Galleri trial data6, we used two published models.12,13 Dai’s microsimulation model12 served as our primary source because it supports the highest level of stage disaggregation (stages I to IV). The alternative model, MCEDsim13, allowing only disaggregation between early- and late-...

2024

[3] [3]

Full results, including of test sensitivity, are in Supp C

Results 3.1 3-, 5- and 9-state MSM models Table 3 presents inference results for MST and stage-MST and the results of explorations of convergence (C), identifiability (I) and precision (P) using a representative dataset (Dai’s model, 50th percentile of predicted primary endpoint). Full results, including of test sensitivity, are in Supp C. Across all mode...

[4] [4]

Discussion Given the inherent heterogeneity in tumor biology, not only in (multi-cancer) test sensitivity but also in preclinical cancer progression, it is essential that analyses of longitudinal cancer screening data reliably estimate mean sojourn time across cancer types and stages to determine the effect of screening on stage shift. In this study, we e...

2021

[5] [5]

Br J Cancer

Cheung LC, Albert PS, Das S, Cook RJ Multistate models for the natural history of cancer progression. Br J Cancer. 2022 Jul 11;127(7):1279–1288. doi: 10.1038/s41416-022-01904-5

work page doi:10.1038/s41416-022-01904-5 2022

[6] [6]

Quantifying the duration of the preclinical detectable phase in cancer screening: a systematic review

Geurts SME, Aarts AMWM, Verbeek ALM, Chen THH, Broeders MJM, Duffy SW. Quantifying the duration of the preclinical detectable phase in cancer screening: a systematic review. Epidemiol Health. 2022;44:e2022008. doi: 10.4178/epih.e2022008

work page doi:10.4178/epih.e2022008 2022

[7] [7]

A Scoping Review on Calibration Methods for Cancer Simulation Models

Zhang Y, Lipa N, Alagoz O. A Scoping Review on Calibration Methods for Cancer Simulation Models. Med Decis Making. 2025 Nov;45(8):965-975. doi: 10.1177/0272989X251353211. 15/26

work page doi:10.1177/0272989x251353211 2025

[8] [8]

Simplified models of screening for chronic disease: Estimation procedures from mass screening programmes

Day NE, Walter SD (1984). Simplified models of screening for chronic disease: Estimation procedures from mass screening programmes. Biometrics, 40(1), 1–14. PMID: 6733223

1984

[9] [9]

Methods Med

Uhry et al., Multi-state Markov models in cancer screening evaluation: a brief review and case study, Stat. Methods Med. Res. 19 (2010) 463–486

2010

[10] [10]

Cell-Free DNA–Based Multi-Cancer Early Detection Test in an Asymptomatic Screening Population (NHS-Galleri): Design of a Pragmatic, Prospective Randomised Controlled Trial

Neal RD, Johnson P, Clarke CA, Hamilton SA, Zhang N, Kumar H, Swanton C, Sasieni P. Cell-Free DNA–Based Multi-Cancer Early Detection Test in an Asymptomatic Screening Population (NHS-Galleri): Design of a Pragmatic, Prospective Randomised Controlled Trial. Cancers 2022, 14(19), 4818; https://doi.org/10.3390/cancers14194818

work page doi:10.3390/cancers14194818 2022

[11] [11]

The National Health Service-Galleri multi-cancer screening trial: explanation and justification of unique and important design issues

Sasieni P, Swanton C, Neal RD. The National Health Service-Galleri multi-cancer screening trial: explanation and justification of unique and important design issues. J Natl Cancer Inst. 2025 Aug 9:djaf218. https://doi.org/10.1093/jnci/djaf218

work page doi:10.1093/jnci/djaf218 2025

[12] [12]

NHS-Galleri trial: Enriched enrolment approaches and sociodemographic characteristics of enrolled participants

Swanton C, Bachtiar V, Mathews C, et al. NHS-Galleri trial: Enriched enrolment approaches and sociodemographic characteristics of enrolled participants. Clinical Trials. 2025;22(2):227-

2025

[13] [13]

https://doi.org/10.1177/174077452413024

work page doi:10.1177/174077452413024

[14] [14]

Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood,

Raue A, Kreutz C, Maiwald T, Bachmann J, Schilling M, Klingmüller U, Timmer J. Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics. 2009 Aug 1;25(15):1923-9. doi: 10.1093/bioinformatics/btp358. Epub 2009 Jun 8. PMID: 19505944

work page doi:10.1093/bioinformatics/btp358 2009

[15] [15]

A confidence building exercise in data and identifiability: Modeling cancer chemotherapy as a case study

Eisenberg MC, Jain HV. A confidence building exercise in data and identifiability: Modeling cancer chemotherapy as a case study. J Theor Biol. 2017 Oct 27;431:63-78. doi: 10.1016/j.jtbi.2017.07.018. Epub 2017 Jul 19. Erratum in: J Theor Biol. 2019 Mar 7;464:179. doi: 10.1016/j.jtbi.2018.12.042

work page doi:10.1016/j.jtbi.2017.07.018 2017

[16] [16]

Nonidentifiability in Model Calibration and Implications for Medical Decision Making

Alarid-Escudero F, MacLehose RF, Peralta Y, Kuntz KM, Enns EA. Nonidentifiability in Model Calibration and Implications for Medical Decision Making. Medical Decision Making. 2018;38(7):810-821. doi:10.1177/0272989X18792283 16/26

work page doi:10.1177/0272989x18792283 2018

[17] [17]

J Med Screen

Dai JY, Zhang J, Braun JV, Simon N, Hubbell E, Zhang N, Clinical performance and utility: A microsimulation model to inform the design of screening trials for a multi-cancer early detection test. J Med Screen. 2024 Feb 2;31(3):140–149. doi: 10.1177/09691413241228041

work page doi:10.1177/09691413241228041 2024

[18] [18]

Projecting the Impact of Multi-Cancer Early Detection on Late-Stage Incidence Using Multi-State Disease Modeling

Lange JM., Gogebakan KC, Gulati R, Etzioni R. Projecting the Impact of Multi-Cancer Early Detection on Late-Stage Incidence Using Multi-State Disease Modeling. Cancer Epidemiol Biomarkers Prev (2024) 33 (6): 830–837. https://doi.org/10.1158/1055-9965.EPI-23-1470

work page doi:10.1158/1055-9965.epi-23-1470 2024

[19] [19]

Klein, E. A., D. Richards, A. Cohn, M. Tummala, R. Lapham, D. Cosgrove, G. Chung, et al

[20] [20]

Annals of Oncology : Official Journal of the European Society for Medical Oncology 32 (9): 1167–77

Clinical Validation of a Targeted Methylation-Based Multi-Cancer Early Detection Test Using an Independent Validation Set. Annals of Oncology : Official Journal of the European Society for Medical Oncology 32 (9): 1167–77. https://doi.org/10.1016/j.annonc.2021.05.806

work page doi:10.1016/j.annonc.2021.05.806 2021

[21] [21]

Estimating stage-specific sensitivity for cancer screening tests

Pinsky P, Lange J, Etzioni R. Estimating stage-specific sensitivity for cancer screening tests. Journal of Medical Screening. 2023;30(2):69-73. doi:10.1177/09691413231154801

work page doi:10.1177/09691413231154801 2023

[22] [22]

A multistate survival model of the natural history of cancer using data from screened and unscreened population

Bhatt R, vanden Hout A, Pashayan N. A multistate survival model of the natural history of cancer using data from screened and unscreened population. Statistics in Medicine. 2021;40:3791–3807. https://doi.org/10.1002/sim.8998

work page doi:10.1002/sim.8998 2021

[23] [23]

Maple2025.0, Maplesoft, Waterloo, Canada

[24] [24]

Moving beyond noninformative priors: why and how to choose weakly informative priors in Bayesian analyses

Lemoine NP. Moving beyond noninformative priors: why and how to choose weakly informative priors in Bayesian analyses. Oikos. 128: 912–928, 2019 doi: 10.1111/oik.05985

work page doi:10.1111/oik.05985 2019

[25] [25]

https://CRAN.R-project.org/package=R2jags

[26] [26]

Rank-Normalization, Folding, and Localization: An Improved R for Assessing Convergence of MCMC (with Discussion)

Vehtari A, Gelman A, Simpson D, Carpenter B, Burkner PC. Rank-Normalization, Folding, and Localization: An Improved R for Assessing Convergence of MCMC (with Discussion). Bayesian Analysis (2021) 16, Number 2, pp. 667–718

2021

[27] [27]

On structural and practical identifiability

Wieland FG, Hauber AL, Rosenblatt M, Tönsing C, Timmer J. On structural and practical identifiability. Current Opinion in Systems Biology, 2021 25:60-69. https://doi.org/10.1016/j.coisb.2021.03.005. 17/26

work page doi:10.1016/j.coisb.2021.03.005 2021

[28] [28]

Bayesian Data Analysis

Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB. Bayesian Data Analysis. 3rd ed. CRC Press; 2013

2013

[29] [29]

J., Best, N

Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & van der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64(4), 583-639

2002

[30] [30]

Gogebakan KC, Lange J, Owens L, Pinderup A, Gulati R, Kessler LG, Lyratzopoulos G, Etzioni R. 2025. Clinical Significance of a Multicancer Screening Trial With Stage-Based End Points. JAMA Network Open 8 (10): e2536247. https://doi.org/10.1001/jamanetworkopen.2025.36247

work page doi:10.1001/jamanetworkopen.2025.36247 2025

[31] [31]

Feasibility of blood testing combined with PET-CT to screen for cancer and guide intervention

Lennon AM, Buchanan AH, Kinde I, Warren A, Honushefsky A, Cohain AT, Ledbetter DH, Sanfilippo F, Sheridan K, Rosica D, Adonizio CS, Hwang HJ, Lahouel K, Cohen JD, Douville C, Patel AA, Hagmann LN, Rolston DD, Malani N, Zhou S, Bettegowda C, Diehl DL, Urban B, Still CD, Kann L, Woods JI, Salvati ZM, Vadakara J, Leeming R, Bhattacharya P, Walter C, Parker A...

work page doi:10.1126/science.abb9601 2020

[32] [32]

https://investors.grail.com/node/8281/pdf, February 2026

2026

[33] [33]

Model Parameter Estimation and Uncertainty: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-6

Briggs AH, Weinstein MC, Fenwick EAL, Karnon J, Sculpher MJ, Paltiel AD, on Behalf of the ISPOR-SMDM Modeling Good Research Practices Task Force “Model Parameter Estimation and Uncertainty: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-6” Value in Health 15 (2012) 835– 842 doi: 10.1016/j.jval.2012.04.014 18/26 Table 1: Exemplar ag...

work page doi:10.1016/j.jval.2012.04.014 2012