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Huang J, Morsomme R, Dunson D, Xu J. Detecting changes in the transmission rate of a stochastic epidemic model. Stat Med 2024; 43:1867-1882. [PMID: 38409877 DOI: 10.1002/sim.10050] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Revised: 10/26/2023] [Accepted: 01/03/2024] [Indexed: 02/28/2024]
Abstract
Throughout the course of an epidemic, the rate at which disease spreads varies with behavioral changes, the emergence of new disease variants, and the introduction of mitigation policies. Estimating such changes in transmission rates can help us better model and predict the dynamics of an epidemic, and provide insight into the efficacy of control and intervention strategies. We present a method for likelihood-based estimation of parameters in the stochastic susceptible-infected-removed model under a time-inhomogeneous transmission rate comprised of piecewise constant components. In doing so, our method simultaneously learns change points in the transmission rate via a Markov chain Monte Carlo algorithm. The method targets the exact model posterior in a difficult missing data setting given only partially observed case counts over time. We validate performance on simulated data before applying our approach to data from an Ebola outbreak in Western Africa and COVID-19 outbreak on a university campus.
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Affiliation(s)
- Jenny Huang
- Department of Statistical Science, Duke University, Durham, North Carolina, USA
| | - Raphaël Morsomme
- Department of Statistical Science, Duke University, Durham, North Carolina, USA
| | - David Dunson
- Department of Statistical Science, Duke University, Durham, North Carolina, USA
| | - Jason Xu
- Department of Statistical Science, Duke University, Durham, North Carolina, USA
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2
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Scarponi D, Iskauskas A, Clark RA, Vernon I, McKinley TJ, Goldstein M, Mukandavire C, Deol A, Weerasuriya C, Bakker R, White RG, McCreesh N. Demonstrating multi-country calibration of a tuberculosis model using new history matching and emulation package - hmer. Epidemics 2023; 43:100678. [PMID: 36913805 DOI: 10.1016/j.epidem.2023.100678] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2022] [Revised: 02/23/2023] [Accepted: 03/06/2023] [Indexed: 03/09/2023] Open
Abstract
Infectious disease models are widely used by epidemiologists to improve the understanding of transmission dynamics and disease natural history, and to predict the possible effects of interventions. As the complexity of such models increases, however, it becomes increasingly challenging to robustly calibrate them to empirical data. History matching with emulation is a calibration method that has been successfully applied to such models, but has not been widely used in epidemiology partly due to the lack of available software. To address this issue, we developed a new, user-friendly R package hmer to simply and efficiently perform history matching with emulation. In this paper, we demonstrate the first use of hmer for calibrating a complex deterministic model for the country-level implementation of tuberculosis vaccines to 115 low- and middle-income countries. The model was fit to 9-13 target measures, by varying 19-22 input parameters. Overall, 105 countries were successfully calibrated. Among the remaining countries, hmer visualisation tools, combined with derivative emulation methods, provided strong evidence that the models were misspecified and could not be calibrated to the target ranges. This work shows that hmer can be used to simply and rapidly calibrate a complex model to data from over 100 countries, making it a useful addition to the epidemiologist's calibration tool-kit.
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Affiliation(s)
- Danny Scarponi
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, UK.
| | | | - Rebecca A Clark
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, UK
| | - Ian Vernon
- Department of Mathematical Sciences, Durham University, UK
| | | | | | - Christinah Mukandavire
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, UK
| | - Arminder Deol
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, UK
| | - Chathika Weerasuriya
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, UK
| | - Roel Bakker
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, UK
| | - Richard G White
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, UK
| | - Nicky McCreesh
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, UK
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3
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Augustin D, Lambert B, Wang K, Walz AC, Robinson M, Gavaghan D. Filter inference: A scalable nonlinear mixed effects inference approach for snapshot time series data. PLoS Comput Biol 2023; 19:e1011135. [PMID: 37216399 DOI: 10.1371/journal.pcbi.1011135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2022] [Accepted: 04/26/2023] [Indexed: 05/24/2023] Open
Abstract
Variability is an intrinsic property of biological systems and is often at the heart of their complex behaviour. Examples range from cell-to-cell variability in cell signalling pathways to variability in the response to treatment across patients. A popular approach to model and understand this variability is nonlinear mixed effects (NLME) modelling. However, estimating the parameters of NLME models from measurements quickly becomes computationally expensive as the number of measured individuals grows, making NLME inference intractable for datasets with thousands of measured individuals. This shortcoming is particularly limiting for snapshot datasets, common e.g. in cell biology, where high-throughput measurement techniques provide large numbers of single cell measurements. We introduce a novel approach for the estimation of NLME model parameters from snapshot measurements, which we call filter inference. Filter inference uses measurements of simulated individuals to define an approximate likelihood for the model parameters, avoiding the computational limitations of traditional NLME inference approaches and making efficient inferences from snapshot measurements possible. Filter inference also scales well with the number of model parameters, using state-of-the-art gradient-based MCMC algorithms such as the No-U-Turn Sampler (NUTS). We demonstrate the properties of filter inference using examples from early cancer growth modelling and from epidermal growth factor signalling pathway modelling.
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Affiliation(s)
- David Augustin
- Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Ben Lambert
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, United Kingdom
| | - Ken Wang
- Research and Early Development, F. Hoffmann-La Roche AG, Basel, Switzerland
| | | | - Martin Robinson
- Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - David Gavaghan
- Department of Computer Science, University of Oxford, Oxford, United Kingdom
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4
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Cunha Jr A, Barton DAW, Ritto TG. Uncertainty quantification in mechanistic epidemic models via cross-entropy approximate Bayesian computation. NONLINEAR DYNAMICS 2023; 111:9649-9679. [PMID: 37025428 PMCID: PMC9961307 DOI: 10.1007/s11071-023-08327-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/09/2022] [Accepted: 02/09/2023] [Indexed: 06/19/2023]
Abstract
This paper proposes a data-driven approximate Bayesian computation framework for parameter estimation and uncertainty quantification of epidemic models, which incorporates two novelties: (i) the identification of the initial conditions by using plausible dynamic states that are compatible with observational data; (ii) learning of an informative prior distribution for the model parameters via the cross-entropy method. The new methodology's effectiveness is illustrated with the aid of actual data from the COVID-19 epidemic in Rio de Janeiro city in Brazil, employing an ordinary differential equation-based model with a generalized SEIR mechanistic structure that includes time-dependent transmission rate, asymptomatics, and hospitalizations. A minimization problem with two cost terms (number of hospitalizations and deaths) is formulated, and twelve parameters are identified. The calibrated model provides a consistent description of the available data, able to extrapolate forecasts over a few weeks, making the proposed methodology very appealing for real-time epidemic modeling.
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Affiliation(s)
- Americo Cunha Jr
- Institute of Mathematics and Statistics, Rio de Janeiro State University – UERJ, Rio de Janeiro, Brazil
| | | | - Thiago G. Ritto
- Department of Mechanical Engineering, Federal University of Rio de Janeiro – UFRJ, Rio de Janeiro, Brazil
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5
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Vernon I, Owen J, Aylett-Bullock J, Cuesta-Lazaro C, Frawley J, Quera-Bofarull A, Sedgewick A, Shi D, Truong H, Turner M, Walker J, Caulfield T, Fong K, Krauss F. Bayesian emulation and history matching of JUNE. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20220039. [PMID: 35965471 PMCID: PMC9376712 DOI: 10.1098/rsta.2022.0039] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Accepted: 06/07/2022] [Indexed: 05/21/2023]
Abstract
We analyze JUNE: a detailed model of COVID-19 transmission with high spatial and demographic resolution, developed as part of the RAMP initiative. JUNE requires substantial computational resources to evaluate, making model calibration and general uncertainty analysis extremely challenging. We describe and employ the uncertainty quantification approaches of Bayes linear emulation and history matching to mimic JUNE and to perform a global parameter search, hence identifying regions of parameter space that produce acceptable matches to observed data, and demonstrating the capability of such methods. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.
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Affiliation(s)
- I. Vernon
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Department of Mathematical Sciences, Durham University, Durham DH13LE, UK
| | - J. Owen
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Department of Mathematical Sciences, Durham University, Durham DH13LE, UK
| | - J. Aylett-Bullock
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH13LE, UK
| | - C. Cuesta-Lazaro
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH13LE, UK
| | - J. Frawley
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Advanced Research Computing, Durham University, Durham DH13LE, UK
| | - A. Quera-Bofarull
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH13LE, UK
| | - A. Sedgewick
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Centre for Extragalactic Astronomy, Durham University, Durham DH13LE, UK
| | - D. Shi
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH13LE, UK
| | - H. Truong
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH13LE, UK
| | - M. Turner
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Advanced Research Computing, Durham University, Durham DH13LE, UK
| | - J. Walker
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH13LE, UK
| | - T. Caulfield
- Department of Computer Science, Durham University, Durham DH13LE, UK
| | - K. Fong
- Department of Science, Technology, Engineering and Public Policy, University College London, London WC1E6BT, UK
- Department of Anaesthesia, University College London Hospital, London NW12BU, UK
| | - F. Krauss
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH13LE, UK
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6
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Vernon I, Owen J, Aylett-Bullock J, Cuesta-Lazaro C, Frawley J, Quera-Bofarull A, Sedgewick A, Shi D, Truong H, Turner M, Walker J, Caulfield T, Fong K, Krauss F. Bayesian emulation and history matching of JUNE. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210039. [PMID: 35965471 DOI: 10.1098/rsta.2021.0039] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2021] [Accepted: 12/06/2021] [Indexed: 05/21/2023]
Abstract
We analyze JUNE: a detailed model of COVID-19 transmission with high spatial and demographic resolution, developed as part of the RAMP initiative. JUNE requires substantial computational resources to evaluate, making model calibration and general uncertainty analysis extremely challenging. We describe and employ the uncertainty quantification approaches of Bayes linear emulation and history matching to mimic JUNE and to perform a global parameter search, hence identifying regions of parameter space that produce acceptable matches to observed data, and demonstrating the capability of such methods. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.
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Affiliation(s)
- I Vernon
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Department of Mathematical Sciences, Durham University, Durham DH13LE, UK
| | - J Owen
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Department of Mathematical Sciences, Durham University, Durham DH13LE, UK
| | - J Aylett-Bullock
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH13LE, UK
| | - C Cuesta-Lazaro
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH13LE, UK
| | - J Frawley
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Advanced Research Computing, Durham University, Durham DH13LE, UK
| | - A Quera-Bofarull
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH13LE, UK
| | - A Sedgewick
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Centre for Extragalactic Astronomy, Durham University, Durham DH13LE, UK
| | - D Shi
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH13LE, UK
| | - H Truong
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH13LE, UK
| | - M Turner
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Advanced Research Computing, Durham University, Durham DH13LE, UK
| | - J Walker
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH13LE, UK
| | - T Caulfield
- Department of Computer Science, Durham University, Durham DH13LE, UK
| | - K Fong
- Department of Science, Technology, Engineering and Public Policy, University College London, London WC1E6BT, UK
- Department of Anaesthesia, University College London Hospital, London NW12BU, UK
| | - F Krauss
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH13LE, UK
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7
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Wood F, Warrington A, Naderiparizi S, Weilbach C, Masrani V, Harvey W, Ścibior A, Beronov B, Grefenstette J, Campbell D, Nasseri SA. Planning as Inference in Epidemiological Dynamics Models. Front Artif Intell 2022; 4:550603. [PMID: 35434605 PMCID: PMC9009395 DOI: 10.3389/frai.2021.550603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2020] [Accepted: 10/25/2021] [Indexed: 01/10/2023] Open
Abstract
In this work we demonstrate how to automate parts of the infectious disease-control policy-making process via performing inference in existing epidemiological models. The kind of inference tasks undertaken include computing the posterior distribution over controllable, via direct policy-making choices, simulation model parameters that give rise to acceptable disease progression outcomes. Among other things, we illustrate the use of a probabilistic programming language that automates inference in existing simulators. Neither the full capabilities of this tool for automating inference nor its utility for planning is widely disseminated at the current time. Timely gains in understanding about how such simulation-based models and inference automation tools applied in support of policy-making could lead to less economically damaging policy prescriptions, particularly during the current COVID-19 pandemic.
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Affiliation(s)
- Frank Wood
- Department of Computer Science, University of British Columbia, Vancouver, BC, Canada
- Associate Academic Member and Canada CIFAR AI Chair, Mila Institute, Montreal, QC, Canada
| | - Andrew Warrington
- Department of Engineering Science, University of Oxford, Oxford, United Kingdom
| | - Saeid Naderiparizi
- Department of Computer Science, University of British Columbia, Vancouver, BC, Canada
| | - Christian Weilbach
- Department of Computer Science, University of British Columbia, Vancouver, BC, Canada
| | - Vaden Masrani
- Department of Computer Science, University of British Columbia, Vancouver, BC, Canada
| | - William Harvey
- Department of Computer Science, University of British Columbia, Vancouver, BC, Canada
| | - Adam Ścibior
- Department of Computer Science, University of British Columbia, Vancouver, BC, Canada
| | - Boyan Beronov
- Department of Computer Science, University of British Columbia, Vancouver, BC, Canada
| | | | | | - S. Ali Nasseri
- Department of Computer Science, University of British Columbia, Vancouver, BC, Canada
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8
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Sher A, Niederer SA, Mirams GR, Kirpichnikova A, Allen R, Pathmanathan P, Gavaghan DJ, van der Graaf PH, Noble D. A Quantitative Systems Pharmacology Perspective on the Importance of Parameter Identifiability. Bull Math Biol 2022; 84:39. [PMID: 35132487 PMCID: PMC8821410 DOI: 10.1007/s11538-021-00982-5] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Accepted: 11/30/2021] [Indexed: 12/31/2022]
Abstract
There is an inherent tension in Quantitative Systems Pharmacology (QSP) between the need to incorporate mathematical descriptions of complex physiology and drug targets with the necessity of developing robust, predictive and well-constrained models. In addition to this, there is no “gold standard” for model development and assessment in QSP. Moreover, there can be confusion over terminology such as model and parameter identifiability; complex and simple models; virtual populations; and other concepts, which leads to potential miscommunication and misapplication of methodologies within modeling communities, both the QSP community and related disciplines. This perspective article highlights the pros and cons of using simple (often identifiable) vs. complex (more physiologically detailed but often non-identifiable) models, as well as aspects of parameter identifiability, sensitivity and inference methodologies for model development and analysis. The paper distills the central themes of the issue of identifiability and optimal model size and discusses open challenges.
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Affiliation(s)
- Anna Sher
- Pfizer Worldwide Research, Development and Medical, Massachusetts, USA.
| | | | - Gary R Mirams
- Centre for Mathematical Medicine and Biology, Mathematical Sciences, University of Nottingham, Nottingham, UK
| | | | - Richard Allen
- Pfizer Worldwide Research, Development and Medical, Massachusetts, USA
| | - Pras Pathmanathan
- Center for Devices and Radiological Health, U.S. Food and Drug Administration, Maryland, USA
| | - David J Gavaghan
- Department of Computer Science, University of Oxford, Oxford, UK
| | | | - Denis Noble
- Department of Physiology, Anatomy and Genetics, University of Oxford, Oxford, UK
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9
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Swallow B, Birrell P, Blake J, Burgman M, Challenor P, Coffeng LE, Dawid P, De Angelis D, Goldstein M, Hemming V, Marion G, McKinley TJ, Overton CE, Panovska-Griffiths J, Pellis L, Probert W, Shea K, Villela D, Vernon I. Challenges in estimation, uncertainty quantification and elicitation for pandemic modelling. Epidemics 2022; 38:100547. [PMID: 35180542 PMCID: PMC7612598 DOI: 10.1016/j.epidem.2022.100547] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2021] [Revised: 12/22/2021] [Accepted: 02/09/2022] [Indexed: 12/15/2022] Open
Affiliation(s)
- Ben Swallow
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK; Scottish COVID-19 Response Consortium, UK.
| | - Paul Birrell
- Analytics & Data Science, UKHSA, UK; MRC Biostatistics Unit, University of Cambridge, Cambridge, UK
| | - Joshua Blake
- MRC Biostatistics Unit, University of Cambridge, Cambridge, UK
| | - Mark Burgman
- Centre for Environmental Policy, Imperial College London, London, UK
| | - Peter Challenor
- The Alan Turing Institute, London, UK; College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK
| | - Luc E Coffeng
- Department of Public Health, Erasmus MC, University Medical Center Rotterdam, Rotterdam, The Netherlands
| | - Philip Dawid
- Statistical Laboratory, University of Cambridge, Cambridge, UK
| | - Daniela De Angelis
- MRC Biostatistics Unit, University of Cambridge, Cambridge, UK; Joint UNIversities Pandemic and Epidemiological Research, UK
| | - Michael Goldstein
- Department of Mathematical Sciences, Durham University, Stockton Road, Durham, UK
| | - Victoria Hemming
- Department of Forest and Conservation Sciences, University of British Columbia, Vancouver, Canada
| | - Glenn Marion
- Scottish COVID-19 Response Consortium, UK; Biomathematics and Statistics Scotland, Edinburgh, UK
| | - Trevelyan J McKinley
- College of Medicine and Health, University of Exeter, Exeter, UK; Joint UNIversities Pandemic and Epidemiological Research, UK
| | - Christopher E Overton
- Department of Mathematics, University of Manchester, Manchester, UK; Clinical Data Science Unit, Manchester University NHS Foundation Trust, Manchester, UK; Joint UNIversities Pandemic and Epidemiological Research, UK
| | - Jasmina Panovska-Griffiths
- The Big Data Institute, University of Oxford, Oxford, UK; The Queen's College, University of Oxford, Oxford, UK
| | - Lorenzo Pellis
- Department of Mathematics, University of Manchester, Manchester, UK; Joint UNIversities Pandemic and Epidemiological Research, UK; The Alan Turing Institute, London, UK
| | - Will Probert
- The Big Data Institute, University of Oxford, Oxford, UK
| | - Katriona Shea
- Department of Biology and Centre for Infectious Disease Dynamics, The Pennsylvania State University, PA 16802, USA
| | - Daniel Villela
- Program of Scientific Computing, Fundação Oswaldo Cruz, Rio de Janeiro, Brazil
| | - Ian Vernon
- Department of Mathematical Sciences, Durham University, Stockton Road, Durham, UK
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10
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Baker E, Barbillon P, Fadikar A, Gramacy RB, Herbei R, Higdon D, Huang J, Johnson LR, Ma P, Mondal A, Pires B, Sacks J, Sokolov V. Analyzing Stochastic Computer Models: A Review with Opportunities. Stat Sci 2022. [DOI: 10.1214/21-sts822] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Evan Baker
- Evan Baker is Postdoctoral Research Fellow, Living Systems Institute, University of Exeter, Stocker Road, Exeter, EX4 4QD, UK
| | - Pierre Barbillon
- Pierre Barbillon is Associate Professor, Université Paris-Saclay, AgroParisTech, INRAE, UMR MIA-Paris, 16 rue Claude Bernard, 75231 Paris Cedex 05, France
| | - Arindam Fadikar
- Arindam Fadikar is Postdoctoral Appointee, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Ave., Lemont, Illinois 60439, USA
| | - Robert B. Gramacy
- Robert B. Gramacy is Professor, Department of Statistics, Virginia Tech, 250 Drillfield Drive Blacksburg, Virginia 24061, USA
| | - Radu Herbei
- Radu Herbei is Professor of Statistics, Department of Statistics, College of Arts and Sciences, The Ohio State University, 1958 Neil Ave., Columbus, Ohio 43210, USA
| | - David Higdon
- David Higdon is Professor, Department of Statistics, Virginia Tech, MC0439, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Jiangeng Huang
- Jiangeng Huang is Senior Statistical Scientist, Genentech, Inc., 1 DNA Way, South San Francisco, California 94080, USA
| | - Leah R. Johnson
- Leah R. Johnson is Associate Professor, Department of Statistics, Computational Modeling and Data Analytics (CMDA), Virginia Tech, Hutcheson Hall, RM 409-B, 250 Drillfield Drive, Blacksburg, Virginia 24061, USA
| | - Pulong Ma
- Pulong Ma is Postdoctoral Fellow, Duke University and Statistical and Applied Mathematical Sciences Institute, 19 T.W. Alexander Drive, P.O. Box 110207, Durham, North Carolina 27709, USA
| | - Anirban Mondal
- Anirban Mondal is Assistant Professor, Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University, 10900 Euclid Avenue, Yost Hall Room 337, Cleveland, Ohio 44106-7058, USA
| | - Bianica Pires
- Bianica Pires is Lead Modeling & Simulation Engineer, The MITRE Corporation, 7515 Colshire Dr, McLean, Virginia 22102, USA
| | - Jerome Sacks
- Jerome Sacks is Ph.D., NISS, 1460 N. Sandburg Ter, Apt 2902, Chicago, Illinois 60610, USA
| | - Vadim Sokolov
- Vadim Sokolov is Assistant Professor, Systems Engineering and Operations Research, George Mason University, Nguyen Engineering Building MS 4A6, Fairfax, Virginia 22302, USA
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11
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DeYoreo M, Rutter CM, Ozik J, Collier N. Sequentially calibrating a Bayesian microsimulation model to incorporate new information and assumptions. BMC Med Inform Decis Mak 2022; 22:12. [PMID: 35022005 PMCID: PMC8756687 DOI: 10.1186/s12911-021-01726-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2021] [Accepted: 12/17/2021] [Indexed: 12/11/2022] Open
Abstract
BACKGROUND Microsimulation models are mathematical models that simulate event histories for individual members of a population. They are useful for policy decisions because they simulate a large number of individuals from an idealized population, with features that change over time, and the resulting event histories can be summarized to describe key population-level outcomes. Model calibration is the process of incorporating evidence into the model. Calibrated models can be used to make predictions about population trends in disease outcomes and effectiveness of interventions, but calibration can be challenging and computationally expensive. METHODS This paper develops a technique for sequentially updating models to take full advantage of earlier calibration results, to ultimately speed up the calibration process. A Bayesian approach to calibration is used because it combines different sources of evidence and enables uncertainty quantification which is appealing for decision-making. We develop this method in order to re-calibrate a microsimulation model for the natural history of colorectal cancer to include new targets that better inform the time from initiation of preclinical cancer to presentation with clinical cancer (sojourn time), because model exploration and validation revealed that more information was needed on sojourn time, and that the predicted percentage of patients with cancers detected via colonoscopy screening was too low. RESULTS The sequential approach to calibration was more efficient than recalibrating the model from scratch. Incorporating new information on the percentage of patients with cancers detected upon screening changed the estimated sojourn time parameters significantly, increasing the estimated mean sojourn time for cancers in the colon and rectum, providing results with more validity. CONCLUSIONS A sequential approach to recalibration can be used to efficiently recalibrate a microsimulation model when new information becomes available that requires the original targets to be supplemented with additional targets.
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Affiliation(s)
- Maria DeYoreo
- RAND Corporation, 1776 Main St., Santa Monica, CA, 90401, USA.
| | | | - Jonathan Ozik
- Argonne National Laboratory, Building 221, 9700 South Cass Avenue, Argonne, IL, 60439, USA
| | - Nicholson Collier
- Argonne National Laboratory, Building 221, 9700 South Cass Avenue, Argonne, IL, 60439, USA
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12
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Aylett-Bullock J, Cuesta-Lazaro C, Quera-Bofarull A, Icaza-Lizaola M, Sedgewick A, Truong H, Curran A, Elliott E, Caulfield T, Fong K, Vernon I, Williams J, Bower R, Krauss F. June: open-source individual-based epidemiology simulation. ROYAL SOCIETY OPEN SCIENCE 2021. [PMID: 34295529 DOI: 10.5281/zenodo.4925939] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
We introduce June, an open-source framework for the detailed simulation of epidemics on the basis of social interactions in a virtual population constructed from geographically granular census data, reflecting age, sex, ethnicity and socio-economic indicators. Interactions between individuals are modelled in groups of various sizes and properties, such as households, schools and workplaces, and other social activities using social mixing matrices. June provides a suite of flexible parametrizations that describe infectious diseases, how they are transmitted and affect contaminated individuals. In this paper, we apply June to the specific case of modelling the spread of COVID-19 in England. We discuss the quality of initial model outputs which reproduce reported hospital admission and mortality statistics at national and regional levels as well as by age strata.
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Affiliation(s)
- Joseph Aylett-Bullock
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH1 3LE, UK
| | - Carolina Cuesta-Lazaro
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH1 3LE, UK
| | - Arnau Quera-Bofarull
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH1 3LE, UK
| | - Miguel Icaza-Lizaola
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH1 3LE, UK
| | - Aidan Sedgewick
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Centre for Extragalactic Astronomy, Durham University, Durham DH1 3LE, UK
| | - Henry Truong
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH1 3LE, UK
| | - Aoife Curran
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH1 3LE, UK
| | - Edward Elliott
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH1 3LE, UK
| | - Tristan Caulfield
- Department of Computer Science, University College London, London WC1E 6BT, UK
| | - Kevin Fong
- Department of Science, Technology, Engineering and Public Policy, University College London, London WC1E 6BT, UK
- Department of Anaesthesia, University College London Hospital, London NW1 2BU, UK
| | - Ian Vernon
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Department of Mathematical Sciences, Durham University, Durham DH1 3LE, UK
| | - Julian Williams
- Institute of Hazard, Risk and Resilience, Durham University, Durham DH1 3LE, UK
| | - Richard Bower
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH1 3LE, UK
| | - Frank Krauss
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH1 3LE, UK
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13
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Aylett-Bullock J, Cuesta-Lazaro C, Quera-Bofarull A, Icaza-Lizaola M, Sedgewick A, Truong H, Curran A, Elliott E, Caulfield T, Fong K, Vernon I, Williams J, Bower R, Krauss F. June: open-source individual-based epidemiology simulation. ROYAL SOCIETY OPEN SCIENCE 2021; 8:210506. [PMID: 34295529 PMCID: PMC8261230 DOI: 10.1098/rsos.210506] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2021] [Accepted: 06/22/2021] [Indexed: 05/09/2023]
Abstract
We introduce June, an open-source framework for the detailed simulation of epidemics on the basis of social interactions in a virtual population constructed from geographically granular census data, reflecting age, sex, ethnicity and socio-economic indicators. Interactions between individuals are modelled in groups of various sizes and properties, such as households, schools and workplaces, and other social activities using social mixing matrices. June provides a suite of flexible parametrizations that describe infectious diseases, how they are transmitted and affect contaminated individuals. In this paper, we apply June to the specific case of modelling the spread of COVID-19 in England. We discuss the quality of initial model outputs which reproduce reported hospital admission and mortality statistics at national and regional levels as well as by age strata.
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Affiliation(s)
- Joseph Aylett-Bullock
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH1 3LE, UK
| | - Carolina Cuesta-Lazaro
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH1 3LE, UK
| | - Arnau Quera-Bofarull
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH1 3LE, UK
| | - Miguel Icaza-Lizaola
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH1 3LE, UK
| | - Aidan Sedgewick
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Centre for Extragalactic Astronomy, Durham University, Durham DH1 3LE, UK
| | - Henry Truong
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH1 3LE, UK
| | - Aoife Curran
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH1 3LE, UK
| | - Edward Elliott
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH1 3LE, UK
| | - Tristan Caulfield
- Department of Computer Science, University College London, London WC1E 6BT, UK
| | - Kevin Fong
- Department of Science, Technology, Engineering and Public Policy, University College London, London WC1E 6BT, UK
- Department of Anaesthesia, University College London Hospital, London NW1 2BU, UK
| | - Ian Vernon
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Department of Mathematical Sciences, Durham University, Durham DH1 3LE, UK
| | - Julian Williams
- Institute of Hazard, Risk and Resilience, Durham University, Durham DH1 3LE, UK
| | - Richard Bower
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH1 3LE, UK
| | - Frank Krauss
- Institute for Data Science, Durham University, Durham DH1 3LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH1 3LE, UK
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14
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Understanding the Sampling Bias: A Case Study on NBA Drafts. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2021. [DOI: 10.1007/s42519-021-00167-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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15
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Modeling poliovirus replication dynamics from live time-lapse single-cell imaging data. Sci Rep 2021; 11:9622. [PMID: 33953215 PMCID: PMC8100109 DOI: 10.1038/s41598-021-87694-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2020] [Accepted: 03/15/2021] [Indexed: 02/03/2023] Open
Abstract
Viruses experience selective pressure on the timing and order of events during infection to maximize the number of viable offspring they produce. Additionally, they may experience variability in cellular environments encountered, as individual eukaryotic cells can display variation in gene expression among cells. This leads to a dynamic phenotypic landscape that viruses must face to replicate. To examine replication dynamics displayed by viruses faced with this variable landscape, we have developed a method for fitting a stochastic mechanistic model of viral infection to time-lapse imaging data from high-throughput single-cell poliovirus infection experiments. The model's mechanistic parameters provide estimates of several aspects associated with the virus's intracellular dynamics. We examine distributions of parameter estimates and assess their variability to gain insight into the root causes of variability in viral growth dynamics. We also fit our model to experiments performed under various drug treatments and examine which parameters differ under these conditions. We find that parameters associated with translation and early stage viral replication processes are essential for the model to capture experimentally observed dynamics. In aggregate, our results suggest that differences in viral growth data generated under different treatments can largely be captured by steps that occur early in the replication process.
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16
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Gao P, Li Y, Gong J, Huang G. Urban land-use planning under multi-uncertainty and multiobjective considering ecosystem service value and economic benefit - A case study of Guangzhou, China. ECOLOGICAL COMPLEXITY 2021. [DOI: 10.1016/j.ecocom.2020.100886] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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17
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Jackson SE, Vernon I, Liu J, Lindsey K. Understanding hormonal crosstalk in Arabidopsis root development via emulation and history matching. Stat Appl Genet Mol Biol 2020; 19:sagmb-2018-0053. [PMID: 32649296 DOI: 10.1515/sagmb-2018-0053] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2018] [Accepted: 05/12/2020] [Indexed: 11/15/2022]
Abstract
A major challenge in plant developmental biology is to understand how plant growth is coordinated by interacting hormones and genes. To meet this challenge, it is important to not only use experimental data, but also formulate a mathematical model. For the mathematical model to best describe the true biological system, it is necessary to understand the parameter space of the model, along with the links between the model, the parameter space and experimental observations. We develop sequential history matching methodology, using Bayesian emulation, to gain substantial insight into biological model parameter spaces. This is achieved by finding sets of acceptable parameters in accordance with successive sets of physical observations. These methods are then applied to a complex hormonal crosstalk model for Arabidopsis root growth. In this application, we demonstrate how an initial set of 22 observed trends reduce the volume of the set of acceptable inputs to a proportion of 6.1 × 10-7 of the original space. Additional sets of biologically relevant experimental data, each of size 5, reduce the size of this space by a further three and two orders of magnitude respectively. Hence, we provide insight into the constraints placed upon the model structure by, and the biological consequences of, measuring subsets of observations.
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Affiliation(s)
- Samuel E Jackson
- Southampton Statistical Sciences Research Institute, University of Southampton, Southampton, UK
| | - Ian Vernon
- Department of Mathematical Sciences, Durham University, Durham, UK
| | - Junli Liu
- School of Biological and Biomedical Sciences, Durham University, Durham, UK
| | - Keith Lindsey
- School of Biological and Biomedical Sciences, Durham University, Durham, UK
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18
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Engblom S, Eriksson R, Widgren S. Bayesian epidemiological modeling over high-resolution network data. Epidemics 2020; 32:100399. [PMID: 32799071 DOI: 10.1016/j.epidem.2020.100399] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2019] [Revised: 02/06/2020] [Accepted: 06/08/2020] [Indexed: 01/10/2023] Open
Abstract
Mathematical epidemiological models have a broad use, including both qualitative and quantitative applications. With the increasing availability of data, large-scale quantitative disease spread models can nowadays be formulated. Such models have a great potential, e.g., in risk assessments in public health. Their main challenge is model parameterization given surveillance data, a problem which often limits their practical usage. We offer a solution to this problem by developing a Bayesian methodology suitable to epidemiological models driven by network data. The greatest difficulty in obtaining a concentrated parameter posterior is the quality of surveillance data; disease measurements are often scarce and carry little information about the parameters. The often overlooked problem of the model's identifiability therefore needs to be addressed, and we do so using a hierarchy of increasingly realistic known truth experiments. Our proposed Bayesian approach performs convincingly across all our synthetic tests. From pathogen measurements of shiga toxin-producing Escherichia coli O157 in Swedish cattle, we are able to produce an accurate statistical model of first-principles confronted with data. Within this model we explore the potential of a Bayesian public health framework by assessing the efficiency of disease detection and -intervention scenarios.
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Affiliation(s)
- Stefan Engblom
- Division of Scientific Computing, Department of Information Technology, Uppsala University, SE-751 05 Uppsala, Sweden.
| | - Robin Eriksson
- Division of Scientific Computing, Department of Information Technology, Uppsala University, SE-751 05 Uppsala, Sweden.
| | - Stefan Widgren
- Department of Disease Control and Epidemiology, National Veterinary Institute, SE-751 89 Uppsala, Sweden.
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19
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Hazelbag CM, Dushoff J, Dominic EM, Mthombothi ZE, Delva W. Calibration of individual-based models to epidemiological data: A systematic review. PLoS Comput Biol 2020; 16:e1007893. [PMID: 32392252 PMCID: PMC7241852 DOI: 10.1371/journal.pcbi.1007893] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2019] [Revised: 05/21/2020] [Accepted: 04/21/2020] [Indexed: 01/24/2023] Open
Abstract
Individual-based models (IBMs) informing public health policy should be calibrated to data and provide estimates of uncertainty. Two main components of model-calibration methods are the parameter-search strategy and the goodness-of-fit (GOF) measure; many options exist for each of these. This review provides an overview of calibration methods used in IBMs modelling infectious disease spread. We identified articles on PubMed employing simulation-based methods to calibrate IBMs informing public health policy in HIV, tuberculosis, and malaria epidemiology published between 1 January 2013 and 31 December 2018. Articles were included if models stored individual-specific information, and calibration involved comparing model output to population-level targets. We extracted information on parameter-search strategies, GOF measures, and model validation. The PubMed search identified 653 candidate articles, of which 84 met the review criteria. Of the included articles, 40 (48%) combined a quantitative GOF measure with an algorithmic parameter-search strategy–either an optimisation algorithm (14/40) or a sampling algorithm (26/40). These 40 articles varied widely in their choices of parameter-search strategies and GOF measures. For the remaining 44 (52%) articles, the parameter-search strategy could either not be identified (32/44) or was described as an informal, non-reproducible method (12/44). Of these 44 articles, the majority (25/44) were unclear about the GOF measure used; of the rest, only five quantitatively evaluated GOF. Only a minority of the included articles, 14 (17%) provided a rationale for their choice of model-calibration method. Model validation was reported in 31 (37%) articles. Reporting on calibration methods is far from optimal in epidemiological modelling studies of HIV, malaria and TB transmission dynamics. The adoption of better documented, algorithmic calibration methods could improve both reproducibility and the quality of inference in model-based epidemiology. There is a need for research comparing the performance of calibration methods to inform decisions about the parameter-search strategies and GOF measures. Calibration—that is, “fitting” the model to data—is a crucial part of using mathematical models to better forecast and control the population-level spread of infectious diseases. Evidence that the mathematical model is well-calibrated improves confidence that the model provides a realistic picture of the consequences of health policy decisions. To make informed decisions, Policymakers need information about uncertainty: i.e., what is the range of likely outcomes (rather than just a single prediction). Thus, modellers should also strive to provide accurate measurements of uncertainty, both for their model parameters and for their predictions. This systematic review provides an overview of the methods used to calibrate individual-based models (IBMs) of the spread of HIV, malaria, and tuberculosis. We found that less than half of the reviewed articles used reproducible, non-subjective calibration methods. For the remaining articles, the method could either not be identified or was described as an informal, non-reproducible method. Only one-third of the articles obtained estimates of parameter uncertainty. We conclude that the adoption of better-documented, algorithmic calibration methods could improve both reproducibility and the quality of inference in model-based epidemiology.
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Affiliation(s)
- C. Marijn Hazelbag
- South African DSI-NRF Centre of Excellence in Epidemiological Modelling and Analysis (SACEMA), Stellenbosch University, Stellenbosch, South Africa
- * E-mail:
| | - Jonathan Dushoff
- South African DSI-NRF Centre of Excellence in Epidemiological Modelling and Analysis (SACEMA), Stellenbosch University, Stellenbosch, South Africa
- Department of Biology, Department of Mathematics and Statistics, Institute for Infectious Disease Research, McMaster University, Hamilton, Ontario, Canada
| | - Emanuel M. Dominic
- South African DSI-NRF Centre of Excellence in Epidemiological Modelling and Analysis (SACEMA), Stellenbosch University, Stellenbosch, South Africa
| | - Zinhle E. Mthombothi
- South African DSI-NRF Centre of Excellence in Epidemiological Modelling and Analysis (SACEMA), Stellenbosch University, Stellenbosch, South Africa
| | - Wim Delva
- South African DSI-NRF Centre of Excellence in Epidemiological Modelling and Analysis (SACEMA), Stellenbosch University, Stellenbosch, South Africa
- School for Data Science and Computational Thinking, Stellenbosch University, Stellenbosch, South Africa
- Center for Statistics, I-BioStat, Hasselt University, Diepenbeek, Belgium
- Department of Global Health, Faculty of Medicine and Health, Stellenbosch University, Stellenbosch, South Africa
- International Centre for Reproductive Health, Ghent University, Ghent, Belgium
- Rega Institute for Medical Research, KU Leuven, Leuven, Belgium
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20
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Buckwar E, Tamborrino M, Tubikanec I. Spectral density-based and measure-preserving ABC for partially observed diffusion processes. An illustration on Hamiltonian SDEs. STATISTICS AND COMPUTING 2020; 30:627-648. [PMID: 32132771 PMCID: PMC7026277 DOI: 10.1007/s11222-019-09909-6] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2019] [Accepted: 10/17/2019] [Indexed: 05/15/2023]
Abstract
Approximate Bayesian computation (ABC) has become one of the major tools of likelihood-free statistical inference in complex mathematical models. Simultaneously, stochastic differential equations (SDEs) have developed to an established tool for modelling time-dependent, real-world phenomena with underlying random effects. When applying ABC to stochastic models, two major difficulties arise: First, the derivation of effective summary statistics and proper distances is particularly challenging, since simulations from the stochastic process under the same parameter configuration result in different trajectories. Second, exact simulation schemes to generate trajectories from the stochastic model are rarely available, requiring the derivation of suitable numerical methods for the synthetic data generation. To obtain summaries that are less sensitive to the intrinsic stochasticity of the model, we propose to build up the statistical method (e.g. the choice of the summary statistics) on the underlying structural properties of the model. Here, we focus on the existence of an invariant measure and we map the data to their estimated invariant density and invariant spectral density. Then, to ensure that these model properties are kept in the synthetic data generation, we adopt measure-preserving numerical splitting schemes. The derived property-based and measure-preserving ABC method is illustrated on the broad class of partially observed Hamiltonian type SDEs, both with simulated data and with real electroencephalography data. The derived summaries are particularly robust to the model simulation, and this fact, combined with the proposed reliable numerical scheme, yields accurate ABC inference. In contrast, the inference returned using standard numerical methods (Euler-Maruyama discretisation) fails. The proposed ingredients can be incorporated into any type of ABC algorithm and directly applied to all SDEs that are characterised by an invariant distribution and for which a measure-preserving numerical method can be derived.
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Affiliation(s)
- Evelyn Buckwar
- Institute for Stochastics, Johannes Kepler University Linz, Altenberger Straße 69, 4040 Linz, Austria
| | - Massimiliano Tamborrino
- Institute for Stochastics, Johannes Kepler University Linz, Altenberger Straße 69, 4040 Linz, Austria
| | - Irene Tubikanec
- Institute for Stochastics, Johannes Kepler University Linz, Altenberger Straße 69, 4040 Linz, Austria
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21
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Funk S, King AA. Choices and trade-offs in inference with infectious disease models. Epidemics 2019; 30:100383. [PMID: 32007792 DOI: 10.1016/j.epidem.2019.100383] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2019] [Revised: 09/29/2019] [Accepted: 12/11/2019] [Indexed: 12/23/2022] Open
Abstract
Inference using mathematical models of infectious disease dynamics can be an invaluable tool for the interpretation and analysis of epidemiological data. However, researchers wishing to use this tool are faced with a choice of models and model types, simulation methods, inference methods and software packages. Given the multitude of options, it can be challenging to decide on the best approach. Here, we delineate the choices and trade-offs involved in deciding on an approach for inference, and discuss aspects that might inform this decision. We provide examples of inference with a dataset of influenza cases using the R packages pomp and rbi.
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Affiliation(s)
- Sebastian Funk
- Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London WC1E 7HT, UK; Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, London WC1E 7HT, UK
| | - Aaron A King
- Department of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, MI, USA; Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI, USA; Department of Mathematics, University of Michigan, Ann Arbor, MI, USA.
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22
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Rutter CM, Ozik J, DeYoreo M, Collier N. MICROSIMULATION MODEL CALIBRATION USING INCREMENTAL MIXTURE APPROXIMATE BAYESIAN COMPUTATION. Ann Appl Stat 2019; 13:2189-2212. [PMID: 34691351 PMCID: PMC8534811 DOI: 10.1214/19-aoas1279] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/22/2023]
Abstract
Microsimulation models (MSMs) are used to inform policy by predicting population-level outcomes under different scenarios. MSMs simulate individual-level event histories that mark the disease process (such as the development of cancer) and the effect of policy actions (such as screening) on these events. MSMs often have many unknown parameters; calibration is the process of searching the parameter space to select parameters that result in accurate MSM prediction of a wide range of targets. We develop Incremental Mixture Approximate Bayesian Computation (IMABC) for MSM calibration, which results in a simulated sample from the posterior distribution of model parameters given calibration targets. IMABC begins with a rejection-based ABC step, drawing a sample of points from the prior distribution of model parameters and accepting points that result in simulated targets that are near observed targets. Next, the sample is iteratively updated by drawing additional points from a mixture of multivariate normal distributions and accepting points that result in accurate predictions. Posterior estimates are obtained by weighting the final set of accepted points to account for the adaptive sampling scheme. We demonstrate IMABC by calibrating CRC-SPIN 2.0, an updated version of a MSM for colorectal cancer (CRC) that has been used to inform national CRC screening guidelines.
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23
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Truong PN, Stein A. Model-based small area estimation at two scales using Moran's spatial filtering. Spat Spatiotemporal Epidemiol 2019; 31:100303. [PMID: 31677761 DOI: 10.1016/j.sste.2019.100303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 09/08/2018] [Revised: 07/02/2019] [Accepted: 08/06/2019] [Indexed: 11/19/2022]
Abstract
In spatial epidemiology and public health studies, including covariates in small area estimation of spatial binary data remains a challenge. In this paper, Moran's spatial filtering is proposed to model two-scale spatial binary data. Two models are developed: the first uses deterministic estimation of the sample size at small areal level; the second generates a random sample size using the multinomial distribution. The models were applied to estimate the underweight among children at Vietnamese district level using sampling survey data at provincial level. The results show that the first model outperformed the second model regarding its accuracy and simplicity. Eigenvector maps improve model parameter estimation, and allow for the effects of spatial spillover and covariates. Prediction at the district level indicates that many underweight children came from the mountainous areas in 2014. The study concludes that the proposed models serve as alternatives to small area estimation of spatial binary data.
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Affiliation(s)
- Phuong N Truong
- Department of Earth observation science, Faculty of Geo-Information Science and Earth Observation, University of Twente, Enschede, the Netherlands.
| | - Alfred Stein
- Department of Earth observation science, Faculty of Geo-Information Science and Earth Observation, University of Twente, Enschede, the Netherlands
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24
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Minter A, Retkute R. Approximate Bayesian Computation for infectious disease modelling. Epidemics 2019; 29:100368. [PMID: 31563466 DOI: 10.1016/j.epidem.2019.100368] [Citation(s) in RCA: 35] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2019] [Revised: 08/20/2019] [Accepted: 08/30/2019] [Indexed: 12/23/2022] Open
Abstract
Approximate Bayesian Computation (ABC) techniques are a suite of model fitting methods which can be implemented without a using likelihood function. In order to use ABC in a time-efficient manner users must make several design decisions including how to code the ABC algorithm and the type of ABC algorithm to use. Furthermore, ABC relies on a number of user defined choices which can greatly effect the accuracy of estimation. Having a clear understanding of these factors in reducing computation time and improving accuracy allows users to make more informed decisions when planning analyses. In this paper, we present an introduction to ABC with a focus of application to infectious disease models. We present a tutorial on coding practice for ABC in R and three case studies to illustrate the application of ABC to infectious disease models.
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Affiliation(s)
- Amanda Minter
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK.
| | - Renata Retkute
- The Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, University of Warwick, UK
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25
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Kim S, Wong WK. Discussion on Optimal treatment allocations in space and time for on-line control of an emerging infectious disease. J R Stat Soc Ser C Appl Stat 2018. [PMID: 30270943 DOI: 10.1111/rssc.12266] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Seongho Kim
- Biostatistics Core, Karmanos Cancer Institute, Department of Oncology, School of Medicine, Wayne State University, Detroit, MI 48201
| | - Weng Kee Wong
- Department of Biostatistics, UCLA School of Public Health, Los Angeles, CA 90095
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26
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Vernon I, Liu J, Goldstein M, Rowe J, Topping J, Lindsey K. Bayesian uncertainty analysis for complex systems biology models: emulation, global parameter searches and evaluation of gene functions. BMC SYSTEMS BIOLOGY 2018; 12:1. [PMID: 29291750 PMCID: PMC5748965 DOI: 10.1186/s12918-017-0484-3] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/28/2017] [Accepted: 11/09/2017] [Indexed: 11/26/2022]
Abstract
Background Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time relative to the needs of the analysis, and need to be compared to observed data of various forms. The correct analysis of such models usually requires a global parameter search, over a high dimensional parameter space, that incorporates and respects the most important sources of uncertainty. This can be an extremely difficult task, but it is essential for any meaningful inference or prediction to be made about any biological system. It hence represents a fundamental challenge for the whole of systems biology. Methods Bayesian statistical methodology for the uncertainty analysis of complex models is introduced, which is designed to address the high dimensional global parameter search problem. Bayesian emulators that mimic the systems biology model but which are extremely fast to evaluate are embeded within an iterative history match: an efficient method to search high dimensional spaces within a more formal statistical setting, while incorporating major sources of uncertainty. Results The approach is demonstrated via application to a model of hormonal crosstalk in Arabidopsis root development, which has 32 rate parameters, for which we identify the sets of rate parameter values that lead to acceptable matches between model output and observed trend data. The multiple insights into the model’s structure that this analysis provides are discussed. The methodology is applied to a second related model, and the biological consequences of the resulting comparison, including the evaluation of gene functions, are described. Conclusions Bayesian uncertainty analysis for complex models using both emulators and history matching is shown to be a powerful technique that can greatly aid the study of a large class of systems biology models. It both provides insight into model behaviour and identifies the sets of rate parameters of interest. Electronic supplementary material The online version of this article (doi:10.1186/s12918-017-0484-3) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Ian Vernon
- Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, UK.
| | - Junli Liu
- Department of Biosciences, Durham University, South Road, Durham, DH1 3LE, UK.
| | - Michael Goldstein
- Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, UK
| | - James Rowe
- Department of Biosciences, Durham University, South Road, Durham, DH1 3LE, UK.,Current address: Department of Molecular Biology and Biotechnology, University of Sheffield, Firth Court, Western Bank, Sheffield, S10 2TN, UK
| | - Jen Topping
- Department of Biosciences, Durham University, South Road, Durham, DH1 3LE, UK
| | - Keith Lindsey
- Department of Biosciences, Durham University, South Road, Durham, DH1 3LE, UK
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