{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T02:03:39Z","timestamp":1790215419862,"version":"4.1.0"},"reference-count":56,"publisher":"Oxford University Press (OUP)","license":[{"start":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T00:00:00Z","timestamp":1783468800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Estimating, understanding, and communicating uncertainty is fundamental to statistical epidemiology, where model-based estimates regularly inform real-world decisions. However, sources of uncertainty are rarely formalised, and existing classifications are often inconsistent. This lack of structure hampers interpretation, model comparison, and targeted data collection. Connecting ideas from machine learning, information theory, experimental design, and health economics, we present a first-principles decision-theoretic framework that defines uncertainty as the expected loss incurred by making an estimate using incomplete information, arguing that this is a practically relevant definition for epidemiology. We show how reasoning about future data leads to a notion of expected uncertainty reduction, which induces formal definitions of reducible and irreducible uncertainty. We illustrate our approach with a simple worked example and a case study of SARS-CoV-2 wastewater surveillance in Aotearoa New Zealand, estimating the uncertainty reduction if wastewater surveillance were expanded to the full population. We then connect our framework to relevant literature from adjacent fields, showing how it unifies and extends many of these ideas. Our article serves as a gateway for applying a wide range of approaches to epidemiological models. Altogether, our framework provides a foundation for more reliable, consistent, and policy-relevant uncertainty quantification in infectious disease epidemiology.<\/jats:p>","DOI":"10.1093\/aje\/kwag154","type":"journal-article","created":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T06:44:57Z","timestamp":1783493097000},"source":"Crossref","is-referenced-by-count":0,"title":["A decision-theoretic framework for uncertainty quantification in epidemiological modelling"],"prefix":"10.1093","author":[{"given":"Nicholas","family":"Steyn","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Oxford , Oxford, OX1 3LB ,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cathal","family":"Mills","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Oxford , Oxford, OX1 3LB ,","place":["United Kingdom"]},{"name":"Pandemic Sciences Institute, University of Oxford , Oxford, OX3 7DQ ,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vik","family":"Shirvaikar","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Oxford , Oxford, OX1 3LB ,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Freddie","family":"Bickford Smith","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Oxford , Oxford, OX1 3LB ,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0195-2463","authenticated-orcid":false,"given":"Christl A","family":"Donnelly","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Oxford , Oxford, OX1 3LB ,","place":["United Kingdom"]},{"name":"Pandemic Sciences Institute, University of Oxford , Oxford, OX3 7DQ ,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kris V","family":"Parag","sequence":"additional","affiliation":[{"name":"Department of Engineering, King\u2019s College London , London, WC2R 2LS ,","place":["United Kingdom"]},{"name":"MRC Centre for Global Infectious Disease Analysis, Imperial College London , London, W12 0BZ ,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,7,8]]},"reference":[{"issue":"2","key":"2026092321213363900_ref1","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1111\/1467-9868.00177","article-title":"Statistical studies of infectious disease incidence","volume":"61","author":"Becker","year":"1999","journal-title":"J R Stat Soc Series B Stat Methodol"},{"key":"2026092321213363900_ref2","doi-asserted-by":"publisher","first-page":"100784","DOI":"10.1016\/j.epidem.2024.100784","article-title":"Inference of epidemic dynamics in the COVID-19 era and beyond","volume":"48","author":"Cori","year":"2024","journal-title":"Epidemics"},{"key":"2026092321213363900_ref3","doi-asserted-by":"publisher","first-page":"100520","DOI":"10.1016\/j.epidem.2021.100520","article-title":"Communicating uncertainty in epidemic models","volume":"37","author":"McCabe","year":"2021","journal-title":"Epidemics"},{"key":"2026092321213363900_ref4","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/978-90-481-2313-1_6","article-title":"Sensitivity of model-based epidemiological parameter estimation to model assumptions","volume-title":"Mathematical and Statistical Estimation Approaches in Epidemiology","author":"Lloyd","year":"2009"},{"issue":"1932","key":"2026092321213363900_ref5","doi-asserted-by":"publisher","first-page":"20201405","DOI":"10.1098\/rspb.2020.1405","article-title":"Key questions for modelling COVID-19 exit strategies","volume":"287","author":"Thompson","year":"2020","journal-title":"Proc R Soc B Biol Sci"},{"issue":"3","key":"2026092321213363900_ref6","doi-asserted-by":"publisher","first-page":"102329","DOI":"10.1016\/j.ttbdis.2024.102329","article-title":"Adapting vector surveillance using Bayesian experimental design: an application to an ongoing tick monitoring program in the southeastern United States","volume":"15","author":"Case","year":"2024","journal-title":"Ticks Tick-borne Dis"},{"key":"2026092321213363900_ref7","doi-asserted-by":"publisher","DOI":"10.1101\/2025.07.20.25331802","article-title":"From metric to action: an evaluation framework to translate infectious disease forecasts into policy decisions","author":"Mills","year":"2025"},{"issue":"4","key":"2026092321213363900_ref8","doi-asserted-by":"publisher","first-page":"e2012704118","DOI":"10.1073\/pnas.2012704118","article-title":"Rational policymaking during a pandemic","volume":"118","author":"Berger","year":"2021","journal-title":"Proc Natl Acad Sci"},{"key":"2026092321213363900_ref9","first-page":"4345","article-title":"Rethinking aleatoric and epistemic uncertainty","author":"Bickford Smith","year":"2025","journal-title":"Proceedings of the 42nd International Conference on Machine Learning"},{"issue":"7","key":"2026092321213363900_ref10","doi-asserted-by":"publisher","first-page":"1377","DOI":"10.1093\/aje\/kwab013","article-title":"Quantifying uncertainty in mechanistic models of infectious disease","volume":"190","author":"D\u2019Agostino McGowan","year":"2021","journal-title":"Am J Epidemiol"},{"issue":"8","key":"2026092321213363900_ref11","doi-asserted-by":"publisher","first-page":"100310","DOI":"10.1016\/j.patter.2021.100310","article-title":"Accounting for uncertainty during a pandemic","volume":"2","author":"Zelner","year":"2021","journal-title":"Patterns"},{"key":"2026092321213363900_ref12","doi-asserted-by":"publisher","first-page":"100547","DOI":"10.1016\/j.epidem.2022.100547","article-title":"Challenges in estimation, uncertainty quantification and elicitation for pandemic modelling","volume":"38","author":"Swallow","year":"2022","journal-title":"Epidemics"},{"issue":"5","key":"2026092321213363900_ref13","doi-asserted-by":"publisher","first-page":"1357","DOI":"10.1093\/jrsssb\/qkad005","article-title":"Martingale posterior distributions","volume":"85","author":"Fong","year":"2023","journal-title":"J R Stat Soc Ser B Stat Methodol"},{"key":"2026092321213363900_ref14","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/10187.001.0001","volume-title":"Decision Making Under Uncertainty: Theory and Application","author":"Kochenderfer","year":"2015"},{"issue":"9","key":"2026092321213363900_ref15","doi-asserted-by":"publisher","first-page":"584","DOI":"10.1038\/s43588-022-00313-1","article-title":"Quantifying the information in noisy epidemic curves","volume":"2","author":"Parag","year":"2022","journal-title":"Nat Comput Sci"},{"issue":"4","key":"2026092321213363900_ref16","doi-asserted-by":"publisher","first-page":"986","DOI":"10.1214\/aoms\/1177728069","article-title":"On a measure of the information provided by an experiment","volume":"27","author":"Lindley","year":"1956","journal-title":"Ann Math Stat"},{"issue":"528","key":"2026092321213363900_ref17","doi-asserted-by":"publisher","first-page":"1436","DOI":"10.1080\/01621459.2018.1562932","article-title":"Value of information: sensitivity analysis and research design in Bayesian evidence synthesis","volume":"114","author":"Jackson","year":"2019","journal-title":"J Am Stat Assoc"},{"issue":"1","key":"2026092321213363900_ref18","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1146\/annurev-statistics-040120-010730","article-title":"Value of information analysis in models to inform health policy","volume":"9","author":"Jackson","year":"2022","journal-title":"Annu Rev Stat Appl"},{"key":"2026092321213363900_ref19","doi-asserted-by":"publisher","DOI":"10.1201\/9781003156109","article-title":"Value of Information for Healthcare Decision Making","volume-title":"Biostatistics Series","author":"Heath","year":"2024"},{"issue":"1","key":"2026092321213363900_ref20","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1111\/insr.12107","article-title":"A review of modern computational algorithms for Bayesian optimal design","volume":"84","author":"Ryan","year":"2016","journal-title":"Int Stat Rev"},{"issue":"1","key":"2026092321213363900_ref21","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/j.idm.2024.10.005","article-title":"Information-guided adaptive learning approach for active surveillance of infectious diseases","volume":"10","author":"Tan","year":"2025","journal-title":"Infect Dis Model"},{"key":"2026092321213363900_ref22","doi-asserted-by":"publisher","first-page":"w20445","DOI":"10.4414\/smw.2020.20445","article-title":"Optimal allocation of limited test resources for the quantification of COVID-19 infections","volume":"150","author":"Chatzimanolakis","year":"2020","journal-title":"Swiss Med Wkly"},{"key":"2026092321213363900_ref23","article-title":"Evaluating forecasts with scoringutils in R","author":"Bosse","year":"2024"},{"issue":"9","key":"2026092321213363900_ref24","doi-asserted-by":"publisher","first-page":"1505","DOI":"10.1093\/aje\/kwt133","article-title":"A new framework and software to estimate time-varying reproduction numbers during epidemics","volume":"178","author":"Cori","year":"2013","journal-title":"Am J Epidemiol"},{"issue":"452","key":"2026092321213363900_ref25","doi-asserted-by":"publisher","first-page":"1340","DOI":"10.1080\/01621459.2000.10474344","article-title":"Conditioning, likelihood, and coherence: a review of some foundational concepts","volume":"95","author":"Robins","year":"2000","journal-title":"J Am Stat Assoc"},{"key":"2026092321213363900_ref26","article-title":"The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation","volume-title":"Springer Texts in Statistics","author":"Robert","year":"2007"},{"issue":"2","key":"2026092321213363900_ref27","doi-asserted-by":"publisher","first-page":"278","DOI":"10.2307\/2981683","article-title":"Present position and potential developments: some personal views: statistical theory: the prequential approach","volume":"147","author":"Dawid","year":"1984","journal-title":"J R Stat Soc Ser A"},{"issue":"1","key":"2026092321213363900_ref28","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1214\/24-STS965","article-title":"Exchangeability, prediction and predictive modeling in Bayesian statistics","volume":"40","author":"Fortini","year":"2025","journal-title":"Stat Sci"},{"issue":"477","key":"2026092321213363900_ref29","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1198\/016214506000001437","article-title":"Strictly proper scoring rules, prediction, and estimation","volume":"102","author":"Gneiting","year":"2007","journal-title":"J Am Stat Assoc"},{"key":"2026092321213363900_ref30","article-title":"The Elements of Statistical Learning: Data Mining, Inference, and Prediction","volume-title":"Springer Series in Statistics","author":"Hastie","year":"2009"},{"key":"2026092321213363900_ref31","volume-title":"Decision Analysis: Introductory Lectures on Choices Under Uncertainty","author":"Raiffa","year":"1968"},{"issue":"2","key":"2026092321213363900_ref32","doi-asserted-by":"publisher","first-page":"404","DOI":"10.1214\/aoms\/1177704567","article-title":"Uncertainty, information, and sequential experiments","volume":"33","author":"DeGroot","year":"1962","journal-title":"Ann Math Stat"},{"key":"2026092321213363900_ref33","article-title":"Coherent Measures of Discrepancy, Uncertainty and Dependence, with Applications to Bayesian Predictive Experimental Design","author":"Dawid","year":"1998"},{"key":"2026092321213363900_ref34","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1146\/annurev-statistics-032921-020240","article-title":"Model diagnostics and forecast evaluation for quantiles","author":"Gneiting","year":"2023","journal-title":"Annual Review of Statistics and Its Application 10"},{"issue":"1","key":"2026092321213363900_ref35","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s42005-023-01265-2","article-title":"Intrinsic randomness in epidemic modelling beyond statistical uncertainty","volume":"6","author":"Penn","year":"2023","journal-title":"Commun Phys"},{"issue":"5","key":"2026092321213363900_ref36","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1111\/rssb.12158","article-title":"A general framework for updating belief distributions","volume":"78","author":"Bissiri","year":"2016","journal-title":"J R Stat Soc Series B Stat Methodol"},{"key":"2026092321213363900_ref37","article-title":"New (and old) predictive schemes with a.c.i.d. sequences","author":"Battiston","year":"2025"},{"issue":"10","key":"2026092321213363900_ref38","doi-asserted-by":"publisher","first-page":"pgae438","DOI":"10.1093\/pnasnexus\/pgae438","article-title":"The utility of wastewater surveillance for monitoring SARS-CoV-2 prevalence","volume":"3","author":"Mills","year":"2024","journal-title":"PNAS Nexus"},{"issue":"1","key":"2026092321213363900_ref39","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s43856-024-00570-3","article-title":"Jointly estimating epidemiological dynamics of Covid-19 from case and wastewater data in Aotearoa New Zealand","volume":"4","author":"Watson","year":"2024","journal-title":"Commun Med"},{"key":"2026092321213363900_ref40","doi-asserted-by":"publisher","first-page":"153290","DOI":"10.1016\/j.scitotenv.2022.153290","article-title":"Factors influencing SARS-CoV-2 RNA concentrations in wastewater up to the sampling stage: a systematic review","volume":"820","author":"Bertels","year":"2022","journal-title":"Sci Total Environ"},{"issue":"1","key":"2026092321213363900_ref41","doi-asserted-by":"publisher","first-page":"20210012","DOI":"10.1515\/em-2021-0012","article-title":"A guide to value of information methods for prioritising research in health impact modelling","volume":"10","author":"Jackson","year":"2021","journal-title":"Epidemiologic Methods"},{"issue":"2","key":"2026092321213363900_ref42","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/j.jval.2020.01.001","article-title":"Value of information analysis for research decisions\u2014an introduction: report 1 of the ISPOR value of information analysis emerging good practices task force","volume":"23","author":"Fenwick","year":"2020","journal-title":"Value Health"},{"key":"2026092321213363900_ref43","article-title":"Applied statistical decision theory","volume-title":"Wiley Classics Library, Wiley Classics","author":"Raiffa","year":"1961"},{"issue":"1","key":"2026092321213363900_ref44","doi-asserted-by":"publisher","DOI":"10.1214\/23-STS915","article-title":"Modern Bayesian experimental design","volume":"39","author":"Rainforth","year":"2024","journal-title":"Stat Sci"},{"key":"2026092321213363900_ref45","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2305.00933","article-title":"A comparison of short-term probabilistic forecasts for the incidence of COVID-19 using mechanistic and statistical time series models","author":"Banholzer","year":"2023"},{"issue":"11","key":"2026092321213363900_ref46","doi-asserted-by":"publisher","first-page":"3355","DOI":"10.1093\/aje\/kwaf165","article-title":"Robust uncertainty quantification in popular estimators of the instantaneous reproduction number","volume":"194","author":"Steyn","year":"2025","journal-title":"Am J Epidemiol"},{"issue":"suppl 4","key":"2026092321213363900_ref47","doi-asserted-by":"publisher","first-page":"S404","DOI":"10.1093\/infdis\/jiw375","article-title":"Epidemic forecasting is messier than weather forecasting: the role of human behavior and internet data streams in epidemic forecast","volume":"214","author":"Moran","year":"2016","journal-title":"J Infect Dis"},{"issue":"9","key":"2026092321213363900_ref48","doi-asserted-by":"crossref","first-page":"e1013426","DOI":"10.1371\/journal.pcbi.1013426","article-title":"Optimal algorithms for controlling infectious diseases in real time using noisy infection data","volume":"21","author":"Beregi","year":"2025","journal-title":"PLoS Comput Biol"},{"key":"2026092321213363900_ref49","volume-title":"Prediction-Powered Machine Learning for Model Selection and Uncertainty","author":"Shirvaikar","year":"2025"},{"issue":"4","key":"2026092321213363900_ref50","doi-asserted-by":"publisher","first-page":"662","DOI":"10.1177\/0272989X11406986","article-title":"A framework for addressing structural uncertainty in decision models","volume":"31","author":"Jackson","year":"2011","journal-title":"Med Decis Making"},{"issue":"4","key":"2026092321213363900_ref51","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1009212519","article-title":"Bayesian model averaging: a tutorial with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors","volume":"14","author":"Hoeting","year":"1999","journal-title":"Stat Sci"},{"issue":"3","key":"2026092321213363900_ref52","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1111\/1467-9868.00294","article-title":"Bayesian calibration of computer models","volume":"63","author":"Kennedy","year":"2001","journal-title":"J R Stat Soc Series B Stat Methodol"},{"key":"2026092321213363900_ref53","article-title":"Neural density estimation and likelihood-free inference","author":"Papamakarios G","year":"2019"},{"issue":"1","key":"2026092321213363900_ref54","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1186\/s12913-023-09479-4","article-title":"Value of information analysis for pandemic response: intensive care unit preparedness at the onset of COVID-19","volume":"23","author":"Eze","year":"2023","journal-title":"BMC Health Serv Res"},{"issue":"Supplement_1","key":"2026092321213363900_ref55","doi-asserted-by":"publisher","first-page":"S5","DOI":"10.1111\/rssa.12867","article-title":"Are epidemic growth rates more informative than reproduction numbers?","volume":"185","author":"Parag","year":"2022","journal-title":"J R Stat Soc Ser A Stat Soc"},{"issue":"9","key":"2026092321213363900_ref56","doi-asserted-by":"crossref","first-page":"e1009347","DOI":"10.1371\/journal.pcbi.1009347","article-title":"Improved estimation of time-varying reproduction numbers at low case incidence and between epidemic waves","volume":"17","author":"Parag","year":"2021","journal-title":"PLoS Comput Biol"}],"container-title":["American Journal of Epidemiology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/aje\/advance-article-pdf\/doi\/10.1093\/aje\/kwag154\/68716662\/kwag154.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/aje\/advance-article-pdf\/doi\/10.1093\/aje\/kwag154\/68716662\/kwag154.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T01:21:41Z","timestamp":1790212901000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/aje\/advance-article\/doi\/10.1093\/aje\/kwag154\/8728046"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,8]]},"references-count":56,"URL":"https:\/\/doi.org\/10.1093\/aje\/kwag154","relation":{},"ISSN":["0002-9262","1476-6256"],"issn-type":[{"value":"0002-9262","type":"print"},{"value":"1476-6256","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,8]]},"article-number":"kwag154"}}