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The biology of the process is encoded by the structure and parameters of the model that can be inferred statistically by fitting to viral load data. The main drawback of mechanistic models is that this inference is computationally expensive because the model must be repeatedly solved. This limits the size of the datasets that can be considered or the complexity of the models fitted. In this paper we develop a much cheaper inference method for this class of models by implementing a novel approximation of the model dynamics that uses a combination of random and deterministic processes. This approximation also properly accounts for process noise early in the infection when cell and virion numbers are small, which is important for the viral dynamics but often overlooked. Our method runs on a consumer laptop and is fast enough to facilitate a full hierarchical Bayesian treatment of the problem with sharing of information to allow for individual level parameter differences. We apply our method to simulated datasets and a reanalysis of COVID-19 monitoring data in an National Basketball Association cohort of 163 individuals.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1013775","type":"journal-article","created":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T19:03:48Z","timestamp":1764875028000},"page":"e1013775","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Random time-shift approximation enables hierarchical Bayesian inference of mechanistic within-host viral dynamics models on large datasets"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7890-1501","authenticated-orcid":true,"given":"Dylan J.","family":"Morris","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lauren","family":"Kennedy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3299-4866","authenticated-orcid":true,"given":"Andrew J.","family":"Black","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2025,12,4]]},"reference":[{"issue":"1","key":"pcbi.1013775.ref001","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1038\/nri700","article-title":"Modelling viral and immune system dynamics","volume":"2","author":"AS Perelson","year":"2002","journal-title":"Nat Rev Immunol."},{"issue":"15","key":"pcbi.1013775.ref002","doi-asserted-by":"crossref","first-page":"7590","DOI":"10.1128\/JVI.01623-05","article-title":"Kinetics of influenza A virus infection in humans","volume":"80","author":"P Baccam","year":"2006","journal-title":"J Virol."},{"issue":"5","key":"pcbi.1013775.ref003","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1007\/s10928-014-9363-3","article-title":"Viral kinetic modeling: State of the art","volume":"41","author":"L Canini","year":"2014","journal-title":"J Pharmacokinet Pharmacodyn."},{"issue":"7","key":"pcbi.1013775.ref004","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pbio.3001333","article-title":"Viral dynamics of acute SARS-CoV-2 infection and applications to diagnostic and public health strategies","volume":"19","author":"SM Kissler","year":"2021","journal-title":"PLoS Biol."},{"issue":"4","key":"pcbi.1013775.ref005","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1011437","article-title":"How robust are estimates of key parameters in standard viral dynamic models?","volume":"20","author":"C Zitzmann","year":"2024","journal-title":"PLoS Comput Biol."},{"issue":"26","key":"pcbi.1013775.ref006","doi-asserted-by":"crossref","first-page":"2489","DOI":"10.1056\/NEJMc2102507","article-title":"Viral dynamics of SARS-CoV-2 variants in vaccinated and unvaccinated persons","volume":"385","author":"SM Kissler","year":"2021","journal-title":"N Engl J Med."},{"key":"pcbi.1013775.ref007","doi-asserted-by":"crossref","first-page":"102780","DOI":"10.1016\/j.simpat.2023.102780","article-title":"A review of multilevel modeling and simulation for human mobility and behavior","volume":"127","author":"L Serena","year":"2023","journal-title":"Simul Modell Pract Theory."},{"issue":"5","key":"pcbi.1013775.ref008","doi-asserted-by":"crossref","first-page":"640","DOI":"10.1038\/s41564-022-01105-z","article-title":"Daily longitudinal sampling of SARS-CoV-2 infection reveals substantial heterogeneity in infectiousness","volume":"7","author":"R Ke","year":"2022","journal-title":"Nat Microbiol."},{"issue":"8","key":"pcbi.1013775.ref009","doi-asserted-by":"crossref","DOI":"10.1073\/pnas.2017962118","article-title":"Modeling SARS-CoV-2 viral kinetics and association with mortality in hospitalized patients from the French COVID cohort","volume":"118","author":"N N\u00e9ant","year":"2021","journal-title":"Proc Natl Acad Sci U S A."},{"issue":"2","key":"pcbi.1013775.ref010","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0263597","article-title":"Test-trace-isolate-quarantine (TTIQ) intervention strategies after symptomatic COVID-19 case identification","volume":"17","author":"P Ashcroft","year":"2022","journal-title":"PLoS One."},{"issue":"1","key":"pcbi.1013775.ref011","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1186\/s12916-021-02220-0","article-title":"Modelling upper respiratory viral load dynamics of SARS-CoV-2","volume":"20","author":"JD Challenger","year":"2022","journal-title":"BMC Med."},{"issue":"49","key":"pcbi.1013775.ref012","article-title":"In vivo kinetics of SARS-CoV-2 infection and its relationship with a person\u2019s infectiousness","volume":"118","author":"R Ke","year":"2021","journal-title":"Proc Natl Acad Sci U S A."},{"key":"pcbi.1013775.ref013","doi-asserted-by":"crossref","unstructured":"Ciupe SM, Heffernan JM. 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