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Liu J, Cai Z, Gustafson P, McDonald DJ. rtestim: Time-varying reproduction number estimation with trend filtering. PLoS Comput Biol 2024; 20:e1012324. [PMID: 39106282 PMCID: PMC11329163 DOI: 10.1371/journal.pcbi.1012324] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2023] [Revised: 08/16/2024] [Accepted: 07/15/2024] [Indexed: 08/09/2024] Open
Abstract
To understand the transmissibility and spread of infectious diseases, epidemiologists turn to estimates of the instantaneous reproduction number. While many estimation approaches exist, their utility may be limited. Challenges of surveillance data collection, model assumptions that are unverifiable with data alone, and computationally inefficient frameworks are critical limitations for many existing approaches. We propose a discrete spline-based approach that solves a convex optimization problem-Poisson trend filtering-using the proximal Newton method. It produces a locally adaptive estimator for instantaneous reproduction number estimation with heterogeneous smoothness. Our methodology remains accurate even under some process misspecifications and is computationally efficient, even for large-scale data. The implementation is easily accessible in a lightweight R package rtestim.
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Affiliation(s)
- Jiaping Liu
- Department of Statistics, The University of British Columbia, Vancouver, British Columbia, Canada
| | - Zhenglun Cai
- Centre for Health Evaluation and Outcome Sciences, The University of British Columbia, Vancouver, British Columbia, Canada
| | - Paul Gustafson
- Department of Statistics, The University of British Columbia, Vancouver, British Columbia, Canada
| | - Daniel J McDonald
- Department of Statistics, The University of British Columbia, Vancouver, British Columbia, Canada
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Sumalinab B, Gressani O, Hens N, Faes C. An Efficient Approach to Nowcasting the Time-varying Reproduction Number. Epidemiology 2024; 35:512-516. [PMID: 38788149 PMCID: PMC11191556 DOI: 10.1097/ede.0000000000001744] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 03/26/2024] [Indexed: 05/26/2024]
Abstract
Estimating the instantaneous reproduction number ( ) in near real time is crucial for monitoring and responding to epidemic outbreaks on a daily basis. However, such estimates often suffer from bias due to reporting delays inherent in surveillance systems. We propose a fast and flexible Bayesian methodology to overcome this challenge by estimating while taking into account reporting delays. Furthermore, the method naturally takes into account the uncertainty associated with the nowcasting of cases to get a valid uncertainty estimation of the nowcasted reproduction number. We evaluate the proposed methodology through a simulation study and apply it to COVID-19 incidence data in Belgium.
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Affiliation(s)
- Bryan Sumalinab
- From the Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat), Data Science Institute (DSI), Hasselt University, Hasselt, Belgium
- Department of Mathematics and Statistics, College of Science and Mathematics, Mindanao State University - Iligan Institute of Technology, Iligan City, Philippines
| | - Oswaldo Gressani
- From the Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat), Data Science Institute (DSI), Hasselt University, Hasselt, Belgium
| | - Niel Hens
- From the Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat), Data Science Institute (DSI), Hasselt University, Hasselt, Belgium
- Centre for Health Economics Research and Modelling Infectious Diseases (CHERMID), Vaccine & Infectious Disease Institute, Antwerp University, Antwerp, Belgium
| | - Christel Faes
- From the Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat), Data Science Institute (DSI), Hasselt University, Hasselt, Belgium
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Bokányi E, Vizi Z, Koltai J, Röst G, Karsai M. Real-time estimation of the effective reproduction number of COVID-19 from behavioral data. Sci Rep 2023; 13:21452. [PMID: 38052841 PMCID: PMC10698193 DOI: 10.1038/s41598-023-46418-z] [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: 01/27/2023] [Accepted: 10/31/2023] [Indexed: 12/07/2023] Open
Abstract
Monitoring the effective reproduction number [Formula: see text] of a rapidly unfolding pandemic in real-time is key to successful mitigation and prevention strategies. However, existing methods based on case numbers, hospital admissions or fatalities suffer from multiple measurement biases and temporal lags due to high test positivity rates or delays in symptom development or administrative reporting. Alternative methods such as web search and social media tracking are less directly indicating epidemic prevalence over time. We instead record age-stratified anonymous contact matrices at a daily resolution using a longitudinal online-offline survey in Hungary during the first two waves of the COVID-19 pandemic. This approach is innovative, cheap, and provides information in near real-time for estimating [Formula: see text] at a daily resolution. Moreover, it allows to complement traditional surveillance systems by signaling periods when official monitoring infrastructures are unreliable due to observational biases.
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Affiliation(s)
- Eszter Bokányi
- Institute of Logic, Language and Computation, University of Amsterdam, 1090GE, Amsterdam, The Netherlands
| | - Zsolt Vizi
- National Laboratory for Health Security, University of Szeged, Szeged, 6720, Hungary
| | - Júlia Koltai
- National Laboratory for Health Security, Centre for Social Sciences, Budapest, 1097, Hungary
- Faculty of Social Sciences, Eötvös Loránd University, Budapest, 1117, Hungary
| | - Gergely Röst
- National Laboratory for Health Security, University of Szeged, Szeged, 6720, Hungary
| | - Márton Karsai
- Department of Network and Data Science, Central European University, 1100, Vienna, Austria.
- National Laboratory for Health Security, Alfréd Rényi Institute of Mathematics, Budapest, 1053, Hungary.
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Li K, Wang J, Xie J, Rui J, Abudunaibi B, Wei H, Liu H, Zhang S, Li Q, Niu Y, Chen T. Advancements in Defining and Estimating the Reproduction Number in Infectious Disease Epidemiology. China CDC Wkly 2023; 5:829-834. [PMID: 37814634 PMCID: PMC10560332 DOI: 10.46234/ccdcw2023.158] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Accepted: 09/11/2023] [Indexed: 10/11/2023] Open
Affiliation(s)
- Kangguo Li
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Jiayi Wang
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Jiayuan Xie
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Jia Rui
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Buasiyamu Abudunaibi
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Hongjie Wei
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Hong Liu
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Shuo Zhang
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
| | - Qun Li
- Chinese Center for Disease Control and Prevention, Beijing, China
| | - Yan Niu
- Chinese Center for Disease Control and Prevention, Beijing, China
| | - Tianmu Chen
- State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, National Innovation Platform for Industry-Education Integration in Vaccine Research, Xiamen University, Xiamen City, Fujian Province, China
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Nash RK, Bhatt S, Cori A, Nouvellet P. Estimating the epidemic reproduction number from temporally aggregated incidence data: A statistical modelling approach and software tool. PLoS Comput Biol 2023; 19:e1011439. [PMID: 37639484 PMCID: PMC10491397 DOI: 10.1371/journal.pcbi.1011439] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2022] [Revised: 09/08/2023] [Accepted: 08/18/2023] [Indexed: 08/31/2023] Open
Abstract
The time-varying reproduction number (Rt) is an important measure of epidemic transmissibility that directly informs policy decisions and the optimisation of control measures. EpiEstim is a widely used opensource software tool that uses case incidence and the serial interval (SI, time between symptoms in a case and their infector) to estimate Rt in real-time. The incidence and the SI distribution must be provided at the same temporal resolution, which can limit the applicability of EpiEstim and other similar methods, e.g. for contexts where the time window of incidence reporting is longer than the mean SI. In the EpiEstim R package, we implement an expectation-maximisation algorithm to reconstruct daily incidence from temporally aggregated data, from which Rt can then be estimated. We assess the validity of our method using an extensive simulation study and apply it to COVID-19 and influenza data. For all datasets, the influence of intra-weekly variability in reported data was mitigated by using aggregated weekly data. Rt estimated on weekly sliding windows using incidence reconstructed from weekly data was strongly correlated with estimates from the original daily data. The simulation study revealed that Rt was well estimated in all scenarios and regardless of the temporal aggregation of the data. In the presence of weekend effects, Rt estimates from reconstructed data were more successful at recovering the true value of Rt than those obtained from reported daily data. These results show that this novel method allows Rt to be successfully recovered from aggregated data using a simple approach with very few data requirements. Additionally, by removing administrative noise when daily incidence data are reconstructed, the accuracy of Rt estimates can be improved.
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Affiliation(s)
- Rebecca K. Nash
- MRC Centre for Global Infectious Disease Analysis, Jameel Institute, School of Public Health, Imperial College London, London, United Kingdom
| | - Samir Bhatt
- MRC Centre for Global Infectious Disease Analysis, Jameel Institute, School of Public Health, Imperial College London, London, United Kingdom
- Section of Epidemiology, Department of Public Health, University of Copenhagen, Copenhagen, Denmark
| | - Anne Cori
- MRC Centre for Global Infectious Disease Analysis, Jameel Institute, School of Public Health, Imperial College London, London, United Kingdom
| | - Pierre Nouvellet
- MRC Centre for Global Infectious Disease Analysis, Jameel Institute, School of Public Health, Imperial College London, London, United Kingdom
- School of Life Sciences, University of Sussex, Brighton, United Kingdom
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Loedy N, Coletti P, Wambua J, Hermans L, Willem L, Jarvis CI, Wong KLM, Edmunds W, Robert A, Leclerc QJ, Gimma A, Molenberghs G, Beutels P, Faes C, Hens N. Longitudinal social contact data analysis: insights from 2 years of data collection in Belgium during the COVID-19 pandemic. BMC Public Health 2023; 23:1298. [PMID: 37415096 PMCID: PMC10326964 DOI: 10.1186/s12889-023-16193-7] [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: 12/21/2022] [Accepted: 06/26/2023] [Indexed: 07/08/2023] Open
Abstract
BACKGROUND During the COVID-19 pandemic, the CoMix study, a longitudinal behavioral survey, was designed to monitor social contacts and public awareness in multiple countries, including Belgium. As a longitudinal survey, it is vulnerable to participants' "survey fatigue", which may impact inferences. METHODS A negative binomial generalized additive model for location, scale, and shape (NBI GAMLSS) was adopted to estimate the number of contacts reported between age groups and to deal with under-reporting due to fatigue within the study. The dropout process was analyzed with first-order auto-regressive logistic regression to identify factors that influence dropout. Using the so-called next generation principle, we calculated the effect of under-reporting due to fatigue on estimating the reproduction number. RESULTS Fewer contacts were reported as people participated longer in the survey, which suggests under-reporting due to survey fatigue. Participant dropout is significantly affected by household size and age categories, but not significantly affected by the number of contacts reported in any of the two latest waves. This indicates covariate-dependent missing completely at random (MCAR) in the dropout pattern, when missing at random (MAR) is the alternative. However, we cannot rule out more complex mechanisms such as missing not at random (MNAR). Moreover, under-reporting due to fatigue is found to be consistent over time and implies a 15-30% reduction in both the number of contacts and the reproduction number ([Formula: see text]) ratio between correcting and not correcting for under-reporting. Lastly, we found that correcting for fatigue did not change the pattern of relative incidence between age groups also when considering age-specific heterogeneity in susceptibility and infectivity. CONCLUSIONS CoMix data highlights the variability of contact patterns across age groups and time, revealing the mechanisms governing the spread/transmission of COVID-19/airborne diseases in the population. Although such longitudinal contact surveys are prone to the under-reporting due to participant fatigue and drop-out, we showed that these factors can be identified and corrected using NBI GAMLSS. This information can be used to improve the design of similar, future surveys.
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Affiliation(s)
- Neilshan Loedy
- Data Science Institute, I-BioStat, Hasselt University, Hasselt, Belgium
| | - Pietro Coletti
- Data Science Institute, I-BioStat, Hasselt University, Hasselt, Belgium
| | - James Wambua
- Data Science Institute, I-BioStat, Hasselt University, Hasselt, Belgium
| | - Lisa Hermans
- Data Science Institute, I-BioStat, Hasselt University, Hasselt, Belgium
| | - Lander Willem
- Centre for Health Economics Research and Modelling Infectious Diseases, Vaccine & Infectious Disease Institute, University of Antwerp, Antwerp, Belgium
| | - Christopher I. Jarvis
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, Faculty of Epidemiology & Population Health, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Kerry L. M. Wong
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, Faculty of Epidemiology & Population Health, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - W. John Edmunds
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, Faculty of Epidemiology & Population Health, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Alexis Robert
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, Faculty of Epidemiology & Population Health, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Quentin J. Leclerc
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, Faculty of Epidemiology & Population Health, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Department of Infectious Disease Epidemiology, Faculty of Epidemiology and Public Health, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Epidemiology and Modelling of Bacterial Escape to Antimicrobials, Institut Pasteur, Paris, France
| | - Amy Gimma
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, Faculty of Epidemiology & Population Health, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Geert Molenberghs
- Data Science Institute, I-BioStat, Hasselt University, Hasselt, Belgium
- L-BioStat, Department of Public Health and Primary Care, Faculty of Medicine, KU Leuven, Leuven, Belgium
| | - Philippe Beutels
- Centre for Health Economics Research and Modelling Infectious Diseases, Vaccine & Infectious Disease Institute, University of Antwerp, Antwerp, Belgium
- School of Public Health and Community Medicine, The University of New South Wales, Sydney, Australia
| | - Christel Faes
- Data Science Institute, I-BioStat, Hasselt University, Hasselt, Belgium
| | - Niel Hens
- Data Science Institute, I-BioStat, Hasselt University, Hasselt, Belgium
- Centre for Health Economics Research and Modelling Infectious Diseases, Vaccine & Infectious Disease Institute, University of Antwerp, Antwerp, Belgium
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Gressani O, Faes C, Hens N. An approximate Bayesian approach for estimation of the instantaneous reproduction number under misreported epidemic data. Biom J 2023:e2200024. [PMID: 36639234 DOI: 10.1002/bimj.202200024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2022] [Revised: 11/04/2022] [Accepted: 11/18/2022] [Indexed: 01/15/2023]
Abstract
In epidemic models, the effective reproduction number is of central importance to assess the transmission dynamics of an infectious disease and to orient health intervention strategies. Publicly shared data during an outbreak often suffers from two sources of misreporting (underreporting and delay in reporting) that should not be overlooked when estimating epidemiological parameters. The main statistical challenge in models that intrinsically account for a misreporting process lies in the joint estimation of the time-varying reproduction number and the delay/underreporting parameters. Existing Bayesian approaches typically rely on Markov chain Monte Carlo algorithms that are extremely costly from a computational perspective. We propose a much faster alternative based on Laplacian-P-splines (LPS) that combines Bayesian penalized B-splines for flexible and smooth estimation of the instantaneous reproduction number and Laplace approximations to selected posterior distributions for fast computation. Assuming a known generation interval distribution, the incidence at a given calendar time is governed by the epidemic renewal equation and the delay structure is specified through a composite link framework. Laplace approximations to the conditional posterior of the spline vector are obtained from analytical versions of the gradient and Hessian of the log-likelihood, implying a drastic speed-up in the computation of posterior estimates. Furthermore, the proposed LPS approach can be used to obtain point estimates and approximate credible intervals for the delay and reporting probabilities. Simulation of epidemics with different combinations for the underreporting rate and delay structure (one-day, two-day, and weekend delays) show that the proposed LPS methodology delivers fast and accurate estimates outperforming existing methods that do not take into account underreporting and delay patterns. Finally, LPS is illustrated in two real case studies of epidemic outbreaks.
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Affiliation(s)
- Oswaldo Gressani
- Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat), Data Science Institute, Hasselt University, Hasselt, Belgium
| | - Christel Faes
- Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat), Data Science Institute, Hasselt University, Hasselt, Belgium
| | - Niel Hens
- Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat), Data Science Institute, Hasselt University, Hasselt, Belgium.,Centre for Health Economics Research and Modelling Infectious Diseases, Vaxinfectio, University of Antwerp, Antwerp, Belgium
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