Differences between the true reproduction number and the apparent reproduction number of an epidemic time series
The time-varying reproduction number R(t) measures the number of new infections per infectious individual and is closely correlated with the time series of infection incidence by definition. The timings of actual infections are rarely known, and analysis of epidemics usually relies on time series da...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-03-01
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| Series: | Epidemics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1755436524000033 |
| _version_ | 1827321767098580992 |
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| author | Oliver Eales Steven Riley |
| author_facet | Oliver Eales Steven Riley |
| author_sort | Oliver Eales |
| collection | DOAJ |
| description | The time-varying reproduction number R(t) measures the number of new infections per infectious individual and is closely correlated with the time series of infection incidence by definition. The timings of actual infections are rarely known, and analysis of epidemics usually relies on time series data for other outcomes such as symptom onset. A common implicit assumption, when estimating R(t) from an epidemic time series, is that R(t) has the same relationship with these downstream outcomes as it does with the time series of incidence. However, this assumption is unlikely to be valid given that most epidemic time series are not perfect proxies of incidence. Rather they represent convolutions of incidence with uncertain delay distributions. Here we define the apparent time-varying reproduction number, RA(t), the reproduction number calculated from a downstream epidemic time series and demonstrate how differences between RA(t) and R(t) depend on the convolution function. The mean of the convolution function sets a time offset between the two signals, whilst the variance of the convolution function introduces a relative distortion between them. We present the convolution functions of epidemic time series that were available during the SARS-CoV-2 pandemic. Infection prevalence, measured by random sampling studies, presents fewer biases than other epidemic time series. Here we show that additionally the mean and variance of its convolution function were similar to that obtained from traditional surveillance based on mass-testing and could be reduced using more frequent testing, or by using stricter thresholds for positivity. Infection prevalence studies continue to be a versatile tool for tracking the temporal trends of R(t), and with additional refinements to their study protocol, will be of even greater utility during any future epidemics or pandemics. |
| first_indexed | 2024-03-08T13:50:32Z |
| format | Article |
| id | doaj.art-af2a749e43b143bb825e2fc75b56d628 |
| institution | Directory Open Access Journal |
| issn | 1755-4365 |
| language | English |
| last_indexed | 2024-04-25T01:12:50Z |
| publishDate | 2024-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Epidemics |
| spelling | doaj.art-af2a749e43b143bb825e2fc75b56d6282024-03-10T05:11:35ZengElsevierEpidemics1755-43652024-03-0146100742Differences between the true reproduction number and the apparent reproduction number of an epidemic time seriesOliver Eales0Steven Riley1Infectious Disease Dynamics Unit, Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, The University of Melbourne, Melbourne, Australia; School of Public Health, Imperial College London, London, United Kingdom; MRC Centre for Global infectious Disease Analysis, Imperial College London, London, United Kingdom; Abdul Latif Jameel Institute for Disease and Emergency Analytics, Imperial College London, London, United Kingdom; Corresponding author at: Infectious Disease Dynamics Unit, Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, The University of Melbourne, Melbourne, Australia.School of Public Health, Imperial College London, London, United Kingdom; MRC Centre for Global infectious Disease Analysis, Imperial College London, London, United Kingdom; Abdul Latif Jameel Institute for Disease and Emergency Analytics, Imperial College London, London, United KingdomThe time-varying reproduction number R(t) measures the number of new infections per infectious individual and is closely correlated with the time series of infection incidence by definition. The timings of actual infections are rarely known, and analysis of epidemics usually relies on time series data for other outcomes such as symptom onset. A common implicit assumption, when estimating R(t) from an epidemic time series, is that R(t) has the same relationship with these downstream outcomes as it does with the time series of incidence. However, this assumption is unlikely to be valid given that most epidemic time series are not perfect proxies of incidence. Rather they represent convolutions of incidence with uncertain delay distributions. Here we define the apparent time-varying reproduction number, RA(t), the reproduction number calculated from a downstream epidemic time series and demonstrate how differences between RA(t) and R(t) depend on the convolution function. The mean of the convolution function sets a time offset between the two signals, whilst the variance of the convolution function introduces a relative distortion between them. We present the convolution functions of epidemic time series that were available during the SARS-CoV-2 pandemic. Infection prevalence, measured by random sampling studies, presents fewer biases than other epidemic time series. Here we show that additionally the mean and variance of its convolution function were similar to that obtained from traditional surveillance based on mass-testing and could be reduced using more frequent testing, or by using stricter thresholds for positivity. Infection prevalence studies continue to be a versatile tool for tracking the temporal trends of R(t), and with additional refinements to their study protocol, will be of even greater utility during any future epidemics or pandemics.http://www.sciencedirect.com/science/article/pii/S1755436524000033Reproduction numberEpidemicsSARS-CoV-2PandemicsCOVID-19Infection prevalence |
| spellingShingle | Oliver Eales Steven Riley Differences between the true reproduction number and the apparent reproduction number of an epidemic time series Epidemics Reproduction number Epidemics SARS-CoV-2 Pandemics COVID-19 Infection prevalence |
| title | Differences between the true reproduction number and the apparent reproduction number of an epidemic time series |
| title_full | Differences between the true reproduction number and the apparent reproduction number of an epidemic time series |
| title_fullStr | Differences between the true reproduction number and the apparent reproduction number of an epidemic time series |
| title_full_unstemmed | Differences between the true reproduction number and the apparent reproduction number of an epidemic time series |
| title_short | Differences between the true reproduction number and the apparent reproduction number of an epidemic time series |
| title_sort | differences between the true reproduction number and the apparent reproduction number of an epidemic time series |
| topic | Reproduction number Epidemics SARS-CoV-2 Pandemics COVID-19 Infection prevalence |
| url | http://www.sciencedirect.com/science/article/pii/S1755436524000033 |
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