Practical considerations for measuring the effective reproductive number, Rt

PLoS Computational Biology, vol. 16, pp. e1008409

Abstract

Estimation of the effective reproductive number Rt is important for detecting changes in disease transmission over time. During the Coronavirus Disease 2019 (COVID-19) pandemic, policy makers and public health officials are using Rt to assess the effectiveness of interventions and to inform policy. However, estimation of Rt from available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make recommendations. For near real-time estimation of Rt, we recommend the approach of Cori and colleagues, which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t, such as Wallinga and Teunis, are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to the spread. We advise caution when using methods derived from the approach of Bettencourt and Ribeiro, as the resulting Rt estimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems in Rt estimation.

Authors 25

1. Katelyn M. Gostic corresponding

   University of Chicago

   Affiliation as printed

   Department of Ecology and Evolution, University of Chicago, Chicago, IL, United States of America

2. Lauren McGough

   University of Chicago

   Affiliation as printed

   Department of Ecology and Evolution, University of Chicago, Chicago, IL, United States of America

3. Edward B. Baskerville

   University of Chicago

   Affiliation as printed

   Department of Ecology and Evolution, University of Chicago, Chicago, IL, United States of America

4. Sam Abbott

   London School of Hygiene & Tropical Medicine

   Affiliation as printed

   Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom

5. Keya Joshi

   Harvard University

   Affiliation as printed

   Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America

6. Christine Tedijanto

   Harvard University

   Affiliation as printed

   Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America

7. Rebecca J. Kahn

   Harvard University

   Affiliation as printed

   Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America

8. René Niehus

   Harvard University

   Affiliation as printed

   Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America

9. James A. Hay

   Harvard University

   Affiliation as printed

   Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America

10. Pablo M. De Salazar

    Harvard University

    Affiliation as printed

    Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America

11. Joel Hellewell

    London School of Hygiene & Tropical Medicine

    Affiliation as printed

    Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom

12. Sophie R. Meakin

    London School of Hygiene & Tropical Medicine

    Affiliation as printed

    Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom

13. James D Munday

    London School of Hygiene & Tropical Medicine

    Affiliation as printed

    Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom

14. Nikos I Bosse

    London School of Hygiene & Tropical Medicine

    Affiliation as printed

    Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom

15. Katharine Sherrat

    London School of Hygiene & Tropical Medicine

    Affiliation as printed

    Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom

16. Robin N. Thompson

    University of Oxford · London School of Hygiene & Tropical Medicine

    Affiliation as printed

    Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom

    Mathematical Institute, University of Oxford, Oxford, United Kingdom

17. Laura Forsberg White

    Boston University

    Affiliation as printed

    Department of Biostatistics, Boston University School of Public Health, Boston, MA, United States of America

18. Jana S. Huisman

    ETH Zurich

    Affiliation as printed

    Department of Biosystems Science and Engineering, ETH Zürich, Switzerland

    Department of Environmental Systems Science, ETH Zürich, Zürich, Switzerland

19. Jérémie Scire

    SIB Swiss Institute of Bioinformatics · ETH Zurich

    Affiliation as printed

    Department of Biosystems Science and Engineering, ETH Zürich, Switzerland

    Swiss Institute of Bioinformatics, Basel, Switzerland

20. Sebastian Bonhoeffer

    ETH Zurich

    Affiliation as printed

    Department of Environmental Systems Science, ETH Zürich, Zürich, Switzerland

21. Tanja Stadler

    SIB Swiss Institute of Bioinformatics · ETH Zurich

    Affiliation as printed

    Department of Biosystems Science and Engineering, ETH Zürich, Switzerland

    Swiss Institute of Bioinformatics, Basel, Switzerland

22. Jacco Wallinga Aachen Department of Biomedical Data Sciences

    Leiden University · Leiden University Medical Center · National Institute for Public Health and the Environment

    Affiliation as printed

    Centre for Infectious Disease Control, National Institute for Public Health and the Environment, Bilthoven, the Netherlands

    Department of Biomedical Data Sciences, Leiden University Medical Centre, Leiden, the Netherlands

23. Sebastian Funk

    London School of Hygiene & Tropical Medicine

    Affiliation as printed

    Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom

24. Marc Lipsitch

    Harvard University

    Affiliation as printed

    Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America

25. Sarah E. Cobey

    University of Chicago

    Affiliation as printed

    Department of Ecology and Evolution, University of Chicago, Chicago, IL, United States of America