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Estimation of reproduction numbers in real time: Conceptual and statistical challenges

Author

Listed:
  • Lorenzo Pellis
  • Paul J. Birrell
  • Joshua Blake
  • Christopher E. Overton
  • Francesca Scarabel
  • Helena B. Stage
  • Ellen Brooks‐Pollock
  • Leon Danon
  • Ian Hall
  • Thomas A. House
  • Matt J. Keeling
  • Jonathan M. Read
  • JUNIPER Consortium
  • Daniela De Angelis

Abstract

The reproduction number R$$ R $$ has been a central metric of the COVID‐19 pandemic response, published weekly by the UK government and regularly reported in the media. Here, we provide a formal definition and discuss the advantages and most common misconceptions around this quantity. We consider the intuition behind different formulations of R$$ R $$, the complexities in its estimation (including the unavoidable lags involved), and its value compared to other indicators (e.g. the growth rate) that can be directly observed from aggregate surveillance data and react more promptly to changes in epidemic trend. As models become more sophisticated, with age and/or spatial structure, formulating R$$ R $$ becomes increasingly complicated and inevitably model‐dependent. We present some models currently used in the UK pandemic response as examples. Ultimately, limitations in the available data streams, data quality and time constraints force pragmatic choices to be made on a quantity that is an average across time, space, social structure and settings. Effectively communicating these challenges is important but often difficult in an emergency.

Suggested Citation

  • Lorenzo Pellis & Paul J. Birrell & Joshua Blake & Christopher E. Overton & Francesca Scarabel & Helena B. Stage & Ellen Brooks‐Pollock & Leon Danon & Ian Hall & Thomas A. House & Matt J. Keeling & Jon, 2022. "Estimation of reproduction numbers in real time: Conceptual and statistical challenges," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S1), pages 112-130, November.
    • Handle: RePEc:bla:jorssa:v:185:y:2022:i:s1:p:s112-s130
    DOI: 10.1111/rssa.12955
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    References listed on IDEAS

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    1. Helen J Wearing & Pejman Rohani & Matt J Keeling, 2005. "Appropriate Models for the Management of Infectious Diseases," PLOS Medicine, Public Library of Science, vol. 2(7), pages 1-1, July.
    2. Katelyn M Gostic & Lauren McGough & Edward B Baskerville & Sam Abbott & Keya Joshi & Christine Tedijanto & Rebecca Kahn & Rene Niehus & James A Hay & Pablo M De Salazar & Joel Hellewell & Sophie Meaki, 2020. "Practical considerations for measuring the effective reproductive number, Rt," PLOS Computational Biology, Public Library of Science, vol. 16(12), pages 1-21, December.
    3. Kris V. Parag & Robin N. Thompson & Christl A. Donnelly, 2022. "Are epidemic growth rates more informative than reproduction numbers?," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S1), pages 5-15, November.
    4. Joël Mossong & Niel Hens & Mark Jit & Philippe Beutels & Kari Auranen & Rafael Mikolajczyk & Marco Massari & Stefania Salmaso & Gianpaolo Scalia Tomba & Jacco Wallinga & Janneke Heijne & Malgorzata Sa, 2008. "Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases," PLOS Medicine, Public Library of Science, vol. 5(3), pages 1-1, March.
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    Cited by:

    1. Sylvia Richardson, 2022. "Statistics in times of increasing uncertainty," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1471-1496, October.

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