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Why are different estimates of the effective reproductive number so different? A case study on COVID-19 in Germany

Author

Listed:
  • Elisabeth K Brockhaus
  • Daniel Wolffram
  • Tanja Stadler
  • Michael Osthege
  • Tanmay Mitra
  • Jonas M Littek
  • Ekaterina Krymova
  • Anna J Klesen
  • Jana S Huisman
  • Stefan Heyder
  • Laura M Helleckes
  • Matthias an der Heiden
  • Sebastian Funk
  • Sam Abbott
  • Johannes Bracher

Abstract

The effective reproductive number Rt has taken a central role in the scientific, political, and public discussion during the COVID-19 pandemic, with numerous real-time estimates of this quantity routinely published. Disagreement between estimates can be substantial and may lead to confusion among decision-makers and the general public. In this work, we compare different estimates of the national-level effective reproductive number of COVID-19 in Germany in 2020 and 2021. We consider the agreement between estimates from the same method but published at different time points (within-method agreement) as well as retrospective agreement across eight different approaches (between-method agreement). Concerning the former, estimates from some methods are very stable over time and hardly subject to revisions, while others display considerable fluctuations. To evaluate between-method agreement, we reproduce the estimates generated by different groups using a variety of statistical approaches, standardizing analytical choices to assess how they contribute to the observed disagreement. These analytical choices include the data source, data pre-processing, assumed generation time distribution, statistical tuning parameters, and various delay distributions. We find that in practice, these auxiliary choices in the estimation of Rt may affect results at least as strongly as the selection of the statistical approach. They should thus be communicated transparently along with the estimates.Author summary: The effective reproductive number describes how many new infections an individual infected with a given disease causes on average in a population which is subject to a certain degree of immunity and intervention measures. Public health agencies and researchers commonly attempt to keep track of its value over time using various data sources and statistical methods. In this work we compare estimates produced by different research groups in a case study on COVID-19 in Germany. We find pronounced differences between different estimates and shed light on how these are shaped by varying analytical choices. Our results indicate that the employed statistical method has some influence on results, but surrounding analytical choices including epidemiological parameterizations and tuning parameter choices are at least as influential. As estimates are subject to regular updates, we moreover assess how strongly real-time estimates based on different methods were revised retrospectively. While for some methods hardly any retrospective changes occurred, for others there were strong revisions, often incoherent with the uncertainty intervals provided for previous estimates. Our results will be helpful for analysts aiming to set up estimation schemes for the effective reproductive number, and for users confronted with a multitude of potentially disagreeing estimates.

Suggested Citation

  • Elisabeth K Brockhaus & Daniel Wolffram & Tanja Stadler & Michael Osthege & Tanmay Mitra & Jonas M Littek & Ekaterina Krymova & Anna J Klesen & Jana S Huisman & Stefan Heyder & Laura M Helleckes & Mat, 2023. "Why are different estimates of the effective reproductive number so different? A case study on COVID-19 in Germany," PLOS Computational Biology, Public Library of Science, vol. 19(11), pages 1-27, November.
    • Handle: RePEc:plo:pcbi00:1011653
    DOI: 10.1371/journal.pcbi.1011653
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    References listed on IDEAS

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    1. 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.
    2. Eric-Jan Wagenmakers & Alexandra Sarafoglou & Balazs Aczel, 2022. "One statistical analysis must not rule them all," Nature, Nature, vol. 605(7910), pages 423-425, May.
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