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Uncertainty and inconsistency of COVID-19 non-pharmaceutical intervention effects with multiple competitive statistical models
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  • Published: 19 January 2026

Uncertainty and inconsistency of COVID-19 non-pharmaceutical intervention effects with multiple competitive statistical models

  • Bernhard Müller1,
  • Inken Padberg2,
  • Michael Lorke3,
  • Ralph Brinks4,
  • Sally Cripps5,
  • M. Gabriela M. Gomes6,7,
  • Daniel Haake8 &
  • …
  • John P. A. Ioannidis9 

Scientific Reports , Article number:  (2026) Cite this article

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We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Communication and replication
  • Epidemiology
  • Statistics

Abstract

Quantifying the effect of non-pharmaceutical interventions (NPIs) is essential for formulating lessons from the COVID-19 pandemic. To enable a more reliable and rigorous evaluation of NPIs based on time series data, we reanalyse the official evaluation of NPIs in Germany. As the first part of a multi-step validation and verification project, we focus on properly analysing statistical uncertainties for time series data. Using a set of 9 competitive statistical methods for estimating the effects of NPIs and other determinants of disease spread on the effective reproduction number \(\mathcal {R}(t)\), we find significantly wider confidence intervals than the official evaluation. In addition to vaccination and seasonality, only few NPIs – such as restrictions in public spaces – can be confidently associated with variations in \(\mathcal {R}(t)\), but even then effect sizes have large uncertainties. Furthermore, due to multicollinearity in NPI activation patterns, it is difficult to distinguish potential effects of NPIs in public spaces from other interventions that came into force early, such as physical distancing. In future, NPIs should be more carefully designed and accompanied by plans for data collections to allow for a timely evaluation of benefits and harms as a basis for an effective and proportionate response.

Data availability

Our Python code is freely available on Zenodo (https://doi.org/10.5281/zenodo.14761068). The code utilises processed data from the original StopptCOVID project [23], which in turn uses NPI data from infas (https://datenkatalog.infas360.de/dataset/cdp), which are freely available after registration. Our code repository contains instructions to download the required third-party data and code to generate the requisite input data for our analysis.

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Acknowledgements

We thank M. an der Heiden and V. Bremer for answering technical questions on the original StopptCOVID project. We acknowledge helpful discussions with W. Baumgarten, O. Beige, G. Meyer, I. Mühlhauser, D. Schuricht, and T. Wieland. We are grateful to the German Network for Evidence-Based Medicine, the German Society for Epidemiology and the German Reproducibility Network for help in distributing the project call.

Author information

Authors and Affiliations

  1. School of Physics and Astronomy, Monash University, Clayton, VIC, 3800, Australia

    Bernhard Müller

  2. Epidemiology Unit, German Rheumatism Research Centre (DRFZ), Charitéplatz 1, 10117, Berlin, Germany

    Inken Padberg

  3. Faculty of Physics, University of Duisburg-Essen, Duisburg, 47057, Germany

    Michael Lorke

  4. Chair for Medical Biometry and Epidemiology, Witten/Herdecke University, Faculty of Health/School of Medicine, D-58448, Witten, Germany

    Ralph Brinks

  5. Human Technology Institute (HTI), University of Technology Sydney, Sydney, NSW, Australia

    Sally Cripps

  6. Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK

    M. Gabriela M. Gomes

  7. NOVA School of Science and Technology, Centre for Mathematics and Applications (NOVA MATH), Caparica, Portugal

    M. Gabriela M. Gomes

  8. Independent Researcher, Potsdam, D-14469, Germany

    Daniel Haake

  9. Departments of Medicine, of Epidemiology and Population Health, and of Biomedical Data Science, and Meta-Research Innovation Center at Stanford (METRICS), Stanford University, 3180 Porter Dr, Room A129, Stanford Research Park, Palo Alto, CA, 94304, USA

    John P. A. Ioannidis

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Contributions

B.M.: Conceptualisation, Project Management, Software, Formal analysis, Visualisation, Writing - Original draft, Review and Editing. I.P.: Conceptualisation, Procedures, Literature Review, Writing - Original draft, Review and Editing. ML: Conceptualisation, Code checks (models DK and Ebisuzaki), Writing - Review. R.B.: Conceptualisation, Writing - Review and Editing. S.C.: Conceptualisation, Writing - Review and Editing. M.G.M.M.: Conceptualisation, Writing - Review. D.H.: Conceptualisation, Writing - Review and Editing. J.P.A.I.: Conceptualisation, Writing - Review and Editing.

Corresponding author

Correspondence to Bernhard Müller.

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Ethical approval

This study did not involve research on humans or animals, and only used publicly available, non-personal data sets.

Competing interests

B.M., I.P., M.L., and R.B. are signatories of a call for a non-partisan pandemic review in Germany (https://pandemieaufarbeitung.net). B.M. has been engaged in discussion and consultation of pandemic policy and science policy with members of several German parties (CDU, CSU, FDP, SPD, BSW, Greens), but is not receiving remuneration. S.C., M.G.M.G., D.H., and J.P.A.I. have no competing interests to declare.

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Müller, B., Padberg, I., Lorke, M. et al. Uncertainty and inconsistency of COVID-19 non-pharmaceutical intervention effects with multiple competitive statistical models. Sci Rep (2026). https://doi.org/10.1038/s41598-026-36265-z

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  • Received: 13 June 2025

  • Accepted: 12 January 2026

  • Published: 19 January 2026

  • DOI: https://doi.org/10.1038/s41598-026-36265-z

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