Robust uncertainty quantification in popular estimators of the instantaneous reproduction number
File(s)
Published version
Author(s)
Steyn, Nicholas
Parag, Kris V
Type
Journal Article
Abstract
The instantaneous reproduction number () is a key measure of the rate of spread of an infectious disease. Correctly quantifying uncertainty in estimates is crucial for making well-informed decisions. Popular estimators leverage smoothing techniques to distinguish signal from noise. Examples include EpiEstim and EpiFilter, which are both controlled by a “smoothing parameter” that is traditionally selected by users. We demonstrate that the values of these smoothing parameters are unknown, vary markedly with epidemic dynamics, and show that data-driven smoothing is crucial for accurate uncertainty quantification of real-time estimates. We derive novel model likelihoods for the smoothing parameters in both EpiEstim and EpiFilter and develop a Bayesian framework to automatically marginalise these parameters when fitting to epidemiological time-series data. This yields marginal posterior predictive distributions which prove integral to rigorous model evaluation. Applying our methods, we find that default parameterisations of these widely-used estimators can negatively impact inference, delaying detection of epidemic growth, and misrepresenting uncertainty (typically producing overconfident estimates), with implications for public health decision-making. Our extensions mitigate these issues, provide a principled approach to uncertainty quantification, improve the robustness of real-time inference, and facilitate model comparison using observable quantities.
Date Issued
2025-11-01
Date Acceptance
2025-07-23
Citation
American Journal of Epidemiology, 2025, 194 (11), pp.3355-3363
ISSN
0002-9262
Publisher
Oxford University Press (OUP)
Start Page
3355
End Page
3363
Journal / Book Title
American Journal of Epidemiology
Volume
194
Issue
11
Copyright Statement
© The Author(s) 2025. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
License URL
Publication Status
Published
Article Number
kwaf165
Date Publish Online
2025-08-04