Estimation of Reproduction Numbers in Real Time: Conceptual and Statistical Challenges

Abstract

The reproduction number 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, 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 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 JUNIPER Consortium (https://maths.org/juniper/)

Are Epidemic Growth Rates More Informative than Reproduction Numbers?

“…However, their relative merits and demerits have been increasingly debated (see Pellis, Birrell, et al (2021) and Jewell and Lewnard (2021) of this issue for example). Recent work has suggested that the benefits of inferring might have been underappreciated, and that this quantity may be particularly useful because of its apparent independence from modelling assumptions and its explicit consideration of the epidemic speed (i.e.…”

“…Consequently, the instantaneous epidemic growth rate, , defined as the rate of change of the log‐transformed case incidence, has been proposed as a more informative and understandable measure of transmission dynamics (Pellis, Birrell, et al, 2021). Growth rates may be estimated directly from the gradient of the log‐transformed observed incidence curve, have a natural temporal interpretation as the speed of case accumulation and still encode key dynamics, for example, the signs of and signify similar transmission trends.…”

Genomic monitoring of SARS‐CoV‐2 variants using sentinel SARI hospital surveillance

“…We defined the epidemic growth phase of a VOC as the period for which the exponential increase of its weekly reported proportion (%) is a constant during at least 4 weeks in the BGS, which was calculated using a linear regression curve. [42][43][44] The slope value a of the linear regression curve (equation format y = ax + b) within that time window represents the relationship between the detection levels (%) of each VOC in relation with time, and thus provides a measure of how quickly a VOC is growing. The R 2 value was used as a measure of the quality of the linear regression curve for the used dataset.…”

Discussion of Presidential Address: Statistics in Times of Increasing Uncertainty by Sylvia Richardson

“…In the specific context of a pandemic, quantifying transmission dynamics, for example by estimating headline summaries such as the effective reproduction number R t (see Pellis et al, 2022) was of key interest to public health officials. At some point, such summaries were discussed daily.…”