Correcting the Reproduction Number for Time-Varying Tests: a Proposal and an Application to COVID-19 in France*

Abstract

We show that the acceleration index, a novel indicator that measures acceleration and deceleration of viral spread (Baunez et al. 2020a,b), is essentially a test-controlled version of the reproduction number. As such it is a more accurate indicator to track the dynamics of an infectious disease outbreak in real time. We indicate a discrepancy between the acceleration index and the reproduction number, based on the infectivity and test rates and we provide a formal decomposition of this difference. When applied to French data for the ongoing COVID-19 pandemic, our decomposition shows that the reproduction number consistently underestimates the resurgence of the pandemic since the summer of 2020, compared to the acceleration index which accounts for the time-varying volume of tests. From the comparison that we present here follows that the acceleration index is a sufficient statistic to track the pandemic's propagation, as it captures in real time the sizeable time variation featured by viral circulation.

Tracking the dynamics and allocating tests for COVID-19 in real-time: An acceleration index with an application to French age groups and départements

“…Because the latter does not control for time-varying amounts of tests while our acceleration index does, it would be informative to relate both indicators, both in theory and in practice. Although this issue is not addressed here, in [9] we report a proper comparative analysis. An additional limitation of the acceleration index is that it compares the daily positive rate to the average positivity rate, which summarizes the entire "past" in the sense that it uses all available date since the outset of the pandemic.…”

“…From the acceleration index and average positivity rate then follows the daily positivity rate, which is still useful to translate the transmission dynamics back into levels (as opposed to normalized ratios). In [9], we relate the acceleration index to the reproduction number that is a core concept in the epidemiological literature. We show that the former is a more accurate measure of the pandemic's dynamics than the latter.…”

Are Epidemiological Indicators Misleading under Uncertainty? An Evaluation and a Remedy from An Economic Perspective

“…Moreover, and as importantly, the reproduction number is, again, not adjusted by the testing rate. With no clear testing strategy, known cases will not represent the true extent of the epidemic outbreak and consequently, even the reproduction number will be a biased measure of viral activity (Baunez et al 2020b), upward as well as downward in principle. Hence, public policies that aim at curbing the pandemic and proclaim as aim to push the reproduction number below 1 or to achieve an incidence rate at a particular number are certainly achieving something, but given biased measurements of what is happening in real time, they may not get what they want.…”