The replication number, or R0, describes the average number of transmissions from a single individual in a population with no immunity. It can only be calculated for coronavirus disease 2019 (COVID-19) in populations before vaccinations, widespread infections, or social distancing measures, leading to a limited window for datasets. The estimated R0 varies greatly, with results ranging from 1.95 to 6.49. Researchers from the University of Wurzburg in Germany have been attempting to create a new method for determining the R0 using excess mortality data.
Study: Estimation of R0 for the spread of SARS-CoV-2 in Germany from Excess Mortality. Image Credit: ffikretow/ Shutterstock
A preprint version of the group’s study is available on the medRxiv* server, while the article undergoes peer review.
The researchers used the German Robert Koch Institute (RKI) website to determine the number of cases, deaths, and PCR tests. Excess deaths were calculated from the data from the Federal Statistical Office, while Apple provided mobility data. To calculate the aforementioned excess deaths, weekly deaths in 2020 were subtracted from the mean of weekly deaths in the three previous years.
R0 was calculated using a freely available R package, using an exponential growth method and simulating the mean serial interval with a gamma distribution equal to 4.7. Weekly incidence of excess mortality was converted to daily incidences where necessary, again using gamma distribution. Only data up to and including March 15th, 2020, could be used, as after this point, many Germans had begun social distancing, even before official guidelines were put into place. Of course, by the time these were removed, immunity was far more common in the population.
The scientists fitted epidemiological datasets provided RKI to gamma distributions and determined the differences between the peaks of the curves. This revealed that the mean time between the occurrence of disease and death was 25 days. This allowed the researchers to use cases that resulted in death up to April 11th in their analysis. As very few tests were performed before March 15th, this allowed a significant increase in statistical power.
From raw incidence data, the initial R0 obtained for disease cases and deaths was 2.56/2.03, respectively. These needed to be corrected for the growth rate of testing, resulting in lower values, with an R0 of 1.86 for disease and 1.47 for deaths. This is significantly lower than many other estimates, and the RKI assumes an R0 in the range of 2.8-3.8. However, many different estimates have been put forward, and an initial estimate in Wuhan showed the R0 at 2.2. The researchers propose that similar to the Wuhan estimates, the limited testing in the initial phase of the pandemic was biased towards the most severely ill, which will result in many estimates tending higher than reality.
The new method used in this study does remain uncertain. The exact number of tests performed in the first weeks is unknown. The incidence data comes almost entirely from individuals who needed hospitalization, or were in situations where cases could be confirmed - such as nursing homes. These areas also tended to show higher transmission rates than the rest of the country. The scientists attribute some differences in infection numbers to these factors and admit that their R0 is unlikely to be representative.
To resolve this issue, they attempted to calculate R0 based on excess mortality data, as the German government collects data on all deaths, and this information is independent of testing. They obtained an R0 of 1.34 across all age groups for the spread of SARS-CoV-2 in Germany. While this method of testing does avoid some of the confounding factors seen in the previous method, influenza mortality may have affected the results - and it could be very difficult to tell, as influenza and COVID-19 mortality are superimposed in total death sets.
The researchers argue that their study shows that R0 can be calculated from excess mortality data and argue for a seasonally adjusted R0 value. They claim that the low range of R0 values is more consistent with observations of the pandemic than many of the earlier estimates. However, with case fatalities in most countries lower than 3%, this method of calculating the R0 is likely to have significantly lower statistical power than many others. Nevertheless, this should provide another valuable tool for epidemiologists and could help provide more accurate information in future pandemics.
medRxiv publishes preliminary scientific reports that are not peer-reviewed and, therefore, should not be regarded as conclusive, guide clinical practice/health-related behavior, or treated as established information