Robust estimation of the time-dependent reproduction number in the presence of weekend reporting effects

During infectious disease outbreaks, changes in pathogen transmissibility are assessed through real-time inference of metrics such as the time-dependent reproduction number (R_t), which can be estimated from disease incidence data. However, such data are often subject to a "day-of-the-week effect" (DOWE), whereby the number of cases on certain days of the week is liable to being under-reported (due to administrative delays) or over-reported (as public health authorities "catch-up" on reporting delayed cases). For example, cases occurring at weekends may only be reported during the following week, leading to under-reporting at weekends and over-reporting on weekdays (a weekend reporting effect; WRE).

We analyse simulated datasets, as well as case reports from San Francisco recorded during the 1918 influenza pandemic. We investigate the impacts of WREs on R_t estimates obtained using two approaches: i) the Cori method (a frequently applied method for estimating R_t from daily disease incidence time series data); ii) an alternative method, involving aggregating the daily incidence data into weekly values to remove the WRE and applying a previous method (the OG1 method) for inferring R_t from weekly data.

Our analyses indicate that R_t estimates obtained from standard approaches such as the Cori method can be affected negatively by WREs. In contrast, since weekly aggregation of daily data can eliminate WREs, the alternative approach generates robust R_t estimates in the presence of WREs. When aggregating the daily data into weekly values, some information is lost. However, in many scenarios, the negative impact of data aggregation on R_t inference is outweighed by the benefit of then using data that are not corrupted by a WRE.

Our research highlights the importance of accounting for DOWEs, such as WREs, when estimating R_t during infectious disease outbreaks.