Estimating the course of the COVID-19 pandemic in Germany via spline-based hierarchical modelling of death counts

TL;DR

This paper introduces a Bayesian hierarchical spline-based model to estimate COVID-19's effective reproduction number in Germany from death counts, providing more robust insights than traditional case-based methods, especially during testing policy shifts.

Contribution

The study develops a novel spline-based hierarchical Bayesian model that estimates reproduction numbers from death data, accounting for undetected infections and testing policy changes.

Findings

Reproduction number estimates from death counts align with classical methods during stable testing.

Death-based estimates are more robust during testing policy shifts.

The model reveals ongoing infection growth during lockdown periods.

Abstract

The effective reproduction number is a key figure to monitor the course of the COVID-19 pandemic. In this study we consider a retrospective modelling approach for estimating the effective reproduction number based on death counts during the first year of the pandemic in Germany. The proposed Bayesian hierarchical model incorporates splines to estimate reproduction numbers flexibly over time while adjusting for varying effective infection fatality rates. The approach also provides estimates of dark figures regarding undetected infections over time. Results for Germany illustrate that estimated reproduction numbers based on death counts are often similar to classical estimates based on confirmed cases. However, considering death counts proves to be more robust against shifts in testing policies: during the second wave of infections, classical estimation of the reproduction number suggests a flattening/ decreasing trend of infections following the "lockdown light" in November 2020, while our results indicate that true numbers of infections continued to rise until the "second lockdown" in December 2020. This observation is associated with more stringent testing criteria introduced concurrently with the "lockdown light", which is reflected in subsequently increasing dark figures of infections estimated by our model. These findings illustrate that the retrospective viewpoint can provide additional insights regarding the course of the pandemic. In light of progressive vaccinations, shifting the focus from modelling confirmed cases to reported deaths with the possibility to incorporate effective infection fatality rates might be of increasing relevance for the future surveillance of the pandemic.