Evaluating the Direct Effect of Vaccination and Non-pharmaceutical Interventions During the COVID-19 Pandemic in Europe

Background: Across Europe, countries have responded to the COVID-19 pandemic with a combination of non-pharmaceutical interventions and vaccination. Evaluating the effectiveness of such interventions is of particular relevance to policy-makers.

Methods: We leverage almost three years of available data across 38 European countries to evaluate the effectiveness of governmental responses in controlling the pandemic. We developed a Bayesian hierarchical model that flexibly relates daily COVID-19 incidence to past levels of vaccination and non-pharmaceutical interventions as summarised in the Stringency Index. Specifically, we use a distributed lag approach to temporally weight past intervention values, a tensor-product smooth to capture non-linearities and interactions between both types of interventions, and a hierarchical approach to parsimoniously address heterogeneity across countries.

Results: We identify a pronounced negative association between daily incidence and the strength of non-pharmaceutical interventions, along with substantial heterogeneity in effectiveness among European countries. Similarly, we observe a strong but more consistent negative association with vaccination levels. Our results show that non-linear interactions shape the effectiveness of interventions, with non-pharmaceutical interventions becoming less effective under high vaccination levels. Finally, our results indicate that the effects of interventions on daily incidence are most pronounced at a lag of 14 days after being in place.

Conclusions: Our Bayesian hierarchical modelling approach reveals clear negative and lagged effects of non-pharmaceutical interventions and vaccination on confirmed COVID-19 cases across European countries.