Fig. 1: Directed acyclic graphs (DAGs) for estimating vaccine effectiveness against symptomatic SARS-CoV-2 infection across two study designs.

DAGs are shown for the retrospective cohort design using relative risk (a) and the retrospective test-negative design using an odds ratio (b). The DAGs depict causal relationships (arrows) and induced associations (dashed lines). Because the vaccine does not decrease the likelihood of developing symptoms once infected, effectiveness against symptomatic infection is equivalent to effectiveness against infection (yellow arrow). Causal relationships between healthcare engagement and vaccination (i), and between healthcare engagement and testing for SARS-CoV-2 (ii) induce an association between vaccination and testing for SARS-CoV-2 (iii) and create a biased relationship between vaccination and testing positive for SARS-CoV-2 in the cohort design (depicted in (a)). In the test-negative design (depicted in (b)), conditioning on testing induces an association between healthcare engagement and being symptomatic (iv). Conditioning additionally on being symptomatic induces an association between healthcare engagement and SARS-CoV-2 infection (v). This induced relationship (v), along with the relationship between healthcare engagement and vaccination (i), introduces confounding by healthcare engagement in the relationship between vaccination and SARS-CoV-2 infection.