Causal Estimands for Infectious Disease Count Outcomes to Investigate the Public Health Impact of Interventions

Causal estimands of infectious disease interventions—direct, indirect, overall, and total effects— are conventionally defined as differences in individual risk under hypothetical treatment conditions. During the coronavirus disease (COVID-19) pandemic, researchers implicitly targeted analogous estimands at the population level by comparing count outcomes (e.g., vaccine-averted deaths) to quantify public health impact of non-pharmaceutical interventions or vaccination campaigns. However, these population-level analogs of conventional estimands have not been rigorously defined. Using potential outcome notation, we introduce a population-level analog of the overall effect and partitioned it into components involving individual-level direct and indirect effects. We further identify conditions under which a population-level analog of direct effect (frequently estimated with empirical data in cases-averted or avertible analyses), can be a useful lower bound of overall effect (arguably the most relevant effect for policy-making and retrospective policy evaluation) at the population level. To illustrate, we describe a susceptible-infected-recovered-death model stratified by vaccination status. When transmission and fatality parameters do not vary and vaccine efficacies do not wane over time, cases averted via direct effect among vaccinated individuals (or cases avertible via direct effect among unvaccinated individuals) is shown to be a lower bound of population-level overall effect—that is, vaccine-averted (or avertible) cases. However, when vaccine efficacies wane, this relation may not hold for avertible cases; when transmission or fatality parameters increase over time, it may not hold for either analysis. By classifying population-level estimands and establishing their relations, this study improves conduct and interpretation of research evaluating impact of infectious disease interventions.