Abstract
During the coronavirus disease (COVID-19) pandemic, researchers attempted to estimate the number of averted and avertible outcomes due to vaccination campaigns to quantify public health impact. However, the estimands used in these analyses have not been previously formalized. It is also unclear how these analyses relate to the broader framework of direct, indirect, total, and overall causal effects under interference. Here, using potential outcome notation, we adjust the direct and overall effects to accommodate analyses of averted and avertible outcomes. We use this framework to interrogate the commonly held assumption that vaccine-averted outcomes via direct impact among vaccinated individuals (or vaccine-avertible outcomes via direct impact among unvaccinated individuals) is a lower bound on vaccine-averted (or -avertible) outcomes overall. To do so, we describe a susceptible-infected-recovered-death model stratified by vaccination status. When vaccine efficacies wane, the lower bound fails for vaccine-avertible outcomes. When transmission or fatality parameters increase over time, the lower bound fails for both vaccine-averted and -avertible outcomes. Only in the simplest scenario where vaccine efficacies, transmission, and fatality parameters are constant over time, outcomes averted via direct impact among vaccinated individuals (or outcomes avertible via direct impact among unvaccinated individuals) is a lower bound on overall impact. In conclusion, the lower bound can fail under common violations to assumptions on time-invariant vaccine efficacy, pathogen properties, or behavioral parameters. In real data analyses, estimating what seems like a lower bound on overall impact through estimating direct impact may be inadvisable without examining the directions of indirect effects.