Investigating the marginal and herd effects of COVID-19 vaccination for reducing case fatality rate: Evidence from the United States

Abstract

Vaccination campaigns have been rolled out in most countries to increase the vaccination coverage and protect against case mortality during the ongoing pandemic. To evaluate the effectiveness of COVID-19 vaccination, it is vital to disentangle the herd effect from the marginal effect and parameterize them separately in a model. To demonstrate this, we study the relationship between the COVID-19 vaccination coverage and case fatality rate (CFR) based on a U.S. vaccination coverage at county level, with daily records from March 11th, 2021 to Jan 26th, 2022 for 3109 U.S. counties. Using segmented regression, we discovered three breakpoints of the vaccination coverage, at which the herd effects could potentially exist. Controlling for county heterogeneity, we found the size of the marginal effect was not constant but actually enlarged as the vaccination coverage increased, and only the herd effect at the first breakpoint was statistically significant, which implied indirect benefit of vaccination may exist at the early stage of a vaccination campaign. Our results have demonstrated that public health researchers should carefully differentiate and quantify the herd and marginal effects in analyzing vaccination data, to better inform vaccination campaign strategies as well as evaluate vaccination effectiveness.