Investigating the Marginal and Herd Effects of COVID-19 Vaccination for Reducing Case Fatality Rate: Evidence from the United States between March 2021 to January 2022.

Vaccination campaigns have been rolled out in most countries to increase 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 U.S. vaccination coverage at county level, with daily records from 11 March 2021 to 26 January 2022 for 3109 U.S. counties. Using segmented regression, we discovered three breakpoints of the vaccination coverage, at which herd effects could potentially exist. Controlling for county heterogeneity, we found the size of the marginal effect was not constant but actually increased as the vaccination coverage increased, and only the herd effect at the first breakpoint to be statistically significant, which implied an indirect benefit of vaccination may exist at the early stage of a vaccination campaign. Our results demonstrated that public-health researchers should carefully differentiate and quantify the herd and marginal effects when analyzing vaccination data, to better inform vaccination-campaign strategies as well as evaluate vaccination effectiveness.