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

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. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This study did not receive any funding ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: The vaccination coverage data was openly available at . The SVI data (year 2018) was openly available at [https://www.atsdr.cdc.gov/placeandhealth/svi/data\_documentation\_download.html][1]. The data about case fatality rate was openly available at . I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes All data produced are available online at the following websites: [https://www.atsdr.cdc.gov/placeandhealth/svi/data\_documentation\_download.html][1] [1]: https://www.atsdr.cdc.gov/placeandhealth/svi/data_documentation_download.html