A Proportional Incidence Rate Model for Aggregated Data to Study the Vaccine Effectiveness Against COVID-19 Hospital and ICU Admissions

Author:

Yan Ping12ORCID,Mullah Muhammad Abu Shadeque13,Tuite Ashleigh4

Affiliation:

1. Infectious Disease Programs Branch, Public Health Agency of Canada , Ottawa, Ontario , Canada

2. Department of Statistics and Actuarial Science, University of Waterloo , Ontario , Canada

3. School of Epidemiology and Public Health, University of Ottawa , Ontario , Canada

4. Dalla Lana School of Public Health, University of Toronto , Ontario , Canada

Abstract

Abstract We develop a proportional incidence model that estimates vaccine effectiveness (VE) at the population level using conditional likelihood for aggregated data. Our model assumes that the population counts of clinical outcomes for an infectious disease arise from a superposition of Poisson processes with different vaccination statuses. The intensity function in the model is calculated as the product of per capita incidence rate and the at-risk population size, both of which are time-dependent. We formulate a log-linear regression model with respect to the relative risk, defined as the ratio between the per capita incidence rates of vaccinated and unvaccinated individuals. In the regression analysis, we treat the baseline incidence rate as a nuisance parameter, similar to the Cox proportional hazard model in survival analysis. We then apply the proposed models and methods to age-stratified weekly counts of COVID-19–related hospital and ICU admissions among adults in Ontario, Canada. The data spanned from 2021 to February 2022, encompassing the Omicron era and the rollout of booster vaccine doses. We also discuss the limitations and confounding effects while advocating for the necessity of more comprehensive and up-to-date individual-level data that document the clinical outcomes and measure potential confounders.

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,General Agricultural and Biological Sciences,General Immunology and Microbiology,General Biochemistry, Genetics and Molecular Biology,General Medicine,Statistics and Probability

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