A proportional incidence rate model for aggregated data to study the vaccine effectiveness against COVID-19 hospital and ICU admissions.

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.