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Monitoring time-varying vaccine effectiveness (e.g., due to waning of immunity and the emergence of novel variants) provides crucial information for outbreak control. Existing studies of time-varying vaccine effectiveness have used individual-level data, most importantly dates of vaccination and variant classification, which are often not available in a timely manner or from a wide range of population groups. We present a novel Bayesian framework for estimating the waning of variant-specific vaccine effectiveness in the presence of multi-variant circulation from population-level surveillance data. Applications to simulated outbreaks and the COVID-19 epidemic in Japan are also presented. Our results show that variant-specific waning vaccine effectiveness estimated from population-level surveillance data could approximately reproduce the estimates from previous test-negative design studies, allowing for rapid, if crude, assessment of the epidemic situation before fine-scale studies are made available.

Although robust divergence, such as density power divergence and γ-divergence, is helpful for robust statistical inference in the presence of outliers, the tuning parameter that controls the degree of robustness is chosen in a rule-of-thumb, which may lead to an inefficient inference. We here propose a selection criterion based on an asymptotic approximation of the Hyvarinen score applied to an unnormalized model defined by robust divergence. The proposed selection criterion only requires first and second-order partial derivatives of an assumed density function with respect to observations, which can be easily computed regardless of the number of parameters. We demonstrate the usefulness of the proposed method via numerical studies using normal distributions and regularized linear regression.