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Real-world vaccine effectiveness has increasingly been studied using matching-based approaches, particularly in observational cohort studies that follow the target trial emulation framework. Although matching is appealing in its simplicity, it has important limitations in terms of clarity of the target estimand and the precision with which it is estimated. Moreover, defining causal estimands of vaccine effectiveness requires care, because vaccine uptake often occurs over calendar time when infection dynamics may also be rapidly changing. We propose a causal estimand of vaccine effectiveness that summarizes vaccine effectiveness over calendar time, similar to how vaccine efficacy is summarized in a randomized controlled trial. We describe the identification of our estimand and propose simple-to-implement estimators based on two hazard regression models. We apply our proposed estimator in simulations and in a study assessing the effectiveness of the Pfizer-BioNTech COVID-19 vaccine to prevent SARS-CoV-2 infections in children 5–11 years old. In both settings, we find that our proposed estimator yields similar scientific inferences while providing significant efficiency gains over commonly used matching-based estimators.