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The test-negative design (TND), which is routinely used for monitoringseasonal flu vaccine effectiveness (VE), has recently become integral toCOVID-19 vaccine surveillance, notably in Qu\'ebec, Canada. Some studies haveaddressed the identifiability and estimation of causal parameters under theTND, but efficiency bounds for nonparametric estimators of the target parameterunder the unconfoundedness assumption have not yet been investigated. Motivatedby the goal of improving adjustment for measured confounders when estimatingCOVID-19 VE among community-dwelling people aged $\geq 60$ years in Qu\'ebec,we propose a one-step doubly robust and locally efficient estimator calledTNDDR (TND doubly robust), which utilizes cross-fitting (sample splitting) andcan incorporate machine learning techniques to estimate the nuisance functionsand thus improve control for measured confounders. We derive the efficientinfluence function (EIF) for the marginal expectation of the outcome under avaccination intervention, explore the von Mises expansion, and establish theconditions for $\sqrt{n}-$consistency, asymptotic normality and doublerobustness of TNDDR. The proposed estimator is supported by both theoreticaland empirical justifications.

A Double Machine Learning Approach for the Evaluation of COVID-19  Vaccine Effectiveness under the Test-Negative Design: Analysis of Qu\'ebec  Administrative Data