While the test-negative design (TND), which is routinely used for monitoring seasonal flu vaccine effectiveness (VE), has recently become integral to COVID-19 vaccine surveillance, it is susceptible to selection bias due to outcome-dependent sampling. Some studies have addressed the identifiability and estimation of causal parameters under the TND, but efficiency bounds for nonparametric estimators of the target parameter under the unconfoundedness assumption have not yet been investigated. We propose a one-step doubly robust and locally efficient estimator called TNDDR (TND doubly robust), which utilizes sample splitting and can incorporate machine learning techniques to estimate the nuisance functions. We derive the efficient influence function (EIF) for the marginal expectation of the outcome under a vaccination intervention, explore the von Mises expansion, and establish the conditions for $\sqrt{n}-$consistency, asymptotic normality and double robustness of TNDDR. The proposed TNDDR is supported by both theoretical and empirical justifications, and we apply it to estimate COVID-19 VE in an administrative dataset of community-dwelling older people (aged $\geq 60$y) in the province of Qu\'ebec, Canada.

翻译：尽管检验阴性设计（TND）作为季节性流感疫苗有效性（VE）监测的常规方法，近期已融入COVID-19疫苗监测体系，但其因依赖结局导向的抽样易产生选择偏倚。部分研究探讨了TND下因果参数的可识别性与估计问题，但尚未探究无混淆假设下目标参数非参数估计量的效率界。我们提出一种名为TNDDR（检验阴性设计双稳健估计）的单步双稳健局部高效估计量，该估计量通过样本分裂整合机器学习技术估计干扰函数。我们推导了疫苗接种干预下结局边际期望的有效影响函数（EIF），探究冯·米塞斯展开，并建立TNDDR的$\sqrt{n}$-相合性、渐近正态性与双稳健性条件。所提出的TNDDR方法兼具理论依据与实证支撑，我们将其应用于加拿大魁北克省社区老年人群（年龄$\geq 60$岁）的管理数据集，以估计COVID-19疫苗有效性。