Identifiability and estimation under the test-negative design with population controls with the goal of identifying risk and preventive factors for SARS-CoV-2 infection
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Due to the rapidly evolving COVID-19 pandemic caused by the SARS-CoV-2 virus, quick public health investigations of the relationships between behaviours and infection risk are essential. Recently the test-negative design was proposed to recruit and survey participants who are being tested for SARS-CoV-2 infection in order to evaluate associations between their characteristics and testing positive on the test. It was also proposed to recruit additional untested controls who are part of the general public in order to have a baseline comparison group. This study design involves two major challenges for statistical risk factor analysis: 1) the selection bias invoked by selecting on people being tested and 2) imperfect sensitivity and specificity of the SARS-CoV-2 test. In this study, we investigate the nonparametric identifiability of potential statistical parameters of interest under a hypothetical data structure, expressed through missing data directed acyclic graphs. We clarify the types of data that must be collected in order to correctly estimate the parameter of interest. We then propose a novel inverse probability weighting estimator that can consistently estimate the parameter of interest under correctly specified nuisance models.
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