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

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 symptomatic and being tested for SARS-CoV-2 infection with the goal of evaluating associations between the survey responses (including behaviours and environment) and testing positive on the test. It was also proposed to recruit additional controls who are part of the general population as a baseline comparison group in order to evaluate risk factors specific to SARS-CoV-2 infection. In this study, we consider an alternative design where we recruit among all individuals, symptomatic and asymptomatic, being tested for the virus in addition to population controls. We define a regression parameter related to a prospective risk factor analysis and investigate its identifiability under the two study designs. We review the difference between the prospective risk factor parameter and the parameter targeted in the typical test-negative design where only symptomatic and tested people are recruited. Using missing data directed acyclic graphs we provide conditions and required data collection under which identifiability of the prospective risk factor parameter is possible and compare the benefits and limitations of the alternative study designs and target parameters. We propose a novel inverse probability weighting estimator and demonstrate the performance of this estimator through simulation study.