Abstract
BACKGROUND: Diagnostic tests are performed in a subset of the population who are at higher risk, resulting in undiagnosed cases among those who do not receive the test. This poses a challenge for estimating the prevalence of the disease in the study population, and also for studying the risk factors for the disease. METHODS: We formulate this problem as a missing data problem because the disease status is unknown for those who do not receive the test. We propose a Bayesian selection model which models the joint distribution of the disease outcome and whether testing was received. The sensitivity analysis allows us to assess how the association of the risk factors with the disease outcome as well as the disease prevalence change with the sensitivity parameter. RESULTS: We illustrated our model using a retrospective cohort study of children with asthma exacerbation that were evaluated for pneumonia in the emergency department. Our model found that female gender, having fever during ED or at triage, and having severe hypoxia are significantly associated with having radiographic pneumonia. In addition, simulation studies demonstrate that the Bayesian selection model works well even under circumstances when both the disease prevalence and the screening proportion is low. CONCLUSION: The Bayesian selection model is a viable tool to consider for estimating the disease prevalence and in studying risk factors of the disease, when only a subset of the target population receive the test.