During a disease outbreak, incidence (the rate of new cases) and prevalence (the fraction of the population currently infected) must be monitored so as to implement and evaluate disease control strategies. These measurements depend on the availability of diagnostic tests as well as the likelihood that each patient would be tested. During an outbreak of a novel agent such as SARS-CoV-2 (in the COVID-19 pandemic), the availability of tests and the likelihood of testing change over time, making it difficult to distinguish the spread of the disease from the increased availability of testing. For example, a greater proportion of test results are likely to be positive early in a disease outbreak because physicians may reserve scarce tests for patients with severe signs and symptoms; however, as tests become more readily available, physicians may also administer tests to patients with less severe signs and symptoms, possibly resulting in a reduced ratio of positive to negative tests.
In this post, we propose a simple probabilistic model that uses the total number of administered tests and the relative proportion of positive and negative test results to estimate cumulative SARS-CoV-2 incidence over time in each state in the United States. The model incorporates beliefs about how testing strategies increase the likelihood of testing infected individuals, and enables us to compare the implications of various prevalence estimates, even for studies which measure very different populations. In this way, we can put studies from very different contexts on similar footing to understand the implications regarding spread of the pandemic. Python code to perform these estimates and daily-updated results are available on Github. As more data, including randomized community testing, become available, we expect these analyses to become much more accurate.
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