Application of pooled testing in screening and estimating the prevalence of COVID-19

The recent emergence of the COVID-19 pandemic has posed an unprecedented healthcare challenge and catastrophic economic and social consequences to the countries across the world. The situation is even worse for emerging economies like India. WHO recommends mass scale testing as one of the most effective ways to contain its spread and fight the pandemic. But, due to the high cost and shortage of test kits, specifically in India, the testing is restricted to only those who are symptomatic. In this context, pooled testing is recommended by some experts as a partial solution to overcome this problem. In this article, we explain the basic statistical theory behind the pooled testing procedure for screening as well as prevalence estimation. In real world situations, the tests are imperfect, and lead to false positive and false negative results. We provide theoretical explanation of the impact of these diagnostic errors on the performances of individual testing and pooled testing procedures. Finally, we study the effect of misspecification of sensitivity and specificity of tests on the estimate of prevalence, an issue, which is debated a lot among the scientists in the context of COVID-19. Our theoretical investigations lead to some interesting and precise understanding of some of these issues.