Modified Dorfman procedure for pool tests with dilution -- COVID-19 case study

The outbreak of the global COVID-19 pandemic results in unprecedented demand for fast and efficient testing of large numbers of patients for the presence of SARS-CoV-2 coronavirus. Beside technical improvements of the cost and speed of individual tests, pool testing may be used to improve efficiency and throughput of a population test. Dorfman pool testing procedure is one of the best known and studied methods of this kind. This procedure is, however, based on unrealistic assumptions that the pool test has perfect sensitivity and the only objective is to minimize the number of tests, and is not well adapted to the case of imperfect pool tests. We propose and analyze a simple modification of this procedure in which test of a pool with negative result is independently repeated up to several times. The proposed procedure is evaluated in a computational study using recent data about dilution effect for SARS-CoV-2 PCR tests, showing that the proposed approach significantly reduces the number of false negatives with a relatively small increase of the number of tests, especially for small prevalence rates. For example, for prevalence rate 0.001 the number of tests could be reduced to 22.1% of individual tests, increasing the expected number of false negatives by no more than 1%, and to 16.8% of individual tests increasing the expected number of false negatives by no more than 10%. At the same time, a similar reduction of the expected number of tests in the standard Dorfman procedure would yield 675% and 821% increase of the expected number of false negatives, respectively. This makes the proposed procedure an interesting choice for screening tests in the case of diseases like COVID-19.