Improving COVID-19 Testing Efficiency using Guided Agglomerative Sampling

Fayyaz Minhas; Dimitris Grammatopoulos; Lawrence Young; Imran Amin; David Snead; Neil Anderson; Asa Ben-Hur; Nasir Rajpoot

All simulation results guarantee that the output of the tests remains unchanged from individual testing, i.e., if the original test identifies a given sample as positive (negative) then using the proposed scheme will identify that given sample as positive (negative) but with fewer number of tests required in overall. Figure 2 shows the number tests required under the proposed scheme for different positive probability values ( ) and different values of ( ) under no a prior belief (uniformly random ) . It can be clearly seen that the mathematical formula for the number of expected tests is in excellent concordance with the simulation results. Figure 2(a) shows that the number of required tests for = 16 with the proposed method remains below up to a probability of = 0.22 as expected. Figure 2 (b) shows the same analysis for = 256. Figure 2 (c) shows that the expected number of tests that can be saved is above 40% for all values of at a positive probability of = 0.1. This clearly shows that the proposed scheme can be very beneficial in practical settings. The number of required tests can be reduced further by incorporating a belief parameter or performing unsupervised agglomeration based on individual features as discussed below.