Noisy Pooled PCR for Virus Testing

Junan Zhu; Kristina Rivera; Dror Baron

Recent work Hanel and Thurner [3] analyzes a two part group testing approach. Their model for PCR uses Pr(Y m = 0|W m > 0) = (1 − p 2 )p 1 , while we use Pr(Y m = 0|W m = w m > 0) = (1 − p 2 )p wm 1 ; we evaluated their approach using ρ = 0.01, p 1 = 0.02, and p 2 = 0.001. Hanel and Thurner's Part 1 pools a block of B = 11 patients at a time. If a pool is negative, all patients in the block are declared healthy; else A simulation over N = 10 7 patients had 935 false positives and 4038 false negatives. Our two part approach modifies Part 2. Instead of testing patients within each positive block individually, we combine all patients within all positive blocks into a new linear inverse problem, and solve the resulting estimation problem (1) with GAMP. For example, let the block size be B = 25 patients in Part 1. In Part 2, we combine all positive blocks and apply R = 0.5 and n pos = 0.5 to the linear inverse problem. Note that (i) positive measurements from Part 1 are reused in the matrix A and measurement vector y of Part 2, because they contain information that helps GAMP; (ii) we decide whether a patient is sick or not by thresholding x. Combining Parts 1 and 2, the measurement rate is R = 0.149. We randomly generate 100 (x, y, A) triples for N = 10000 patients in Part 1, Among 100N = 10 6 patients, there are 92 false positives and 366 false negatives. Our false positive and negative rates are both lower than those of Hanel and Thurner [3] .