Noisy Pooled PCR for Virus Testing

Junan Zhu; Kristina Rivera; Dror Baron

We evaluate N = 5000 patients at a time, where the fraction of infected patients is ρ = 0.01. The measurement rate is R = M/N = 0.3, meaning that we take M = N R = 1500 RT-PCR measurements. 2 The matrix A is designed to pick up n pos sick patients per measurement on average; we let n pos = 0.5. The numbers of ones per row and column are kept close to n pos /ρ and Rn pos /ρ, respectively. For the RT-PCR channel, we assume a false negative probability, p 1 = 0.02, and false positive probability, p 2 = 0.001. 3 We quantify GAMP signal estimation quality using the area under the receiver operating curve (AUC-ROC). In words, the ROC captures trade-offs between false positives and negatives, and 2 Our GAMP-based algorithm is relatively fast; problems of size (M = 1500, N = 5000) take a few seconds to run on a laptop computer. 3 The parameters p 1 and p 2 resemble Hanel and Thurner [3] ; other sources suggest larger false positive and negative probabilities. For our software, these are merely parameters that are easily modified.