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. increasing the AUC reflects better estimation. While standard GAMP minimizes the MSE [7] , other error metrics can be minimized [10] , [11] . The top pannel of Fig. 2 plots the 2 norms of the input channel noise (dashed red line) and output channel noise (solid blue). We can see that the input and output channels improve over iterations. The bottom panel shows the first 1000 entries of the input signal vector x and their estimates. We can see that patient illness status is estimated well.