In the current COVID19 crisis many national healthcare systems are confronted with an acute shortage of tests for confirming SARS-CoV-2 infections. For low overall infection levels in the population, pooling of samples can drastically amplify the testing efficiency. Here we present a formula to estimate the optimal pooling size, the efficiency gain (tested persons per test), and the expected upper bound of missed infections in the pooled testing, all as a function of the populationwide infection levels and the false negative/positive rates of the currently used PCR tests. Assuming an infection level of 0.1 % and a false negative rate of 2 %, the optimal pool size is about 32, the efficiency gain is about 15 tested persons per test. For an infection level of 1 % the optimal pool size is 11, the efficiency gain is 5.1 tested persons per test. For an infection level of 10 % the optimal pool size reduces to about 4, the efficiency gain is about 1.7 tested persons per test. For infection levels of 30 % and higher there is no more benefit from pooling. To see to what extent replicates of the pooled tests improve the estimate of the maximal number of missed infections, we present all results for 1, 3, and 5 replicates.
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