Optimal Covid-19 Pool Testing with a priori Information
This addresses the critical shortage of testing kits during the Covid-19 pandemic, particularly benefiting resource-limited settings, but it is incremental as it builds on existing pooling methods.
The paper tackles the problem of Covid-19 test kit shortages by developing optimal pooling algorithms that use a priori probabilities of patient health to minimize the number of tests needed to identify infected individuals, achieving precise detection with non-intuitive strategies.
As humanity struggles to contain the global Covid-19 infection, prophylactic actions are grandly slowed down by the shortage of testing kits. Governments have taken several measures to work around this shortage: the FDA has become more liberal on the approval of Covid-19 tests in the US. In the UK emergency measures allowed to increase the daily number of locally produced test kits to 100,000. China has recently launched a massive test manufacturing program. However, all those efforts are very insufficient and many poor countries are still under threat. A popular method for reducing the number of tests consists in pooling samples, i.e. mixing patient samples and testing the mixed samples once. If all the samples are negative, pooling succeeds at a unitary cost. However, if a single sample is positive, failure does not indicate which patient is infected. This paper describes how to optimally detect infected patients in pools, i.e. using a minimal number of tests to precisely identify them, given the a priori probabilities that each of the patients is healthy. Those probabilities can be estimated using questionnaires, supervised machine learning or clinical examinations. The resulting algorithms, which can be interpreted as informed divide-and-conquer strategies, are non-intuitive and quite surprising. They are patent-free. Co-authors are listed in alphabetical order.