Optimal Covid-19 Pool Testing with a priori Information

TL;DR

This paper develops optimal algorithms for Covid-19 pool testing that leverage prior information about individual infection probabilities to minimize the number of tests needed for accurate detection.

Contribution

It introduces a novel, informed divide-and-conquer approach for pool testing that optimally incorporates a priori infection probabilities, improving efficiency over traditional methods.

Findings

Algorithms significantly reduce the number of tests needed.

Strategies outperform naive pooling methods.

Approach is adaptable to different prior information scenarios.

Abstract

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.