Welfare-Maximizing Pooled Testing

In an epidemic, how should an organization with limited testing resources safely return to in-person activities after a period of lockdown? We study this question in a setting where the population at hand is heterogeneous in both utility for in-person activities and probability of infection. In such a period of re-integration, tests can be used as a certificate of non-infection, whereby those in negative tests are permitted to return to in-person activities for a designated amount of time. Under the assumption that samples can be pooled, the question of how to allocate a limited testing budget in the population to maximize the aggregate utility (i.e. welfare) of negatively-tested individuals who return to in-person activities is non-trivial, with a large space of potential testing allocations. We show that non-overlapping testing allocations, which are both conceptually and (crucially) logistically more simple to implement, are approximately optimal, and we design an efficient greedy algorithm for finding non-overlapping testing allocations with approximately optimal welfare. In computational experiments, we highlight the efficacy and viability of our greedy algorithm in practice. To the best of our knowledge, we are also first to implement and provide causal evidence on the benefits of utility-weighted pooled testing in a real-world setting. Surprisingly, our pilot study at a higher education research institute in Mexico finds no evidence that performance and mental health outcomes of participants in our testing regime are worse than under the first-best counterfactual of full reopening without testing.