Welfare-Maximizing Pooled Testing

TL;DR

This paper investigates the optimal design of pooled testing strategies in heterogeneous populations, demonstrating that simple non-overlapping testing is nearly optimal and proposing a heuristic for practical implementation, supported by real-world experiments.

Contribution

It introduces a welfare-maximizing framework for pooled testing, showing non-overlapping testing is nearly optimal and providing a heuristic for real-world application.

Findings

Non-overlapping testing is nearly optimal in welfare terms.

The proposed heuristic effectively finds near-optimal test allocations.

Real-world pilot shows no negative impact on health or mental health outcomes.

Abstract

Large-scale testing is crucial in pandemic containment, but resources are often prohibitively constrained. We study the optimal application of pooled testing for populations that are heterogeneous with respect to an individual's infection probability and utility that materializes if included in a negative test. We show that the welfare gain from overlapping testing over non-overlapping testing is bounded. Moreover, non-overlapping allocations, which are both conceptually and logistically simpler to implement, are empirically near-optimal, and we design a heuristic mechanism for finding these near-optimal test allocations. In numerical experiments, we highlight the efficacy and viability of our heuristic in practice. We also implement and provide experimental evidence on the benefits of utility-weighted pooled testing in a real-world setting. 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 access for individuals without testing.