Distributionally Robust Group Testing with Correlation Information

Motivated by the need for more efficient and reliable methods of group testing during widespread infectious outbreaks, this paper introduces a novel operational improvement to the widely used Dorfman’s group testing procedure, where a single test is conducted on the pooled sample, followed by individual testing of positive pools. Our method minimizes a weighted sum of testing volume and misclassifications, taking prevalence rates and interindividual Pearson correlation coefficients as inputs, and employs a distributionally robust optimization (DRO) framework to address the ambiguity in the joint infection distribution induced by these correlations. We study two correlation structures within a population. In single-cluster cases, where all subject pairs share equal correlation, we connect our analysis to Nash equilibrium principles and show that higher correlation favors larger testing groups, whereas higher prevalence often calls for individual testing. In multicluster cases, where the population consists of several intracorrelated but interindependent clusters, we highlight the effectiveness of mixed-cluster testing strategies, particularly under low prevalence and correlation. This is a notable addition to the prevailing view that advocates pooling correlated individuals. We provide polynomial-time solutions for both correlation structures and demonstrate the trade-offs and benefits of our DRO approach through a thorough comparison with stochastic alternatives. Using a case study based on a real-world COVID-19 data set, we show that our proposed pooling strategy can save up to 0.1 tests per individual compared with an independence-based pooling scheme and up to 0.5 tests per individual compared with a heuristic pooling strategy implemented in the studied region.

This paper was accepted by Jeannette Song, operations management.

Funding: This research was supported by the National Natural Science Foundation of China [Grants 72293582 and 72422005], the Hong Kong Research Grants Council [Collaborative Research Fund C6103-20GF, General Research Fund 14210523, 16209923, and 16213424], and the Natural Sciences and Engineering Research Council of Canada [Grants RGPIN-2024-05910 and DGECR-2024-00094].

Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.04308.