Distributionally Robust Group Testing with Correlation Information

76 Pages Posted: 12 Dec 2022 Last revised: 2 Jan 2024

See all articles by Daniel Zhuoyu Long

Daniel Zhuoyu Long

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering and Engineering Management

Jin QI

Hong Kong University of Science & Technology (HKUST) - Dept. of Industrial Engineering and Decision Analytics

Yu Sun

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management

Aiqi Zhang

Wilfrid Laurier University - School of Business & Economics

Date Written: November 23, 2022

Abstract

Motivated by the need for more efficient and reliable methods of group testing during widespread infectious outbreaks, such as the COVID-19 pandemic, this paper introduces a novel operational improvement to Dorfman's widely-used group testing procedure. Our method minimizes a weighted sum of tests and misclassifications, predicated on the known Pearson correlation coefficient between individuals and their prevalence rates. Recognizing the inherent ambiguity in the population-level probability distribution that arises from correlations, our approach leverages a distributionally robust optimization (DRO) framework to counteract the worst-case probability distribution. In fully-correlated cases, where each pair of subjects are equally correlated, we establish uniform group sizes and connect our analysis to Nash equilibrium principles. Larger testing groups are generally favored under high correlation, whereas individual testing becomes optimal under high prevalence. In partially-correlated cases, where the population is formed by several intra-correlated but inter-independent clusters, we highlight the effectiveness of mixed-cluster testing strategies, particularly at lower levels of prevalence and correlation. Conversely, scenarios with high prevalence or high correlation tend to favor individual testing or same-cluster pooling. For both fully- and partially-correlated cases, we develop polynomial-time solutions and conduct a thorough exploration on the change of optimal pooling strategy as a function of imperfect tests. We demonstrate the benefits of adopting the DRO framework through a comprehensive comparison with stochastic alternatives, and we illustrate the significant impact of considering correlated infections through a case study on a COVID-19 dataset from Hong Kong.

Keywords: group testing, distributionally robust optimization, healthcare operations management

Suggested Citation

Long, Daniel Zhuoyu and QI, Jin and Sun, Yu and Zhang, Aiqi, Distributionally Robust Group Testing with Correlation Information (November 23, 2022). Available at SSRN: https://ssrn.com/abstract=4284685 or http://dx.doi.org/10.2139/ssrn.4284685

Daniel Zhuoyu Long

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering and Engineering Management ( email )

Hong Kong
China

Jin QI

Hong Kong University of Science & Technology (HKUST) - Dept. of Industrial Engineering and Decision Analytics ( email )

Hong Kong

Yu Sun (Contact Author)

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management ( email )

Shatin, New Territories
Hong Kong

Aiqi Zhang

Wilfrid Laurier University - School of Business & Economics ( email )

Waterloo, Ontario N2L 3C5
Canada

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