Distributionally Robust Group Testing with Correlation Information

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