Contact Tracing Enhances the Efficiency of Covid-19 Group Testing

Abstract

Group testing can save testing resources in the context of the ongoing COVID-19 pandemic. In group testing, we are given n samples, one per individual, and arrange them into m < n pooled samples, where each pool is obtained by mixing a subset of the n individual samples. Infected individuals are then identified using a group testing algorithm. In this paper, we use side information (SI) collected from contact tracing (CT) within nonadaptive/single-stage group testing algorithms. We generate data by incorporating CT SI and characteristics of disease spread between individuals. These data are fed into two signal and measurement models for group testing, where numerical results show that our algorithms provide improved sensitivity and specificity. While Nikolopoulos et al. utilized family structure to improve nonadaptive group testing, ours is the first work to explore and demonstrate how CT SI can further improve group testing performance.

Model-Based and Graph-Based Priors for Group Testing

“…Observe that the upper and lower bounds match as α * → 0. More generally, recent results in [16], [17] demonstrated that (9) that is tight for general designs (i.e., there exists a matching achievability result), whereas Bernoulli designs cannot do better than (8), so they are mildly suboptimal in terms of the dependence on α * .…”

“…Two algorithms in [8] are proposed for exploiting information from contact tracing with two different test models. In particular, in the case of a binary-valued testing model (as we consider), they propose a Generalized Approximate Message Passing (GAMP) algorithm based on a dynamic infection model with known infection times and physical proximity levels.…”

“…• Theoretical bounds for model-based priors: Focusing primarily on the noiseless setting, we characterize the information-theoretic limits for approximate recovery when the space of defective sets, S, is a strict subset of all size-k sets, and This is in contrast with previous approaches exploiting prior information, which often lead to Belief Propagation (BP) based decoders [8], [25]. We provide synthetic numerical experiments demonstrating the improvement of our decoders over standard baselines that do not exploit prior information.…”

“…The current state-of-the-art group testing schemes can reliably identify the defective set using an asymptotically optimal number of tests [4]. In this paper, we build on a recent line of works demonstrating that we can further decrease the number of tests by leveraging structural dependencies between the items [5], [6], [7], [8]. We study such dependencies from two different perspectives, adopting a natural generlization of the uniform combinatorial prior for the purpose of theoretical analysis, and introducing a new prior based on Ising models as a more practical alternative that generalizes the i.i.d.…”

Group Testing on General Set-Systems

“…The paper leverages the structure of H = (V, E) to maximize the efficiency of the group testing algorithms in the adaptive, non-adaptive, and probabilistic settings. A few related papers [9], [10] focus on leveraging side-information (e.g., that can be obtained from contact tracing) to make the decoding algorithm faster. Finally, graph-constrained group testing, a variant of the group testing problem where the tests must conform to constraints imposed by a graph, is considered, e.g., in [11]- [13].…”