Reader reaction: A note on the evaluation of group testing algorithms in the presence of misclassification

Leveraging network structure to improve pooled testing efficiency

Screening is a powerful tool for infection control, allowing for infectious individuals, whether they be symptomatic or asymptomatic, to be identified and isolated. The resource burden of regular and comprehensive screening can often be prohibitive, however. One such measure to address this is pooled testing, whereby groups of individuals are each given a composite test; should a group receive a positive diagnostic test result, those comprising the group are then tested individually. Infectious disease is spread through a transmission network, and this paper shows how assigning individuals to pools based on this underlying network can improve the efficiency of the pooled testing strategy, thereby reducing the resource burden. We designed a simulated annealing algorithm to improve the pooled testing efficiency as measured by the ratio of the expected number of correct classifications to the expected number of tests performed. We then evaluated our approach using an agent-based model designed to simulate the spread of SARS-CoV-2 in a school setting. Our results suggest that our approach can decrease the number of tests required to regularly screen the student body, and that these reductions are quite robust to assigning pools based on partially observed or noisy versions of the network.

Simulation of group testing scenarios can boost COVID-19 screening power

The COVID-19 has severely affected economies and health systems around the world. Mass testing could work as a powerful alternative to restrain disease dissemination, but the shortage of reagents is a limiting factor. A solution to optimize test usage relies on ‘grouping’ or ‘pooling’ strategies, which combine a set of individuals in a single reaction. To compare different group testing configurations, we developed the poolingr package, which performs an innovative hybrid in silico/in vitro approach to search for optimal testing configurations. We used 6759 viral load values, observed in 2389 positive individuals, to simulate a wide range of scenarios. We found that larger groups (>100) framed into multi-stage setups (up to six stages) could largely boost the power to detect spreaders. Although the boost was dependent on the disease prevalence, our method could point to cheaper grouping schemes to better mitigate COVID-19 dissemination through identification and quarantine recommendation for positive individuals.

Network-Informed Constrained Divisive Pooled Testing Assignments

Frequent universal testing in a finite population is an effective approach to preventing large infectious disease outbreaks. Yet when the target group has many constituents, this strategy can be cost prohibitive. One approach to alleviate the resource burden is to group multiple individual tests into one unit in order to determine if further tests at the individual level are necessary. This approach, referred to as a group testing or pooled testing, has received much attention in finding the minimum cost pooling strategy. Existing approaches, however, assume either independence or very simple dependence structures between individuals. This assumption ignores the fact that in the context of infectious diseases there is an underlying transmission network that connects individuals. We develop a constrained divisive hierarchical clustering algorithm that assigns individuals to pools based on the contact patterns between individuals. In a simulation study based on real networks, we show the benefits of using our proposed approach compared to random assignments even when the network is imperfectly measured and there is a high degree of missingness in the data.

The efficient design of Nested Group Testing algorithms for disease identification in clustered data

Group testing study designs have been used since the 1940s to reduce screening costs for uncommon diseases; for rare diseases, all cases are identifiable with substantially fewer tests than the population size. Substantial research has identified efficient designs under this paradigm. However, little work has focused on the important problem of disease screening among clustered data, such as geographic heterogeneity in HIV prevalence. We evaluated designs where we first estimate disease prevalence and then apply efficient group testing algorithms using these estimates. Specifically, we evaluate prevalence using individual testing on a fixed-size subset of each cluster and use these prevalence estimates to choose group sizes that minimize the corresponding estimated average number of tests per subject. We compare designs where we estimate cluster-specific prevalences as well as a common prevalence across clusters, use different group testing algorithms, construct groups from individuals within and in different clusters, and consider misclassification. For diseases with low prevalence, our results suggest that accounting for clustering is unnecessary. However, for diseases with higher prevalence and sizeable between-cluster heterogeneity, accounting for clustering in study design and implementation improves efficiency. We consider the practical aspects of our design recommendations with two examples with strong clustering effects: (1) Identification of HIV carriers in the US population and (2) Laboratory screening of anti-cancer compounds using cell lines.

Pooled testing of traced contacts under superspreading dynamics

Testing is recommended for all close contacts of confirmed COVID-19 patients. However, existing pooled testing methods are oblivious to the circumstances of contagion provided by contact tracing. Here, we build upon a well-known semi-adaptive pooled testing method, Dorfman's method with imperfect tests, and derive a simple pooled testing method based on dynamic programming that is specifically designed to use information provided by contact tracing. Experiments using a variety of reproduction numbers and dispersion levels, including those estimated in the context of the COVID-19 pandemic, show that the pools found using our method result in a significantly lower number of tests than those found using Dorfman's method. Our method provides the greatest competitive advantage when the number of contacts of an infected individual is small, or the distribution of secondary infections is highly overdispersed. Moreover, it maintains this competitive advantage under imperfect contact tracing and significant levels of dilution.

Is group testing ready for prime-time in disease identification?

Large-scale disease screening is a complicated process in which high costs must be balanced against pressing public health needs. When the goal is screening for infectious disease, one approach is group testing in which samples are initially tested in pools and individual samples are retested only if the initial pooled test was positive. Intuitively, if the prevalence of infection is small, this could result in a large reduction of the total number of tests required. Despite this, the use of group testing in medical studies has been limited, largely due to skepticism about the impact of pooling on the accuracy of a given assay. While there is a large body of research addressing the issue of testing errors in group testing studies, it is customary to assume that the misclassification parameters are known from an external population and/or that the values do not change with the group size. Both of these assumptions are highly questionable for many medical practitioners considering group testing in their study design. In this article, we explore how the failure of these assumptions might impact the efficacy of a group testing design and, consequently, whether group testing is currently feasible for medical screening. Specifically, we look at how incorrect assumptions about the sensitivity function at the design stage can lead to poor estimation of a procedure's overall sensitivity and expected number of tests. Furthermore, if a validation study is used to estimate the pooled misclassification parameters of a given assay, we show that the sample sizes required are so large as to be prohibitive in all but the largest screening programs.

The objective function controversy for group testing: Much ado about nothing?

Group testing is an indispensable tool for laboratories when testing high volumes of clinical specimens for infectious diseases. An important decision that needs to be made prior to implementation is determining what group sizes to use. In best practice, an objective function is chosen and then minimized to determine an optimal set of these group sizes, known as the optimal testing configuration (OTC). There are a few options for objective functions, and they differ based on how the expected number of tests, assay characteristics, and testing constraints are taken into account. These varied options have led to a recent controversy in the literature regarding which of two different objective functions is better. In our paper, we examine these objective functions over a number of realistic situations for infectious disease testing. We show that this controversy may be much ado about nothing because the OTCs and corresponding results (eg, number of tests and accuracy) are largely the same for standard testing algorithms in a wide variety of situations.

Revisiting Nested Group Testing Procedures: New Results, Comparisons, and Robustness

Group testing has its origin in the identification of syphilis in the U.S. army during World War II. Much of the theoretical framework of group testing was developed starting in the late 1950s, with continued work into the 1990s. Recently, with the advent of new laboratory and genetic technologies, there has been an increasing interest in group testing designs for cost saving purposes. In this article, we compare different nested designs, including Dorfman, Sterrett and an optimal nested procedure obtained through dynamic programming. To elucidate these comparisons, we develop closed-form expressions for the optimal Sterrett procedure and provide a concise review of the prior literature for other commonly used procedures. We consider designs where the prevalence of disease is known as well as investigate the robustness of these procedures, when it is incorrectly assumed. This article provides a technical presentation that will be of interest to researchers as well as from a pedagogical perspective. Supplementary material for this article available online.

Group testing case identification with biomarker information

Screening procedures for infectious diseases, such as HIV, often involve pooling individual specimens together and testing the pools. For diseases with low prevalence, group testing (or pooled testing) can be used to classify individuals as diseased or not while providing considerable cost savings when compared to testing specimens individually. The pooling literature is replete with group testing case identification algorithms including Dorfman testing, higher-stage hierarchical procedures, and array testing. Although these algorithms are usually evaluated on the basis of the expected number of tests and classification accuracy, most evaluations in the literature do not account for the continuous nature of the testing responses and thus invoke potentially restrictive assumptions to characterize an algorithm's performance. Commonly used case identification algorithms in group testing are considered and are evaluated by taking a different approach. Instead of treating testing responses as binary random variables (i.e., diseased/not), evaluations are made by exploiting an assay's underlying continuous biomarker distributions for positive and negative individuals. In doing so, a general framework to describe the operating characteristics of group testing case identification algorithms is provided when these distributions are known. The methodology is illustrated using two HIV testing examples taken from the pooling literature.

Hierarchical group testing for multiple infections

Group testing, where individuals are tested initially in pools, is widely used to screen a large number of individuals for rare diseases. Triggered by the recent development of assays that detect multiple infections at once, screening programs now involve testing individuals in pools for multiple infections simultaneously. Tebbs, McMahan, and Bilder (2013, Biometrics) recently evaluated the performance of a two-stage hierarchical algorithm used to screen for chlamydia and gonorrhea as part of the Infertility Prevention Project in the United States. In this article, we generalize this work to accommodate a larger number of stages. To derive the operating characteristics of higher-stage hierarchical algorithms with more than one infection, we view the pool decoding process as a time-inhomogeneous, finite-state Markov chain. Taking this conceptualization enables us to derive closed-form expressions for the expected number of tests and classification accuracy rates in terms of transition probability matrices. When applied to chlamydia and gonorrhea testing data from four states (Region X of the United States Department of Health and Human Services), higher-stage hierarchical algorithms provide, on average, an estimated 11% reduction in the number of tests when compared to two-stage algorithms. For applications with rarer infections, we show theoretically that this percentage reduction can be much larger.