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

binGroup2: Statistical Tools for Infection Identification via Group Testing

Group testing is the process of testing items as an amalgamation, rather than separately, to determine the binary status for each item. Its use was especially important during the COVID-19 pandemic through testing specimens for SARS-CoV-2. The adoption of group testing for this and many other applications is because members of a negative testing group can be declared negative with potentially only one test. This subsequently leads to significant increases in laboratory testing capacity. Whenever a group testing algorithm is put into practice, it is critical for laboratories to understand the algorithm's operating characteristics, such as the expected number of tests. Our paper presents the binGroup2 package that provides the statistical tools for this purpose. This R package is the first to address the identification aspect of group testing for a wide variety of algorithms. We illustrate its use through COVID-19 and chlamydia/gonorrhea applications of group testing.

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.

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.

An Expectation Maximization based Adaptive Group Testing Method for Improving Efficiency and Sensitivity of Large-Scale Screening of COVID-19

The pathogen of the ongoing coronavirus disease 2019 (COVID-19) pandemic is a newly discovered virus called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Testing individuals for SARS-CoV-2 plays a critical role in containing COVID-19. For saving medical personnel and consumables, many countries are implementing group testing against SARS-CoV-2. However, existing group testing methods have the following limitations: (1) The group size is determined without theoretical analysis, and hence is usually not optimal. This adversely impacts the screening efficiency. (2) These methods neglect the fact that mixing samples together usually leads to substantial dilution of the SARS-CoV-2 virus, which seriously impacts the sensitivity of tests. In this paper, we aim to screen individuals infected with COVID-19 with as few tests as possible, under the premise that the sensitivity of tests is high enough. We propose an eXpectation Maximization based Adaptive Group Testing (XMAGT) method. The basic idea is to adaptively adjust its testing strategy between a group testing strategy and an individual testing strategy such that the expected number of samples identified by a single test is larger. During the screening process, the XMAGT method can estimate the ratio of positive samples. With this ratio, the XMAGT method can determine a group size under which the group testing strategy can achieve a maximal expected number of negative samples and the sensitivity of tests is higher than a user-specified threshold. Experimental results show that the XMAGT method outperforms existing methods in terms of both efficiency and sensitivity.

Group Testing for SARS-CoV-2 Allows for Up to 10-Fold Efficiency Increase Across Realistic Scenarios and Testing Strategies

Background: Due to the ongoing COVID-19 pandemic, demand for diagnostic testing has increased drastically, resulting in shortages of necessary materials to conduct the tests and overwhelming the capacity of testing laboratories. The supply scarcity and capacity limits affect test administration: priority must be given to hospitalized patients and symptomatic individuals, which can prevent the identification of asymptomatic and presymptomatic individuals and hence effective tracking and tracing policies. We describe optimized group testing strategies applicable to SARS-CoV-2 tests in scenarios tailored to the current COVID-19 pandemic and assess significant gains compared to individual testing. Methods: We account for biochemically realistic scenarios in the context of dilution effects on SARS-CoV-2 samples and consider evidence on specificity and sensitivity of PCR-based tests for the novel coronavirus. Because of the current uncertainty and the temporal and spatial changes in the prevalence regime, we provide analysis for several realistic scenarios and propose fast and reliable strategies for massive testing procedures. Key Findings: We find significant efficiency gaps between different group testing strategies in realistic scenarios for SARS-CoV-2 testing, highlighting the need for an informed decision of the pooling protocol depending on estimated prevalence, target specificity, and high- vs. low-risk population. For example, using one of the presented methods, all 1.47 million inhabitants of Munich, Germany, could be tested using only around 141 thousand tests if the infection rate is below 0.4% is assumed. Using 1 million tests, the 6.69 million inhabitants from the city of Rio de Janeiro, Brazil, could be tested as long as the infection rate does not exceed 1%. Moreover, we provide an interactive web application, available at www.grouptexting.com, for visualizing the different strategies and designing pooling schemes according to specific prevalence scenarios and test configurations. Interpretation: Altogether, this work may help provide a basis for an efficient upscaling of current testing procedures, which takes the population heterogeneity into account and is fine-grained towards the desired study populations, e.g., mild/asymptomatic individuals vs. symptomatic ones but also mixtures thereof. Funding: German Science Foundation (DFG), German Federal Ministry of Education and Research (BMBF), Chan Zuckerberg Initiative DAF, and Austrian Science Fund (FWF).

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.

Specimen Pooling to Conserve Additional Testing Resources When Persons' Infection Status Is Correlated: A Simulation Study

In the early stages of a novel pandemic, testing is simultaneously in high demand and low supply, making efficient use of tests of paramount importance. One approach to improve the efficiency of tests is to mix samples from multiple individuals, only testing individuals when the pooled sample returns a positive. To reflect potential clusters of cases that might queue at a testing site and that might increase the efficiency of batch testing, I simulate 10,000 persons being tested in sequence. I use a prevalence ranging from 1% to 45% and batch sizes ranging from 3 to 25 and assume the increased probability of consecutive infections ranges from 0% to 45%. I find that as the likelihood of clustered infections increases, the efficiency of specimen pooling increases. This analysis suggests that when clusters of infected persons exist at testing sites, specimen pooling can remain efficient even as prevalence increases. See video abstract: http://links.lww.com/EDE/B729.

Cost Effectiveness of Sample Pooling to Test for SARS-CoV-2

.

Assessment of Specimen Pooling to Conserve SARS CoV-2 Testing Resources

OBJECTIVES

To establish the optimal parameters for group testing of pooled specimens for the detection of SARS-CoV-2.

METHODS

The most efficient pool size was determined to be five specimens using a web-based application. From this analysis, 25 experimental pools were created using 50 µL from one SARS-CoV-2 positive nasopharyngeal specimen mixed with 4 negative patient specimens (50 µL each) for a total volume of 250 µL. Viral RNA was subsequently extracted from each pool and tested using the CDC SARS-CoV-2 RT-PCR assay. Positive pools were consequently split into individual specimens and tested by extraction and PCR. This method was also tested on an unselected group of 60 nasopharyngeal specimens grouped into 12 pools.

RESULTS

All 25 pools were positive with cycle threshold (Ct) values within 0 and 5.03 Ct of the original individual specimens. The analysis of 60 specimens determined that 2 pools were positive followed by identification of 2 individual specimens among the 60 tested. This testing was accomplished while using 22 extractions/PCR tests, a savings of 38 reactions.

CONCLUSIONS

When the incidence rate of SARS-CoV-2 infection is 10% or less, group testing will result in the saving of reagents and personnel time with an overall increase in testing capability of at least 69%.

Assessment of Specimen Pooling to Conserve SARS CoV-2 Testing Resources

Objectives To establish the optimal parameters for group testing of pooled specimens for the detection of SARS-CoV-2. Methods The most efficient pool size was determined to be 5 specimens using a web-based application. From this analysis, 25 experimental pools were created using 50 microliter from one SARS-CoV-2 positive nasopharyngeal specimen mixed with 4 negative patient specimens (50 microliter each) for a total volume of 250 microliter l. Viral RNA was subsequently extracted from each pool and tested using the CDC SARS-CoV-2 RT-PCR assay. Positive pools were consequently split into individual specimens and tested by extraction and PCR. This method was also tested on an unselected group of 60 nasopharyngeal specimens grouped into 12-pools. Results All 25 pools were positive with Cycle threshold (Ct) values within 0 and 5.03 Ct of the original individual specimens. The analysis of 60 specimens determined that two pools were positive followed by identification of two individual specimens among the 60 tested. This testing was accomplished while using 22 extractions/PCR tests, a savings of 38 reactions. Conclusions When the incidence rate of SARS-CoV-2 infection is 10% or less, group testing will result in the saving of reagents and personnel time with an overall increase in testing capability of at least 69%.