Comparison of Group Testing Algorithms for Case Identification in the Presence of Test Error

Semi-quantitative group testing for efficient and accurate qPCR screening of pathogens with a wide range of loads

BACKGROUND

Pathogenic infections pose a significant threat to global health, affecting millions of people every year and presenting substantial challenges to healthcare systems worldwide. Efficient and timely testing plays a critical role in disease control and transmission prevention. Group testing is a well-established method for reducing the number of tests needed to screen large populations when the disease prevalence is low. However, it does not fully utilize the quantitative information provided by qPCR methods, nor is it able to accommodate a wide range of pathogen loads.

RESULTS

To address these issues, we introduce a novel adaptive semi-quantitative group testing (SQGT) scheme to efficiently screen populations via two-stage qPCR testing. The SQGT method quantizes cycle threshold (Ct) values into multiple bins, leveraging the information from the first stage of screening to improve the detection sensitivity. Dynamic Ct threshold adjustments mitigate dilution effects and enhance test accuracy. Comparisons with traditional binary outcome GT methods show that SQGT reduces the number of tests by 24% on the only complete real-world qPCR group testing dataset from Israel, while maintaining a negligible false negative rate.

CONCLUSION

In conclusion, our adaptive SQGT approach, utilizing qPCR data and dynamic threshold adjustments, offers a promising solution for efficient population screening. With a reduction in the number of tests and minimal false negatives, SQGT holds potential to enhance disease control and testing strategies on a global scale.

Estimation of odds ratio from group testing data with misclassified exposure

For low prevalence disease, we consider estimation of the odds ratio for two specified groups of individuals using group testing data. Broadly the two groups may be classified as "the exposed" and "the unexposed." Often in observational studies, the exposure status is not correctly recorded. In addition, diagnostic tests are rarely completely accurate. The proposed model accounts for imperfect sensitivity and specificity of diagnostic tests along with the misclassification in the exposure status. For model identifiability, we make use of internal validation data, where a subsample of reasonably small size is selected from the original sample by simple random sampling without replacement. Pseudo-maximum likelihood method is employed for the estimation of the model parameters. The performance of group testing methodology is compared with individual testing for different parametric configurations. A limited data study related to COVID-19 prevalence is performed to illustrate the methodology.

Bayesian group testing with dilution effects

A Bayesian framework for group testing under dilution effects has been developed, using lattice-based models. This work has particular relevance given the pressing public health need to enhance testing capacity for coronavirus disease 2019 and future pandemics, and the need for wide-scale and repeated testing for surveillance under constantly varying conditions. The proposed Bayesian approach allows for dilution effects in group testing and for general test response distributions beyond just binary outcomes. It is shown that even under strong dilution effects, an intuitive group testing selection rule that relies on the model order structure, referred to as the Bayesian halving algorithm, has attractive optimal convergence properties. Analogous look-ahead rules that can reduce the number of stages in classification by selecting several pooled tests at a time are proposed and evaluated as well. Group testing is demonstrated to provide great savings over individual testing in the number of tests needed, even for moderately high prevalence levels. However, there is a trade-off with higher number of testing stages, and increased variability. A web-based calculator is introduced to assist in weighing these factors and to guide decisions on when and how to pool under various conditions. High-performance distributed computing methods have also been implemented for considering larger pool sizes, when savings from group testing can be even more dramatic.

Estimating the prevalence of two or more diseases using outcomes from multiplex group testing

When screening a population for infectious diseases, pooling individual specimens (e.g., blood, swabs, urine, etc.) can provide enormous cost savings when compared to testing specimens individually. In the biostatistics literature, testing pools of specimens is commonly known as group testing or pooled testing. Although estimating a population-level prevalence with group testing data has received a large amount of attention, most of this work has focused on applications involving a single disease, such as human immunodeficiency virus. Modern methods of screening now involve testing pools and individuals for multiple diseases simultaneously through the use of multiplex assays. Hou et al. (2017, Biometrics, 73, 656-665) and Hou et al. (2020, Biostatistics, 21, 417-431) recently proposed group testing protocols for multiplex assays and derived relevant case identification characteristics, including the expected number of tests and those which quantify classification accuracy. In this article, we describe Bayesian methods to estimate population-level disease probabilities from implementing these protocols or any other multiplex group testing protocol which might be carried out in practice. Our estimation methods can be used with multiplex assays for two or more diseases while incorporating the possibility of test misclassification for each disease. We use chlamydia and gonorrhea testing data collected at the State Hygienic Laboratory at the University of Iowa to illustrate our work. We also provide an online R resource practitioners can use to implement the methods in this article.

Seasonal Patterns in the Frequency of Candidatus Liberibacter Asiaticus in Populations of Diaphorina citri (Hemiptera: Psyllidae) in Florida

Candidatus Liberibacter asiaticus (CLas) is one of the putative causal agents of huanglongbing, which is a serious disease in citrus production. The pathogen is transmitted by Diaphorina citri Kuwayama (Hemiptera: Psyllidae). As an observational study, six groves in central Florida and one grove at the southern tip of Florida were sampled monthly from January 2008 through February 2012 (50 months). The collected psyllids were sorted by sex and abdominal color. Disease prevalence in adults peaked in November, with a minor peak in February. Gray/brown females had the highest prevalence, and blue/green individuals of either sex had the lowest prevalence. CLas prevalence in blue/green females was highly correlated with the prevalence in other sexes and colors. Thus, the underlying causes for seasonal fluctuations in prevalence operated in a similar fashion for all psyllids. The pattern was caused by larger nymphs displacing smaller ones from the optimal feeding sites and immunological robustness in different sex-color morphotypes. Alternative hypotheses were also considered. Improving our understanding of biological interactions and how to sample them will improve management decisions. We agree with other authors that psyllid management is critical year-round.

Statistical modeling and evaluation of the impact of multiplicity classification thresholds on the COVID-19 pool testing accuracy

Prior research on pool testing focus on developing testing methods with the main objective of reducing the total number of tests. However, pool testing can also be used to improve the accuracy of the testing process. The objective of this paper is to improve the accuracy of pool testing using the same number of tests as that of individual testing taking into consideration the probability of testing errors and pool multiplicity classification thresholds. Statistical models are developed to evaluate the impact of pool multiplicity classiffcation thresholds on pool testing accuracy using the receiver operating characteristic (ROC) curve and the area under the curve (AUC). The findings indicate that under certain conditions, pool testing multiplicity yields superior testing accuracy compared to individual testing without additional cost. The results reveal that selecting the multiplicity classification threshold is a critical factor in improving the pool testing accuracy and show that the lower the prevalence level the higher the gains in accuracy using multiplicity pool testing. The findings also indicate that performance can be improved using a batch size that is inversely proportional to the prevalence level. Furthermore, the results indicate that multiplicity pool testing not only improves the testing accuracy but also reduces the total cost of the testing process. Based on the findings, the manufacturer's test sensitivity has more significant impact on the accuracy of multiplicity pool testing compared to that of manufacturer's test specificity.

Effective matrix designs for COVID-19 group testing

BACKGROUND

Grouping samples with low prevalence of positives into pools and testing these pools can achieve considerable savings in testing resources compared with individual testing in the context of COVID-19. We review published pooling matrices, which encode the assignment of samples into pools and describe decoding algorithms, which decode individual samples from pools. Based on the findings we propose new one-round pooling designs with high compression that can efficiently be decoded by combinatorial algorithms. This expands the admissible parameter space for the construction of pooling matrices compared to current methods.

RESULTS

By arranging samples in a grid and using polynomials to construct pools, we develop direct formulas for an Algorithm (Polynomial Pools (PP)) to generate assignments of samples into pools. Designs from PP guarantee to correctly decode all samples with up to a specified number of positive samples. PP includes recent combinatorial methods for COVID-19, and enables new constructions that can result in more effective designs.

CONCLUSION

For low prevalences of COVID-19, group tests can save resources when compared to individual testing. Constructions from the recent literature on combinatorial methods have gaps with respect to the designs that are available. We develop a method (PP), which generalizes previous constructions and enables new designs that can be advantageous in various situations.

Novel application of one-step pooled molecular testing and maximum likelihood approaches to estimate the prevalence of malaria parasitaemia among rapid diagnostic test negative samples in western Kenya

Background

Detection of malaria parasitaemia in samples that are negative by rapid diagnostic tests (RDTs) requires resource-intensive molecular tools. While pooled testing using a two-step strategy provides a cost-saving alternative to the gold standard of individual sample testing, statistical adjustments are needed to improve accuracy of prevalence estimates for a single step pooled testing strategy.

Methods

A random sample of 4670 malaria RDT negative dried blood spot samples were selected from a mass testing and treatment trial in Asembo, Gem, and Karemo, western Kenya. Samples were tested for malaria individually and in pools of five, 934 pools, by one-step quantitative polymerase chain reaction (qPCR). Maximum likelihood approaches were used to estimate subpatent parasitaemia (RDT-negative, qPCR-positive) prevalence by pooling, assuming poolwise sensitivity and specificity was either 100% (strategy A) or imperfect (strategy B). To improve and illustrate the practicality of this estimation approach, a validation study was constructed from pools allocated at random into main (734 pools) and validation (200 pools) subsets. Prevalence was estimated using strategies A and B and an inverse-variance weighted estimator and estimates were weighted to account for differential sampling rates by area.

Results

The prevalence of subpatent parasitaemia was 14.5% (95% CI 13.6–15.3%) by individual qPCR, 9.5% (95% CI (8.5–10.5%) by strategy A, and 13.9% (95% CI 12.6–15.2%) by strategy B. In the validation study, the prevalence by individual qPCR was 13.5% (95% CI 12.4–14.7%) in the main subset, 8.9% (95% CI 7.9–9.9%) by strategy A, 11.4% (95% CI 9.9–12.9%) by strategy B, and 12.8% (95% CI 11.2–14.3%) using inverse-variance weighted estimator from poolwise validation. Pooling, including a 20% validation subset, reduced costs by 52% compared to individual testing.

Conclusions

Compared to individual testing, a one-step pooled testing strategy with an internal validation subset can provide accurate prevalence estimates of PCR-positivity among RDT-negatives at a lower cost.

Capturing the pool dilution effect in group testing regression: A Bayesian approach

Group (pooled) testing is becoming a popular strategy for screening large populations for infectious diseases. This popularity is owed to the cost savings that can be realized through implementing group testing methods. These methods involve physically combining biomaterial (eg, saliva, blood, urine) collected on individuals into pooled specimens which are tested for an infection of interest. Through testing these pooled specimens, group testing methods reduce the cost of diagnosing all individuals under study by reducing the number of tests performed. Even though group testing offers substantial cost reductions, some practitioners are hesitant to adopt group testing methods due to the so-called dilution effect. The dilution effect describes the phenomenon in which biomaterial from negative individuals dilute the contributions from positive individuals to such a degree that a pool is incorrectly classified. Ignoring the dilution effect can reduce classification accuracy and lead to bias in parameter estimates and inaccurate inference. To circumvent these issues, we propose a Bayesian regression methodology which directly acknowledges the dilution effect while accommodating data that arises from any group testing protocol. As a part of our estimation strategy, we are able to identify pool specific optimal classification thresholds which are aimed at maximizing the classification accuracy of the group testing protocol being implemented. These two features working in concert effectively alleviate the primary concerns raised by practitioners regarding group testing. The performance of our methodology is illustrated via an extensive simulation study and by being applied to Hepatitis B data collected on Irish prisoners.

Nested Group Testing Procedure

We investigated the false-negative, true-negative, false-positive, and true-positive predictive values from a general group testing procedure for a heterogeneous population. We show that its false (true)-negative predictive value of a specimen is larger (smaller), and the false (true)-positive predictive value is smaller (larger) than that from individual testing procedure, where the former is in aversion. Then we propose a nested group testing procedure, and show that it can keep the sterling characteristics and also improve the false-negative predictive values for a specimen, not larger than that from individual testing. These characteristics are studied from both theoretical and numerical points of view. The nested group testing procedure is better than individual testing on both false-positive and false-negative predictive values, while retains the efficiency as a basic characteristic of a group testing procedure. Applications to Dorfman's, Halving and Sterrett procedures are discussed. Results from extensive simulation studies and an application to malaria infection in microscopy-negative Malawian women exemplify the findings.

Optimizing Pooled Testing for Estimating the Prevalence of Multiple Diseases

Pooled testing can enhance the efficiency of diagnosing individuals with diseases of low prevalence. Often, pooling is implemented using standard groupings (2, 5, 10, etc.). On the other hand, optimization theory can provide specific guidelines in finding the ideal pool size and pooling strategy. This article focuses on optimizing the precision of disease prevalence estimators calculated from multiplex pooled testing data. In the context of a surveillance application of animal diseases, we study the estimation efficiency (i.e., precision) and cost efficiency of the estimators with adjustments for the number of expended tests. This enables us to determine the pooling strategies that offer the highest benefits when jointly estimating the prevalence of multiple diseases, such as theileriosis and anaplasmosis. The outcomes of our work can be used in designing pooled testing protocols, not only in simple pooling scenarios but also in more complex scenarios where individual retesting is performed in order to identify positive cases. A software application using the shiny package in R is provided with this article to facilitate implementation of our methods. Supplementary materials accompanying this paper appear online.

covidscreen: a web app and R Package for assessing asymptomatic COVID-19 testing strategies

Background

COVID-19 has caused over 305 million infections and nearly 5.5 million deaths globally. With complete eradication unlikely, organizations will need to evaluate their risk and the benefits of mitigation strategies, including the effects of regular asymptomatic testing. We developed a web application and R package that provides estimates and visualizations to aid the assessment of organizational infection risk and testing benefits to facilitate decision-making, which combines internal and community information with malleable assumptions.

Results

Our web application, covidscreen, presents estimated values of risk metrics in an intuitive graphical format. It shows the current expected number of active, primarily community-acquired infections among employees in an organization. It calculates and explains the absolute and relative risk reduction of an intervention, relative to the baseline scenario, and shows the value of testing vaccinated and unvaccinated employees. In addition, the web interface allows users to profile risk over a chosen range of input values. The performance and output are illustrated using simulations and a real-world example from the employee testing program of a pediatric oncology specialty hospital.

Conclusions

As the COVID-19 pandemic continues to evolve, covidscreen can assist organizations in making informed decisions about whether to incorporate covid test based screening as part of their on-campus risk-mitigation strategy. The web application, R package, and source code are freely available online (see “Availability of data and materials”).

Supplementary Information

The online version contains supplementary material available at 10.1186/s12889-022-13718-4.

Group testing via hypergraph factorization applied to COVID-19

Large scale screening is a critical tool in the life sciences, but is often limited by reagents, samples, or cost. An important recent example is the challenge of achieving widespread COVID-19 testing in the face of substantial resource constraints. To tackle this challenge, screening methods must efficiently use testing resources. However, given the global nature of the pandemic, they must also be simple (to aid implementation) and flexible (to be tailored for each setting). Here we propose HYPER, a group testing method based on hypergraph factorization. We provide theoretical characterizations under a general statistical model, and carefully evaluate HYPER with alternatives proposed for COVID-19 under realistic simulations of epidemic spread and viral kinetics. We find that HYPER matches or outperforms the alternatives across a broad range of testing-constrained environments, while also being simpler and more flexible. We provide an online tool to aid lab implementation: http://hyper.covid19-analysis.org .

Real-world Evaluation of a Sample Pooling Strategy for Large-Scale Rapid COVID-19 Testing

Background

The worldwide outbreak of COVID-19 has become a public health crisis of unprecedented proportions. The fast spread of emerging variants increases the needs of rapid diagnostic and screening testing. Sample pooling efficiently expands the testing capacity under limited resources.

Objectives

We evaluated the performance of sample pooling on the Point-of-Care (POC) Liat® and cobas® 6800 systems and provided real-world experiences for implementing these systems in large-scale screenings.

Methods

Positive nasopharyngeal (NP) specimens with Ct values < 25, 25∼30 or > 30 were tested individually and in pools to optimize the POC Liat® and cobas® 6800 systems, which were then implemented in community screenings.

Results

The 5-sample pooling strategy did not affect the positive detection rates on Liat® or cobas® 6800 in samples with Ct values <25 or 25∼30. However, in samples with low viral loads (Ct values >30), five-sample pooling has a higher positive detection rate on POC Liat® (20/20; 100%), compared to cobas® 6800 (9/20; 45%). Five-sample pooled on POC Liat® and two-sample pooled on cobas® 6800 appear to be appropriate for SARS-CoV-2 detection. By implementing the pooling strategies in two large-scale community screenings, 7,606 NP specimens was tested within 36 h; the average turn-around time was 4.8 h for cobas® 6800 and 1.3 h for POC Liat®. Eight positive specimens (0.11%; 8/7,606) were identified, with Ct values ranging from 18.85 to 37.68.

Conclusion

The performance of sample pooling on POC Liat® was demonstrated to be an effective, accurate, and economical approach for large-scale community screenings for COVID-19.

Screening multi-dimensional heterogeneous populations for infectious diseases under scarce testing resources, with application to COVID-19

Testing provides essential information for managing infectious disease outbreaks, such as the COVID-19 pandemic. When testing resources are scarce, an important managerial decision is who to test. This decision is compounded by the fact that potential testing subjects are heterogeneous in multiple dimensions that are important to consider, including their likelihood of being disease-positive, and how much potential harm would be averted through testing and the subsequent interventions. To increase testing coverage, pooled testing can be utilized, but this comes at a cost of increased false-negatives when the test is imperfect. Then, the decision problem is to partition the heterogeneous testing population into three mutually exclusive sets: those to be individually tested, those to be pool tested, and those not to be tested. Additionally, the subjects to be pool tested must be further partitioned into testing pools, potentially containing different numbers of subjects. The objectives include the minimization of harm (through detection and mitigation) or maximization of testing coverage. We develop data-driven optimization models and algorithms to design pooled testing strategies, and show, via a COVID-19 contact tracing case study, that the proposed testing strategies can substantially outperform the current practice used for COVID-19 contact tracing (individually testing those contacts with symptoms). Our results demonstrate the substantial benefits of optimizing the testing design, while considering the multiple dimensions of population heterogeneity and the limited testing capacity.

Pooled testing efficiency increases with test frequency

Pooled testing increases efficiency by grouping individual samples and testing the combined sample, such that many individuals can be cleared with one negative test. This short paper demonstrates that pooled testing is particularly advantageous in the setting of pandemics, given repeated testing, rapid spread, and uncertain risk. Repeated testing mechanically lowers the infection probability at the time of the next test by removing positives from the population. This effect alone means that increasing frequency by x times only increases expected tests by around [Formula: see text] However, this calculation omits a further benefit of frequent testing: Removing infections from the population lowers intragroup transmission, which lowers infection probability and generates further efficiency. For this reason, increasing testing frequency can paradoxically reduce total testing cost. Our calculations are based on the assumption that infection rates are known, but predicting these rates is challenging in a fast-moving pandemic. However, given that frequent testing naturally suppresses the mean and variance of infection rates, we show that our results are very robust to uncertainty and misprediction. Finally, we note that efficiency further increases given natural sampling pools (e.g., workplaces, classrooms) that induce correlated risk via local transmission. We conclude that frequent pooled testing using natural groupings is a cost-effective way to provide consistent testing of a population to suppress infection risk in a pandemic.

BAYESIAN GROUP TESTING WITH DILUTION EFFECTS

A Bayesian framework for group testing under dilution effects has been developed, using lattice-based models. This work has particular relevance given the pressing public health need to enhance testing capacity for COVID-19 and future pandemics, and the need for wide-scale and repeated testing for surveillance under constantly varying conditions. The proposed Bayesian approach allows for dilution effects in group testing and for general test response distributions beyond just binary outcomes. It is shown that even under strong dilution effects, an intuitive group testing selection rule that relies on the model order structure, referred to as the Bayesian halving algorithm, has attractive optimal convergence properties. Analogous look-ahead rules that can reduce the number of stages in classification by selecting several pooled tests at a time are proposed and evaluated as well. Group testing is demonstrated to provide great savings over individual testing in the number of tests needed, even for moderately high prevalence levels. However, there is a trade-off with higher number of testing stages, and increased variability. A web-based calculator is introduced to assist in weighing these factors and to guide decisions on when and how to pool under various conditions. High performance distributed computing methods have also been implemented for considering larger pool sizes, when savings from group testing can be even more dramatic.

An accurate model for SARS-CoV-2 pooled RT-PCR test errors

Pooling is a method of simultaneously testing multiple samples for the presence of pathogens. Pooling of SARS-CoV-2 tests is increasing in popularity, due to its high testing throughput. A popular pooling scheme is Dorfman pooling: test N individuals simultaneously, if the test is positive, each individual is then tested separately; otherwise, all are declared negative. Most analyses of the error rates of pooling schemes assume that including more than a single infected sample in a pooled test does not increase the probability of a positive outcome. We challenge this assumption with experimental data and suggest a novel and parsimonious probabilistic model for the outcomes of pooled tests. As an application, we analyse the false-negative rate (i.e. the probability of a negative result for an infected individual) of Dorfman pooling. We show that the false-negative rates under Dorfman pooling increase when the prevalence of infection decreases. However, low infection prevalence is exactly the condition when Dorfman pooling achieves highest throughput efficiency. We therefore urge the cautious use of pooling and development of pooling schemes that consider correctly accounting for tests' error rates.

Generalized additive regression for group testing data

In screening applications involving low-prevalence diseases, pooling specimens (e.g., urine, blood, swabs, etc.) through group testing can be far more cost effective than testing specimens individually. Estimation is a common goal in such applications and typically involves modeling the probability of disease as a function of available covariates. In recent years, several authors have developed regression methods to accommodate the complex structure of group testing data but often under the assumption that covariate effects are linear. Although linearity is a reasonable assumption in some applications, it can lead to model misspecification and biased inference in others. To offer a more flexible framework, we propose a Bayesian generalized additive regression approach to model the individual-level probability of disease with potentially misclassified group testing data. Our approach can be used to analyze data arising from any group testing protocol with the goal of estimating multiple unknown smooth functions of covariates, standard linear effects for other covariates, and assay classification accuracy probabilities. We illustrate the methods in this article using group testing data on chlamydia infection in Iowa.

Nested pool testing strategy for the diagnosis of infectious diseases

The progress of the SARS-CoV-2 pandemic requires the design of large-scale, cost-effective testing programs. Pooling samples provides a solution if the tests are sensitive enough. In this regard, the use of the gold standard, RT-qPCR, raises some concerns. Recently, droplet digital PCR (ddPCR) was shown to be 10-100 times more sensitive than RT-qPCR, making it more suitable for pooling. Furthermore, ddPCR quantifies the RNA content directly, a feature that, as we show, can be used to identify nonviable samples in pools. Cost-effective strategies require the definition of efficient deconvolution and re-testing procedures. In this paper we analyze the practical implementation of an efficient hierarchical pooling strategy for which we have recently derived the optimal, determining the best ways to proceed when there are impediments for the use of the absolute optimum or when multiple pools are tested simultaneously and there are restrictions on the throughput time. We also show how the ddPCR RNA quantification and the nested nature of the strategy can be combined to perform self-consistency tests for a better identification of infected individuals and nonviable samples. The studies are useful to those considering pool testing for the identification of infected individuals.

Prediction-driven pooled testing methods: Application to HIV treatment monitoring in Rakai, Uganda

Chronic medical conditions often necessitate regular testing for proper treatment. Regular testing of all afflicted individuals may not be feasible due to limited resources, as is true with HIV monitoring in resource-limited settings. Pooled testing methods have been developed in order to allow regular testing for all while reducing resource burden. However, the most commonly used methods do not make use of covariate information predictive of treatment failure, which could improve performance. We propose and evaluate four prediction-driven pooled testing methods that incorporate covariate information to improve pooled testing performance. We then compare these methods in the HIV treatment management setting to current methods with respect to testing efficiency, sensitivity, and number of testing rounds using simulated data and data collected in Rakai, Uganda. Results show that the prediction-driven methods increase efficiency by up to 20% compared with current methods while maintaining equivalent sensitivity and reducing number of testing rounds by up to 70%. When predictions were incorrect, the performance of prediction-based matrix methods remained robust. The best performing method using our motivating data from Rakai was a prediction-driven hybrid method, maintaining sensitivity over 96% and efficiency over 75% in likely scenarios. If these methods perform similarly in the field, they may contribute to improving mortality and reducing transmission in resource-limited settings. Although we evaluate our proposed pooling methods in the HIV treatment setting, they can be applied to any setting that necessitates testing of a quantitative biomarker for a threshold-based decision.

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).

DOPE: D-Optimal Pooling Experimental design with application for SARS-CoV-2 screening

OBJECTIVE

Testing individuals for the presence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the pathogen causing the coronavirus disease 2019 (COVID-19), is crucial for curtailing transmission chains. Moreover, rapidly testing many potentially infected individuals is often a limiting factor in controlling COVID-19 outbreaks. Hence, pooling strategies, wherein individuals are grouped and tested simultaneously, are employed. Here, we present a novel pooling strategy that builds on the Bayesian D-optimal experimental design criterion.

MATERIALS AND METHODS

Our strategy, called DOPE (D-Optimal Pooling Experimental design), is built on a novel Bayesian formulation of pooling. DOPE defines optimal pooled tests as those maximizing the mutual information between data and infection states. We estimate said mutual information via Monte-Carlo sampling and employ a discrete optimization heuristic to maximize it.

RESULTS

We compare DOPE to other, commonly used pooling strategies, as well as to individual testing. DOPE dominates the other strategies as it yields lower error rates while utilizing fewer tests. We show that DOPE maintains this dominance for a variety of infection prevalence values.

DISCUSSION

DOPE has several additional advantages over common pooling strategies: it provides posterior distributions of the probability of infection, rather than only binary classification outcomes; it naturally incorporates prior information of infection probabilities and test error rates; and finally, it can be easily extended to include other, newly discovered information regarding COVID-19.

CONCLUSION

DOPE can substantially improve accuracy and throughput over current pooling strategies. Hence, DOPE can facilitate rapid testing and aid the efforts of combating COVID-19 and other future pandemics.

Array testing for multiplex assays

Group testing involves pooling individual specimens (e.g., blood, urine, swabs, etc.) and testing the pools for the presence of disease. When the proportion of diseased individuals is small, group testing can greatly reduce the number of tests needed to screen a population. Statistical research in group testing has traditionally focused on applications for a single disease. However, blood service organizations and large-scale disease surveillance programs are increasingly moving towards the use of multiplex assays, which measure multiple disease biomarkers at once. Tebbs and others (2013, Two-stage hierarchical group testing for multiple infections with application to the Infertility Prevention Project. Biometrics69, 1064-1073) and Hou and others (2017, Hierarchical group testing for multiple infections. Biometrics73, 656-665) were the first to examine hierarchical group testing case identification procedures for multiple diseases. In this article, we propose new non-hierarchical procedures which utilize two-dimensional arrays. We derive closed-form expressions for the expected number of tests per individual and classification accuracy probabilities and show that array testing can be more efficient than hierarchical procedures when screening individuals for multiple diseases at once. We illustrate the potential of using array testing in the detection of chlamydia and gonorrhea for a statewide screening program in Iowa. Finally, we describe an R/Shiny application that will help practitioners identify the best multiple-disease case identification algorithm.

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.

Informative array testing with multiplex assays

High-volume testing of clinical specimens for sexually transmitted diseases is performed frequently by a process known as group testing. This algorithmic process involves testing portions of specimens from separate individuals together as one unit (or "group") to detect diseases. Retesting is performed on groups that test positively in order to differentiate between positive and negative individual specimens. The overall goal is to use the least number of tests possible across all individuals without sacrificing diagnostic accuracy. One of the most efficient group testing algorithms is array testing. In its simplest form, specimens are arranged into a grid-like structure so that row and column groups can be formed. Positive-testing rows/columns indicate which specimens to retest. With the growing use of multiplex assays, the increasing number of diseases tested by these assays, and the availability of subject-specific risk information, opportunities exist to make this testing process even more efficient. We propose specific specimen arrangements within an array that can reduce the number of retests needed when compared with other array testing algorithms. We examine how to calculate operating characteristics, including the expected number of tests and the SD for the number of tests, and then subsequently find a best arrangement. Our methods are illustrated for chlamydia and gonorrhea detection with the Aptima Combo 2 Assay. We also provide R functions to make our research accessible to laboratories.

Incorporating the dilution effect in group testing regression

When screening for infectious diseases, group testing has proven to be a cost efficient alternative to individual level testing. Cost savings are realized by testing pools of individual specimens (eg, blood, urine, saliva, and so on) rather than by testing the specimens separately. However, a common concern that arises in group testing is the so-called "dilution effect." This occurs if the signal from a positive individual's specimen is diluted past an assay's threshold of detection when it is pooled with multiple negative specimens. In this article, we propose a new statistical framework for group testing data that merges estimation and case identification, which are often treated separately in the literature. Our approach considers analyzing continuous biomarker levels (eg, antibody levels, antigen concentrations, and so on) from pooled samples to estimate both a binary regression model for the probability of disease and the biomarker distributions for cases and controls. To increase case identification accuracy, we then show how estimates of the biomarker distributions can be used to select diagnostic thresholds on a pool-by-pool basis. Our proposals are evaluated through numerical studies and are illustrated using hepatitis B virus data collected on a prison population in Ireland.

Active Surveillance of Asymptomatic, Presymptomatic, and Oligosymptomatic SARS-CoV-2-Infected Individuals in Communities Inhabiting Closed or Semi-closed Institutions

Background: The high COVID-19 dissemination rate demands active surveillance to identify asymptomatic, presymptomatic, and oligosymptomatic (APO) SARS-CoV-2-infected individuals. This is of special importance in communities inhabiting closed or semi-closed institutions such as residential care homes, prisons, neuropsychiatric hospitals, etc., where risk people are in close contact. Thus, a pooling approach-where samples are mixed and tested as single pools-is an attractive strategy to rapidly detect APO-infected in these epidemiological scenarios. Materials and Methods: This study was done at different pandemic periods between May 28 and August 31 2020 in 153 closed or semi-closed institutions in the Province of Buenos Aires (Argentina). We setup pooling strategy in two stages: first a pool-testing followed by selective individual-testing according to pool results. Samples included in negative pools were presumed as negative, while samples from positive pools were re-tested individually for positives identification. Results: Sensitivity in 5-sample or 10-sample pools was adequate since only 2 Ct values were increased with regard to single tests on average. Concordance between 5-sample or 10-sample pools and individual-testing was 100% in the Ct ≤ 36. We tested 4,936 APO clinical samples in 822 pools, requiring 86-50% fewer tests in low-to-moderate prevalence settings compared to individual testing. Conclusions: By this strategy we detected three COVID-19 outbreaks at early stages in these institutions, helping to their containment and increasing the likelihood of saving lives in such places where risk groups are concentrated.

Considerations for Pooled Testing of Employees for SARS-CoV-2

OBJECTIVES

To identify important background information on pooled tested of employees that employers workers, and health authorities should consider.

METHODS

This paper is a commentary based on the review by the authors of pertinent literature generally from preprints in medrixiv.org prior to August 2020.

RESULTS/CONCLUSIONS

Pooled testing may be particularly useful to employers in communities with low prevalence of COVID-19. It can be used to reduce the number of tests and associated financial costs. For effective and efficient pooled testing employers should consider it as part of a broader, more comprehensive workplace COVID-19 prevention and control program. Pooled testing of asymptomatic employees can prevent transmission of SARS-CoV-2 and help assure employers and customers that employees are not infectious.

Boosting test-efficiency by pooled testing for SARS-CoV-2-Formula for optimal pool size

In the current COVID19 crisis many national healthcare systems are confronted with an acute shortage of tests for confirming SARS-CoV-2 infections. For low overall infection levels in the population the pooling of samples can drastically amplify the testing capacity. Here we present a formula to estimate the optimal group-size for pooling, the efficiency gain (tested persons per test), and the expected upper bound of missed infections in pooled testing, all as a function of the population-wide infection levels and the false negative/positive rates of the currently used PCR tests. Assuming an infection level of 0.1% and a false negative rate of 2%, the optimal pool-size is about 34, and an efficiency gain of about 15 tested persons per test is possible. For an infection level of 1% the optimal pool-size is 11, the efficiency gain is 5.1 tested persons per test. For an infection level of 10% the optimal pool-size reduces to about 4, the efficiency gain is about 1.7 tested persons per test. For infection levels of 30% and higher there is no more benefit from pooling. To see to what extent replicates of the pooled tests improve the estimate of the maximal number of missed infections, we present results for 1 to 5 replicates.

From mixed effects modeling to spike and slab variable selection: A Bayesian regression model for group testing data

Due to reductions in both time and cost, group testing is a popular alternative to individual-level testing for disease screening. These reductions are obtained by testing pooled biospecimens (eg, blood, urine, swabs, etc.) for the presence of an infectious agent. However, these reductions come at the expense of data complexity, making the task of conducting disease surveillance more tenuous when compared to using individual-level data. This is because an individual's disease status may be obscured by a group testing protocol and the effect of imperfect testing. Furthermore, unlike individual-level testing, a given participant could be involved in multiple testing outcomes and/or may never be tested individually. To circumvent these complexities and to incorporate all available information, we propose a Bayesian generalized linear mixed model that accommodates data arising from any group testing protocol, estimates unknown assay accuracy probabilities and accounts for potential heterogeneity in the covariate effects across population subgroups (eg, clinic sites, etc.); this latter feature is of key interest to practitioners tasked with conducting disease surveillance. To achieve model selection, our proposal uses spike and slab priors for both fixed and random effects. The methodology is illustrated through numerical studies and is applied to chlamydia surveillance data collected in Iowa.

Incorporating retesting outcomes for estimation of disease prevalence

Group testing has been widely used as a cost-effective strategy to screen for and estimate the prevalence of a rare disease. While it is well-recognized that retesting is necessary for identifying infected subjects, it is not required for estimating the prevalence. For a test without misclassification, gains in statistical efficiency are expected from incorporating retesting results in the estimation of the prevalence. However, when the test is subject to misclassification, it is not clear how much gain should be expected. There are a number of theoretical challenges in addressing this issue, including (1) enumerating the potential test results from retesting individual subjects in a group, (2) the dependence among these test results and the test result from testing at the group level, and (3) differential misclassification due to pooling of biospecimens. Overcoming some of these challenges, we show that retesting subjects in either positive or negative groups can substantially improve the efficiency of the estimation and that retesting positive groups yields higher efficiency than retesting a same number or proportion of negative groups.

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.

Regression analysis and variable selection for two-stage multiple-infection group testing data

Group testing, as a cost-effective strategy, has been widely used to perform large-scale screening for rare infections. Recently, the use of multiplex assays has transformed the goal of group testing from detecting a single disease to diagnosing multiple infections simultaneously. Existing research on multiple-infection group testing data either exclude individual covariate information or ignore possible retests on suspicious individuals. To incorporate both, we propose a new regression model. This new model allows us to perform a regression analysis for each infection using multiple-infection group testing data. Furthermore, we introduce an efficient variable selection method to reveal truly relevant risk factors for each disease. Our methodology also allows for the estimation of the assay sensitivity and specificity when they are unknown. We examine the finite sample performance of our method through extensive simulation studies and apply it to a chlamydia and gonorrhea screening data set to illustrate its practical usefulness.

Adaptive elastic net for group testing

For disease screening, group (pooled) testing can be a cost-saving alternative to one-at-a-time testing, with savings realized through assaying pooled biospecimen (eg, urine, blood, saliva). In many group testing settings, practitioners are faced with the task of conducting disease surveillance. That is, it is often of interest to relate individuals' true disease statuses to covariate information via binary regression. Several authors have developed regression methods for group testing data, which is challenging due to the effects of imperfect testing. That is, all testing outcomes (on pools and individuals) are subject to misclassification, and individuals' true statuses are never observed. To further complicate matters, individuals may be involved in several testing outcomes. For analyzing such data, we provide a novel regression methodology which generalizes and extends the aforementioned regression techniques and which incorporates regularization. Specifically, for model fitting and variable selection, we propose an adaptive elastic net estimator under the logistic regression model which can be used to analyze data from any group testing strategy. We provide an efficient algorithm for computing the estimator along with guidance on tuning parameter selection. Moreover, we establish the asymptotic properties of the proposed estimator and show that it possesses "oracle" properties. We evaluate the performance of the estimator through Monte Carlo studies and illustrate the methodology on a chlamydia data set from the State Hygienic Laboratory in Iowa City.

Estimation of log-odds ratio from group testing data using Firth correction

We consider the estimation of the prevalence of a rare disease, and the log-odds ratio for two specified groups of individuals from group testing data. For a low-prevalence disease, the maximum likelihood estimate of the log-odds ratio is severely biased. However, Firth correction to the score function leads to a considerable improvement of the estimator. Also, for a low-prevalence disease, if the diagnostic test is imperfect, the group testing is found to yield more precise estimate of the log-odds ratio than the individual testing.

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.

Bayesian regression for group testing data

Group testing involves pooling individual specimens (e.g., blood, urine, swabs, etc.) and testing the pools for the presence of a disease. When individual covariate information is available (e.g., age, gender, number of sexual partners, etc.), a common goal is to relate an individual's true disease status to the covariates in a regression model. Estimating this relationship is a nonstandard problem in group testing because true individual statuses are not observed and all testing responses (on pools and on individuals) are subject to misclassification arising from assay error. Previous regression methods for group testing data can be inefficient because they are restricted to using only initial pool responses and/or they make potentially unrealistic assumptions regarding the assay accuracy probabilities. To overcome these limitations, we propose a general Bayesian regression framework for modeling group testing data. The novelty of our approach is that it can be easily implemented with data from any group testing protocol. Furthermore, our approach will simultaneously estimate assay accuracy probabilities (along with the covariate effects) and can even be applied in screening situations where multiple assays are used. We apply our methods to group testing data collected in Iowa as part of statewide screening efforts for chlamydia, and we make user-friendly R code available to practitioners.

Improved HIV-1 Viral Load Monitoring Capacity Using Pooled Testing With Marker-Assisted Deconvolution

OBJECTIVE

Improve pooled viral load (VL) testing to increase HIV treatment monitoring capacity, particularly relevant for resource-limited settings.

DESIGN

We developed marker-assisted mini-pooling with algorithm (mMPA), a new VL pooling deconvolution strategy that uses information from low-cost, routinely collected clinical markers to determine an efficient order of sequential individual VL testing and dictates when the sequential testing can be stopped.

METHODS

We simulated the use of pooled testing to ascertain virological failure status on 918 participants from 3 studies conducted at the Academic Model Providing Access to Healthcare in Eldoret, Kenya, and estimated the number of assays needed when using mMPA and other pooling methods. We also evaluated the impact of practical factors, such as specific markers used, prevalence of virological failure, pool size, VL measurement error, and assay detection cutoffs on mMPA, other pooling methods, and single testing.

RESULTS

Using CD4 count as a marker to assist deconvolution, mMPA significantly reduces the number of VL assays by 52% [confidence interval (CI): 48% to 57%], 40% (CI: 38% to 42%), and 19% (CI: 15% to 22%) compared with individual testing, simple mini-pooling, and mini-pooling with algorithm, respectively. mMPA has higher sensitivity and negative/positive predictive values than mini-pooling with algorithm, and comparable high specificity. Further improvement is achieved with additional clinical markers, such as age and time on therapy, with or without CD4 values. mMPA performance depends on prevalence of virological failure and pool size but is insensitive to VL measurement error and VL assay detection cutoffs.

CONCLUSIONS

mMPA can substantially increase the capacity of VL monitoring.

Group testing regression models with dilution submodels

Group testing, where specimens are tested initially in pools, is widely used to screen individuals for sexually transmitted diseases. However, a common problem encountered in practice is that group testing can increase the number of false negative test results. This occurs primarily when positive individual specimens within a pool are diluted by negative ones, resulting in positive pools testing negatively. If the goal is to estimate a population-level regression model relating individual disease status to observed covariates, severe bias can result if an adjustment for dilution is not made. Recognizing this as a critical issue, recent binary regression approaches in group testing have utilized continuous biomarker information to acknowledge the effect of dilution. In this paper, we have the same overall goal but take a different approach. We augment existing group testing regression models (that assume no dilution) with a parametric dilution submodel for pool-level sensitivity and estimate all parameters using maximum likelihood. An advantage of our approach is that it does not rely on external biomarker test data, which may not be available in surveillance studies. Furthermore, unlike previous approaches, our framework allows one to formally test whether dilution is present based on the observed group testing data. We use simulation to illustrate the performance of our estimation and inference methods, and we apply these methods to 2 infectious disease data sets.

Improved matrix pooling

Pooled testing is useful to identify positive specimens for large-scale screening. Matrix pooling is one of the commonly used algorithms. In this work, we investigate the properties of matrix pooling and reveal that the efficiency of matrix pooling is related with the magnitude of overlapping among groups. Based on this property, we develop a new design to further improve the efficiency while taking into account of testing error. The efficiency, pooling sensitivity and specificity of this algorithm are explicitly derived and verified through plasmode simulation of detecting acute human immunodeficiency virus among patients who were suspected to have malaria in rural Ugandan. We show that the new design outperforms matrix pooling in efficiency while retain the pooling sensitivity and specificity.

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.