Bayesian group testing regression models for spatial data.

Spatial patterns are common in infectious disease epidemiology. Disease mapping is essential to infectious disease surveillance. Under a group testing protocol, biomaterial from multiple individuals is physically combined into a pooled specimen, which is then tested for infection. If the pool tests negative, all contributing individuals are generally assumed to be uninfected. If the pool tests positive, the individuals are usually retested to determine who is infected. When the prevalence of infection is low, group testing provides significant cost savings over traditional individual testing by reducing the number of tests required. However, the lack of statistical methods capable of producing maps from group testing data has limited the use of group testing in disease mapping. We develop a Bayesian methodology that can simultaneously map disease prevalence using group testing data and identify risk factors for infection. We illustrate its real-world utility using two datasets from vector-borne disease surveillance.

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.

An optimization framework for large-scale screening under limited testing capacity with application to COVID-19.

We consider the problem of targeted mass screening of heterogeneous populations under limited testing capacity. Mass screening is an essential tool that arises in various settings, e.g., ensuring a safe supply of blood, reducing prevalence of sexually transmitted diseases, and mitigating the spread of infectious disease outbreaks. The goal of mass screening is to classify whole population groups as positive or negative for an infectious disease as efficiently and accurately as possible. Under limited testing capacity, it is not possible to screen the entire population and hence administrators must reserve testing and target those among the population that are most in need or most susceptible. This paper addresses this decision problem by taking advantage of accessible population-level risk information to identify the optimal set of sub-populations to target for screening. We conduct a comprehensive analysis that considers the two most commonly adopted schemes: Individual testing and Dorfman group testing. For both schemes, we formulate an optimization model that aims to minimize the number of misclassifications under a testing capacity constraint. By analyzing the formulations, we establish key structural properties which we use to construct efficient and accurate solution techniques. We conduct a case study on COVID-19 in the United States using geographic-based data. Our results reveal that the considered proactive targeted schemes outperform commonly adopted practices by substantially reducing misclassifications. Our case study provides important managerial insights with regards to optimal allocation of tests, testing designs, and protocols that dictate the optimality of schemes. Such insights can inform policy-makers with tailored and implementable data-driven recommendations.

Collaborative Assessment in the Gross Anatomy Lab.

Purpose: In 2018, the Michigan State University College of Human Medicine incorporated two-stage examinations into the gross anatomy curriculum. Multiple studies have investigated two-stage examinations and have largely reported positive findings. Here, we used a mixed-methods approach to further investigate the feasibility and student perceptions of the two-stage examination in the context of a medical school curriculum that emphasizes longitudinal group-based learning and formative assessments. Methods: Three student cohorts were assessed with a formative two-stage examination at the end of their first-year anatomy experience. Data for the quantitative analysis included examination scores from the individual and group portions of the two-stage examination. For the qualitative stage of this project, we utilized a constructivist grounded theory methodology in which data, including both post-examination survey results and one-on-one semi-structured student interviews, were transcribed (interviews), coded, inductively and iteratively reviewed, and thematically interpreted. Results: Survey and interview results revealed an overwhelmingly positive perception of the collaborative assessment experience. Student comments demonstrated educational value in the immediate feedback provided by this examination format and suggested that collaboration during the examination transformed the assessment into a learning experience. Conclusions: While two-stage examinations have the potential to positively transform an assessment into a learning experience, we also identified complex relationships between content knowledge and anxiety that may affect student perceptions. In addition, examination logistics (e.g., curricular timing) have the potential to negatively affect student perceptions, indicating that faculty should consider these factors when implementing collaborative assessments into their curriculum.

Multiple testing of composite null hypotheses for discrete data using randomized p-values.

P-values that are derived from continuously distributed test statistics are typically uniformly distributed on (0,1) under least favorable parameter configurations (LFCs) in the null hypothesis. Conservativeness of a p-value P (meaning that P is under the null hypothesis stochastically larger than uniform on (0,1)) can occur if the test statistic from which P is derived is discrete, or if the true parameter value under the null is not an LFC. To deal with both of these sources of conservativeness, we present two approaches utilizing randomized p-values. We illustrate their effectiveness for testing a composite null hypothesis under a binomial model. We also give an example of how the proposed p-values can be used to test a composite null in group testing designs. We find that the proposed randomized p-values are less conservative compared to nonrandomized p-values under the null hypothesis, but that they are stochastically not smaller under the alternative. The problem of establishing the validity of randomized p-values has received attention in previous literature. We show that our proposed randomized p-values are valid under various discrete statistical models, which are such that the distribution of the corresponding test statistic belongs to an exponential family. The behavior of the power function for the tests based on the proposed randomized p-values as a function of the sample size is also investigated. Simulations and a real data example are used to compare the different considered p-values.

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.

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.

An approach for joint optimization of probabilistic group test based on cost and time value: taking nucleic acid detection of COVID-19 as an example.

In recent years, the world has encountered many epidemic impacts caused by various viruses, COVID-19 has spread and mutated globally since its outbreak in 2019, causing global impact. Nucleic acid detection is an important means for the prevention and control of infectious diseases. Aiming at people who are susceptible to sudden and infectious diseases, considering the control of viral nucleic acid detection cost and completion time, a probabilistic group test optimization method based on the cost and time value is proposed. Firstly, different cost functions to express the pooling and testing costs are used, a probability group test optimization model that considers the pooling and testing costs is established, the optimal combination number of samples for nucleic acid testing is obtained, and the positive probability and the cost functions of the group testing on the optimization result are explored. Secondly, considering the impact of the detection completion time on epidemic control, the sampling ability and detection ability were incorporated into the optimization objective function, then a probability group testing optimization model based on time value is established. Finally, taking COVID-19 nucleic acid detection as an example, the applicability of the model is verified, and the Pareto optimal curve under the minimum cost and shortest detection completion time is obtained. The results show that under normal circumstances, the optimal combination number of samples for nucleic acid detection is about 10. Generally, 10 is used to calculate for the convenience of organization, arrangement and statistics, except for cases where there are special requirements for testing cost and detection completion time.

Optimal group testing with heterogeneous risks.

We consider optimal group testing of individuals with heterogeneous risks for an infectious disease. Our algorithm significantly reduces the number of tests needed compared to Dorfman (Ann Math Stat 14(4):436-440, 1943). When both low-risk and high-risk samples have sufficiently low infection probabilities, it is optimal to form heterogeneous groups with exactly one high-risk sample per group. Otherwise, it is not optimal to form heterogeneous groups, but homogeneous group testing may still be optimal. For a range of parameters including the U.S. Covid-19 positivity rate for many weeks during the pandemic, the optimal size of a group test is four. We discuss the implications of our results for team design and task assignment.

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.

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.

Next-Generation Sequencing Data-Based Association Testing of a Group of Genetic Markers for Complex Responses Using a Generalized Linear Model Framework.

Association testing has been widely used to study the relationship between genetic variants and phenotypes. Most association testing methods are genotype-based, i.e. first estimate genotype and then regress phenotype on estimated genotype and other variables. Directly testing methods based on next generation sequencing (NGS) data without genotype calling have been proposed and shown advantage over genotype-based methods in the scenarios when genotype calling is not accurate. NGS data-based single-variant testing have been proposed including our previously proposed single-variant testing method, i.e. UNC combo method [1]. NGS data-based group testing methods for continuous phenotype have also been proposed by us using a linear model framework which can handle continuous responses [2]. In this paper, we extend our linear model-based framework to a generalized linear model-based framework so that the methods can handle other types of responses especially binary responses which is commonly-faced in association studies. We have conducted extensive simulation studies to evaluate the performance of different estimators and compare our estimators with their corresponding genotype-based methods. We found that all methods have Type I errors controlled, and our NGS data-based testing methods have better performance than their corresponding genotype-based methods in the literature for other types of responses including binary responses (logistic regression) and count responses (Poisson regression especially when sequencing depth is low. In conclusion, we have extended our previous linear model (LM) framework to a generalized linear model (GLM) framework and derived NGS data-based testing methods for a group of genetic variants. Compared with our previously proposed LM-based methods [2], the new GLM-based methods can handle more complex responses (for example, binary responses and count responses) in addition to continuous responses. Our methods have filled the literature gap and shown advantage over their corresponding genotype-based methods in the literature.

Using group testing in a two-phase epidemiologic design to identify the effects of a large number of antibody reactions on disease risk.

BACKGROUND: The role of immunological responses to exposed bacteria on disease incidence is increasingly under investigation. With many bacterial species, and many potential antibody reactions to a particular species, the large number of assays required for this type of discovery can make it prohibitively expensive. We propose a two-phase group testing design to more efficiently screen numerous antibody effects in a case-control setting. METHODS: Phase 1 uses group testing to select antibodies that are differentially expressed between cases and controls. The selected antibodies go on to Phase 2 individual testing. RESULTS: We evaluate the two-phase group testing design through simulations and example data and find that it substantially reduces the number of assays required relative to standard case-control and group testing designs, while maintaining similar statistical properties. CONCLUSION: The proposed two-phase group testing design can dramatically reduce the number of assays required, while providing comparable results to a case-control design.

Group Testing Matrix Design for PCR Screening with Real-Valued Measurements.

Single-step nonadaptive group testing approaches for reducing the number of tests required to detect a small subset of positive samples from a larger set require solving two algorithmic problems. First, how to design the samples-to-tests measurement matrix, and second, how to decode the results of the tests to uncover positive samples. In this study, we focus on the first challenge. We introduce real-valued group testing, which matches the characteristics of existing PCR testing pipelines more closely than combinatorial group testing or compressed sensing settings. We show a set of conditions that allow measurement matrices to guarantee unambiguous decoding of positives in this new setting. For small matrix sizes, we also propose an algorithm for constructing matrices that meet the proposed condition. On simulated data sets, we show that the matrices resulting from the algorithm can successfully recover positive samples at higher positivity rates than matrices designed for combinatorial group testing setting. We use wet laboratory experiments involving SARS-CoV-2 nasopharyngeal swab samples to further validate the approach.

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.

Group Testing with Blocks of Positives and Inhibitors.

The main goal of group testing is to identify a small number of specific items among a large population of items. In this paper, we consider specific items as positives and inhibitors and non-specific items as negatives. In particular, we consider a novel model called group testing with blocks of positives and inhibitors. A test on a subset of items is positive if the subset contains at least one positive and does not contain any inhibitors, and it is negative otherwise. In this model, the input items are linearly ordered, and the positives and inhibitors are subsets of small blocks (at unknown locations) of consecutive items over that order. We also consider two specific instantiations of this model. The first instantiation is that model that contains a single block of consecutive items consisting of exactly known numbers of positives and inhibitors. The second instantiation is the model that contains a single block of consecutive items containing known numbers of positives and inhibitors. Our contribution is to propose efficient encoding and decoding schemes such that the numbers of tests used to identify only positives or both positives and inhibitors are less than the ones in the state-of-the-art schemes. Moreover, the decoding times mostly scale to the numbers of tests that are significantly smaller than the state-of-the-art ones, which scale to both the number of tests and the number of items.

Algorithmic lifestyle optimization.

OBJECTIVE: A hallmark of personalized medicine and nutrition is to identify effective treatment plans at the individual level. Lifestyle interventions (LIs), from diet to exercise, can have a significant effect over time, especially in the case of food intolerances and allergies. The large set of candidate interventions, make it difficult to evaluate which intervention plan would be more favorable for any given individual. In this study, we aimed to develop a method for rapid identification of favorable LIs for a given individual. MATERIALS AND METHODS: We have developed a method, algorithmic lifestyle optimization (ALO), for rapid identification of effective LIs. At its core, a group testing algorithm identifies the effectiveness of each intervention efficiently, within the context of its pertinent group. RESULTS: Evaluations on synthetic and real data show that ALO is robust to noise, data size, and data heterogeneity. Compared to the standard of practice techniques, such as the standard elimination diet (SED), it identifies the effective LIs 58.9%-68.4% faster when used to discover an individual's food intolerances and allergies to 19-56 foods. DISCUSSION: ALO achieves its superior performance by: (1) grouping multiple LIs together optimally from prior statistics, and (2) adapting the groupings of LIs from the individual's subsequent responses. Future extensions to ALO should enable incorporating nutritional constraints. CONCLUSION: ALO provides a new approach for the discovery of effective interventions in nutrition and medicine, leading to better intervention plans faster and with less inconvenience to the patient compared to SED.

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.

Circular Whole-Transcriptome Amplification (cWTA) and mNGS Screening Enhanced by a Group Testing Algorithm (mEGA) Enable High-Throughput and Comprehensive Virus Identification.

Metagenomic next-generation sequencing (mNGS) offers a hypothesis-free approach for pathogen detection, but its applicability in clinical diagnosis, in addition to other factors, remains limited due to complicated library construction. The present study describes a PCR-free isothermal workflow for mNGS targeting RNA, based on a multiple displacement amplification, termed circular whole-transcriptome amplification (cWTA), as the template is circularized before amplification. The cWTA approach was validated with clinical samples and nanopore sequencing. Reads homologous to dengue virus 2 and chikungunya virus were detected in clinical samples from Bangladesh and Brazil, respectively. In addition, the practicality of a high-throughput detection system that combines mNGS and a group testing algorithm termed mNGS screening enhanced by a group testing algorithm (mEGA) was established. This approach enabled significant library size reduction while permitting trackability between samples and diagnostic results. Serum samples of patients with undifferentiated febrile illnesses from Vietnam (n = 43) were also amplified with cWTA, divided into 11 pools, processed for library construction, and sequenced. Dengue virus 2, hepatitis B virus, and parvovirus B19 were successfully detected without prior knowledge of their existence. Collectively, cWTA with the nanopore platform opens the possibility of hypothesis-free on-site comprehensive pathogen diagnosis, while mEGA contributes to the scaling up of sample throughput. IMPORTANCE Given the breadth of pathogens that cause infections, a single approach that can detect a wide range of pathogens is ideal but is impractical due to the available tests being highly specific to a certain pathogen. Recent developments in sequencing technology have introduced mNGS as an alternative that provides detection of a wide-range of pathogens by detecting the presence of their nucleic acids in the sample. However, sequencing library preparation is still a bottleneck, as it is complicated, costly, and time-consuming. In our studies, alternative approaches to optimize library construction for mNGS were developed. This included isothermal nucleic acid amplification and expansion of sample throughput with a group testing algorithm. These methods can improve the utilization of mNGS as a diagnostic tool and can serve as a high-throughput screening system aiding infectious disease surveillance.

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. Supplementary materials for this article are available at 10.1007/s13253-022-00511-4.