Hierarchical group testing for multiple infections

Bayesian Additive Regression Trees for Group Testing Data

When screening for low-prevalence diseases, pooling specimens (e.g., blood, urine, swabs, etc.) through group testing has the potential to substantially reduce costs when compared to testing specimens individually. A common goal in group testing applications is to estimate the relationship between an individual's true disease status and their individual-level covariate information. However, estimating such a relationship is a non-trivial problem because true individual disease statuses are unknown due to the group testing protocol and the possibility of imperfect testing. While several regression methods have been developed in recent years to accommodate the complexity of group testing data, the functional form of covariate effects is typically assumed to be known. To avoid model misspecification and to provide a more flexible approach, we propose a Bayesian additive regression trees framework to model the individual-level probability of disease with potentially misclassified group testing data. Our methods can be used to analyze data arising from any group testing protocol with the goal of estimating unknown functions of covariates and assay classification accuracy probabilities.

A mixed-effects Bayesian regression model for multivariate group testing data

Laboratories use group (pooled) testing with multiplex assays to reduce the time and cost associated with screening large populations for infectious diseases. Multiplex assays test for multiple diseases simultaneously, and combining their use with group testing can lead to highly efficient screening protocols. However, these benefits come at the expense of a more complex data structure which can hinder surveillance efforts. To overcome this challenge, we develop a general Bayesian framework to estimate a mixed multivariate probit model with data arising from any group testing protocol that uses multiplex assays. In the formulation of this model, we account for the correlation between true disease statuses and heterogeneity across population subgroups, and we provide for automated variable selection through the adoption of spike and slab priors. To perform model fitting, we develop an attractive posterior sampling algorithm which is straightforward to implement. We illustrate our methodology through numerical studies and analyze chlamydia and gonorrhea group testing data collected by the State Hygienic Laboratory at the University of Iowa.

Regression analysis of group-tested current status data

Group testing is an effective way to reduce the time and cost associated with conducting large-scale screening for infectious diseases. Benefits are realized through testing pools formed by combining specimens, such as blood or urine, from different individuals. In some studies, individuals are assessed only once and a time-to-event endpoint is recorded, for example, the time until infection. Combining group testing with this type of endpoint results in group-tested current status data (Petito & Jewell, 2016). To analyse these complex data, we propose methods that estimate a proportional hazard regression model based on test outcomes from measuring the pools. A sieve maximum likelihood estimation approach is developed that approximates the cumulative baseline hazard function with a piecewise constant function. To identify the sieve estimator, a computationally efficient expectation-maximization algorithm is derived by using data augmentation. Asymptotic properties of both the parametric and nonparametric components of the sieve estimator are then established by applying modern empirical process theory. Numerical results from simulation studies show that our proposed method performs nominally and has advantages over the corresponding estimation method based on individual testing results. We illustrate our work by analysing a chlamydia dataset collected by the State Hygienic Laboratory at the University of Iowa.

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.

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.

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.

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

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

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.

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.

Sample pooling strategies for SARS-CoV-2 detection

The worldwide COVID-19 pandemic outburst has caused a serious public health issue with increasing needs of accurate and rapid diagnostic and screening testing. This situation requires an optimized management of the chemical reagents, the consumables, and the human resources, in order to respond accurately and effectively, controlling the spread of the disease. Testing on pooled samples maximizes the number of tested samples, by minimizing the time and the lab supplies needed. The general conceptualization of the pooling method is based on mixing samples together in a batch. Individual testing is needed only if a specific pool exhibits a positive result. The development of alternative hybrid methods, based on "in house" protocols, utilizing commercially available consumables, in combination with a reliable pooling method would provide a solution, focusing on the better exploitation of the personnel and the lab supplies, allowing for rapid screening of a population in a reasonably short time.

Nonparametric estimation of distributions and diagnostic accuracy based on group-tested results with differential misclassification

This article concerns the problem of estimating a continuous distribution in a diseased or nondiseased population when only group-based test results on the disease status are available. The problem is challenging in that individual disease statuses are not observed and testing results are often subject to misclassification, with further complication that the misclassification may be differential as the group size and the number of the diseased individuals in the group vary. We propose a method to construct nonparametric estimation of the distribution and obtain its asymptotic properties. The performance of the distribution estimator is evaluated under various design considerations concerning group sizes and classification errors. The method is exemplified with data from the National Health and Nutrition Examination Survey study to estimate the distribution and diagnostic accuracy of C-reactive protein in blood samples in predicting chlamydia incidence.

Survival analysis under the Cox proportional hazards model with pooled covariates

For a continuous time-to-event outcome and an expensive-to-measure exposure, we develop a pooling design and propose a likelihood-based approach to estimate the hazard ratios (HRs) of a Cox proportional hazards (PH) model. Our proposed approach fits a PH model based on pooled exposures with individually observed time-to-event outcomes. The design and estimation exploits the equivalence of the conditional logistic likelihood functions arising from a matched case-control study and the partial likelihood function of a riskset-matched, nested case-control (NCC) subset of a cohort study. To create the pools, we first focus on an NCC subcohort. Pools are formed at random while keeping the matching intact. Pool-level exposure and confounders are then evaluated and used in the likelihood to estimate the HR and the standard error of the estimates. The estimators are MLEs, provide consistent estimates of the individual-level HRs, and are asymptotically normal. Our simulation results indicate that the pooled estimates are comparable to the estimates obtained from the NCC subcohort. The units of analysis for the pooled design are the pools and not the individual participants. Hence the effective sample size is reduced. Therefore, the variance of the HR estimate increases with increasing poolsize. However, this variance inflation in small samples can be offset by including more matched controls per case within the NCC subcohort. An application is demonstrated with the Second Manifestations of ARTerial disease (SMART) study.

Informative group testing for multiplex assays

Infectious disease testing frequently takes advantage of two tools-group testing and multiplex assays-to make testing timely and cost effective. Until the work of Tebbs et al. (2013) and Hou et al. (2017), there was no research available to understand how best to apply these tools simultaneously. This recent work focused on applications where each individual is considered to be identical in terms of the probability of disease. However, risk-factor information, such as past behavior and presence of symptoms, is very often available on each individual to allow one to estimate individual-specific probabilities. The purpose of our paper is to propose the first group testing algorithms for multiplex assays that take advantage of individual risk-factor information as expressed by these probabilities. We show that our methods significantly reduce the number of tests required while preserving accuracy. Throughout this paper, we focus on applying our methods with the Aptima Combo 2 Assay that is used worldwide for chlamydia and gonorrhea screening.