A general regression framework for group testing data, which incorporates pool dilution effects

Pool testing with dilution effects and heterogeneous priors

The Dorfman pooled testing scheme is a process in which individual specimens (e.g., blood, urine, swabs, etc.) are pooled and tested together; if the merged sample tests positive for infection, then each specimen from the pool is tested individually. Through this procedure, laboratories can reduce the expected number of tests required to screen the population, as individual tests are only carried out when the pooled test detects an infection. Several different partitions of the population can be used to form the pools. In this study, we analyze the performance of ordered partitions, those in which subjects with similar probability of infection are pooled together. We derive sufficient conditions under which ordered partitions outperform other types of partitions in terms of minimizing the expected number of tests, the expected number of false negatives, and the expected number of false positive classifications. These sufficient conditions can be easily verified in practical applications once the dilution effect has been estimated. We also propose a measure of equity and present conditions under which this measure is maximized by ordered partitions.

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.

Optimal uses of pooled testing for COVID-19 incorporating imperfect test performance and pool dilution effect: An application to congregate settings in Los Angeles County

INTRODUCTION

Pooled testing is a potentially efficient alternative strategy for COVID-19 testing in congregate settings. We evaluated the utility and cost-savings of pooled testing based on imperfect test performance and potential dilution effect due to pooling and created a practical calculator for online use.

METHODS

We developed a 2-stage pooled testing model accounting for dilution. The model was applied to hypothetical scenarios of 100 specimens collected during a one-week time-horizon cycle for varying levels of COVID-19 prevalence and test sensitivity and specificity, and to 338 skilled nursing facilities (SNFs) in Los Angeles County (Los Angeles) (data collected and analyzed in 2020).

RESULTS

Optimal pool sizes ranged from 1 to 12 in instances where there is a least one case in the batch of specimens. 40% of Los Angeles SNFs had more than one case triggering a response-testing strategy. The median number (minimum; maximum) of tests performed per facility were 56 (14; 356) for a pool size of 4, 64 (13; 429) for a pool size of 10, and 52 (11; 352) for an optimal pool size strategy among response-testing facilities. The median costs of tests in response-testing facilities were $8250 ($1100; $46,100), $6000 ($1340; $37,700), $6820 ($1260; $43,540), and $5960 ($1100; $37,380) when adopting individual testing, a pooled testing strategy using pool sizes of 4, 10, and optimal pool size, respectively.

CONCLUSIONS

Pooled testing is an efficient strategy for congregate settings with a low prevalence of COVID-19. Dilution as a result of pooling can lead to erroneous false-negative results.

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.

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.

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.

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.

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.

Estimating the prevalence of multiple diseases from two-stage hierarchical pooling

Testing protocols in large-scale sexually transmitted disease screening applications often involve pooling biospecimens (e.g., blood, urine, and swabs) to lower costs and to increase the number of individuals who can be tested. With the recent development of assays that detect multiple diseases, it is now common to test biospecimen pools for multiple infections simultaneously. Recent work has developed an expectation-maximization algorithm to estimate the prevalence of two infections using a two-stage, Dorfman-type testing algorithm motivated by current screening practices for chlamydia and gonorrhea in the USA. In this article, we have the same goal but instead take a more flexible Bayesian approach. Doing so allows us to incorporate information about assay uncertainty during the testing process, which involves testing both pools and individuals, and also to update information as individuals are tested. Overall, our approach provides reliable inference for disease probabilities and accurately estimates assay sensitivity and specificity even when little or no information is provided in the prior distributions. We illustrate the performance of our estimation methods using simulation and by applying them to chlamydia and gonorrhea data collected in Nebraska. Copyright © 2016 John Wiley & Sons, Ltd.