1
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Huang R, McLain AC, Herrin BH, Nolan M, Cai B, Self S. Bayesian group testing regression models for spatial data. Spat Spatiotemporal Epidemiol 2024; 50:100677. [PMID: 39181610 PMCID: PMC11347770 DOI: 10.1016/j.sste.2024.100677] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 12/19/2023] [Revised: 07/12/2024] [Accepted: 07/15/2024] [Indexed: 08/27/2024]
Abstract
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.
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Affiliation(s)
- Rongjie Huang
- Department of Epidemiology and Biostatistics, University of South Carolina, 915 Greene Street, Columbia, 29208, SC, USA
| | - Alexander C McLain
- Department of Epidemiology and Biostatistics, University of South Carolina, 915 Greene Street, Columbia, 29208, SC, USA
| | - Brian H Herrin
- College of Veterinary Medicine, Kansas State University, 1700 Denison Ave, Manhattan, 66502, KS, USA
| | - Melissa Nolan
- Department of Epidemiology and Biostatistics, University of South Carolina, 915 Greene Street, Columbia, 29208, SC, USA
| | - Bo Cai
- Department of Epidemiology and Biostatistics, University of South Carolina, 915 Greene Street, Columbia, 29208, SC, USA
| | - Stella Self
- Department of Epidemiology and Biostatistics, University of South Carolina, 915 Greene Street, Columbia, 29208, SC, USA.
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2
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Roy S, Adhya S, Rana S. Estimation of odds ratio from group testing data with misclassified exposure. Biom J 2024; 66:e2200254. [PMID: 38285402 DOI: 10.1002/bimj.202200254] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2022] [Revised: 08/21/2023] [Accepted: 09/17/2023] [Indexed: 01/30/2024]
Abstract
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.
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Affiliation(s)
- Surupa Roy
- Department of Statistics, St Xavier's College (Autonomous), Kolkata, West Bengal, India
| | - Sumanta Adhya
- Department of Statistics, West Bengal State University, Kolkata, West Bengal, India
| | - Subrata Rana
- Department of Statistics, Krishnagar Government College, Kolkata, West Bengal, India
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3
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Ebert TA, Shawer D, Brlansky RH, Rogers ME. Seasonal Patterns in the Frequency of Candidatus Liberibacter Asiaticus in Populations of Diaphorina citri (Hemiptera: Psyllidae) in Florida. INSECTS 2023; 14:756. [PMID: 37754724 PMCID: PMC10532026 DOI: 10.3390/insects14090756] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Revised: 09/04/2023] [Accepted: 09/06/2023] [Indexed: 09/28/2023]
Abstract
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.
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Affiliation(s)
- Timothy A. Ebert
- Citrus Research and Education Center, University of Florida, 700 Experiment Station Rd., Lake Alfred, FL 33850, USA; (R.H.B.); (M.E.R.)
| | - Dalia Shawer
- Department of Economic Entomology, Faculty of Agriculture, Kafr Elsheikh University, Kafr Elsheikh 33516, Egypt;
| | - Ron H. Brlansky
- Citrus Research and Education Center, University of Florida, 700 Experiment Station Rd., Lake Alfred, FL 33850, USA; (R.H.B.); (M.E.R.)
| | - Michael E. Rogers
- Citrus Research and Education Center, University of Florida, 700 Experiment Station Rd., Lake Alfred, FL 33850, USA; (R.H.B.); (M.E.R.)
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4
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Delaigle A, Tan R. Group testing regression analysis with covariates and specimens subject to missingness. Stat Med 2023; 42:731-744. [PMID: 36646446 DOI: 10.1002/sim.9640] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Revised: 09/06/2022] [Accepted: 12/16/2022] [Indexed: 01/18/2023]
Abstract
We develop parametric estimators of a conditional prevalence in the group testing context. Group testing is applied when a binary outcome variable, often a disease indicator, is assessed by testing a specimen for the presence of the disease. Instead of testing all individual specimens separately, these are pooled in groups and the grouped specimens are tested for the disease, which permits to significantly reduce the number of tests to be performed. Various techniques have been developed in the literature for estimating a conditional prevalence from group testing data, but most of them are not valid when the data are subject to missingness. We consider this problem in the case where the specimen and the covariates are subject to nonmonotone missingness. We propose parametric estimators of the conditional prevalence, establish identifiability conditions for a logistic missing not at random model, and introduce an ignorable missing at random model. In theory, our estimators could be applied with multiple covariates missing, but in practice, they face numerical challenges when more than one covariate is missing for given individuals. We illustrate the method on simulated data and on a dataset from the Demographics and Health Survey.
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Affiliation(s)
- Aurore Delaigle
- School of Mathematics and Statistics, University of Melbourne, 3010, Victoria, Parkville, Australia
| | - Ruoxu Tan
- School of Mathematics and Statistics, University of Melbourne, 3010, Victoria, Parkville, Australia
- Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong SAR, China
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5
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Self S, McMahan C, Mokalled S. Capturing the pool dilution effect in group testing regression: A Bayesian approach. Stat Med 2022; 41:4682-4696. [PMID: 35879887 PMCID: PMC9489666 DOI: 10.1002/sim.9532] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2021] [Revised: 07/01/2022] [Accepted: 07/05/2022] [Indexed: 01/07/2023]
Abstract
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.
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Affiliation(s)
- Stella Self
- Department of Epidemiology and Biostatistics, Arnold School of Public HealthUniversity of South CarolinaColumbiaSouth CarolinaUSA
| | - Christopher McMahan
- School of Mathematical and Statistical SciencesClemson UniversityClemsonSouth CarolinaUSA
| | - Stefani Mokalled
- School of Mathematical and Statistical SciencesClemson UniversityClemsonSouth CarolinaUSA
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6
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Warasi MS, Hungerford LL, Lahmers K. Optimizing Pooled Testing for Estimating the Prevalence of Multiple Diseases. JOURNAL OF AGRICULTURAL, BIOLOGICAL AND ENVIRONMENTAL STATISTICS 2022; 27:713-727. [PMID: 35975123 PMCID: PMC9373899 DOI: 10.1007/s13253-022-00511-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Revised: 05/27/2022] [Accepted: 07/27/2022] [Indexed: 11/25/2022]
Abstract
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.
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Affiliation(s)
- Md S. Warasi
- Department of Mathematics and Statistics, Radford University, Whitt Hall 224, Radford, VA 24142 USA
| | - Laura L. Hungerford
- Virginia-Maryland College of Veterinary Medicine, Virginia Tech, Blacksburg, VA 24061 USA
| | - Kevin Lahmers
- Virginia-Maryland College of Veterinary Medicine, Virginia Tech, Blacksburg, VA 24061 USA
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7
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Warasi MS. groupTesting: an R package for group testing estimation. COMMUN STAT-SIMUL C 2021. [DOI: 10.1080/03610918.2021.2009867] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Md S. Warasi
- Department of Mathematics and Statistics, Radford University, Radford, VA, USA
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8
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Yu J, Huang Y, Shen ZJ. Optimizing and evaluating PCR-based pooled screening during COVID-19 pandemics. Sci Rep 2021; 11:21460. [PMID: 34728759 PMCID: PMC8564549 DOI: 10.1038/s41598-021-01065-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2020] [Accepted: 10/19/2021] [Indexed: 12/13/2022] Open
Abstract
Population screening played a substantial role in safely reopening the economy and avoiding new outbreaks of COVID-19. PCR-based pooled screening makes it possible to test the population with limited resources by pooling multiple individual samples. Our study compared different population-wide screening methods as transmission-mitigating interventions, including pooled PCR, individual PCR, and antigen screening. Incorporating testing-isolation process and individual-level viral load trajectories into an epidemic model, we further studied the impacts of testing-isolation on test sensitivities. Results show that the testing-isolation process could maintain a stable test sensitivity during the outbreak by removing most infected individuals, especially during the epidemic decline. Moreover, we compared the efficiency, accuracy, and cost of different screening methods during the pandemic. Our results show that PCR-based pooled screening is cost-effective in reversing the pandemic at low prevalence. When the prevalence is high, PCR-based pooled screening may not stop the outbreak. In contrast, antigen screening with sufficient frequency could reverse the epidemic, despite the high cost and the large numbers of false positives in the screening process.
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Affiliation(s)
- Jiali Yu
- Tsinghua-Berkeley Shenzhen Institute (TBSI), Tsinghua University, Shenzhen, China
| | - Yiduo Huang
- Department of Civil and Environmental Engineering, University of California Berkeley, Berkeley, CA, USA
| | - Zuo-Jun Shen
- College of Engineering, University of California Berkeley, Berkeley, CA, USA.
- Faculty of Engineering and Faculty of Business and Economics, University of Hong Kong, Hong Kong, China.
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9
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Liu Y, McMahan CS, Tebbs JM, Gallagher CM, Bilder CR. Generalized additive regression for group testing data. Biostatistics 2021; 22:873-889. [PMID: 32061081 PMCID: PMC8511943 DOI: 10.1093/biostatistics/kxaa003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2019] [Revised: 01/04/2020] [Accepted: 01/13/2020] [Indexed: 11/13/2022] Open
Abstract
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.
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Affiliation(s)
- Yan Liu
- School of Community Health Sciences, University of Nevada, Reno, 1664 N. Virginia St, Reno, NV 89557, USA
| | - Christopher S McMahan
- School of Mathematical and Statistical Sciences, Clemson University, O-110 Martin Hall, Box 340975, Clemson, SC 29634, USA
| | - Joshua M Tebbs
- Department of Statistics, University of South Carolina, 1523 Greene St, Columbia, SC 29208, USA
| | - Colin M Gallagher
- School of Mathematical and Statistical Sciences, Clemson University, O-110 Martin Hall, Box 340975, Clemson, SC 29634, USA
| | - Christopher R Bilder
- Department of Statistics, University of Nebraska-Lincoln, 340 Hardin Hall North, Lincoln, NE 68583, USA
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10
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Yuan A, Piao J, Ning J, Qin J. Semiparametric isotonic regression modelling and estimation for group testing data. CAN J STAT 2021; 49:659-677. [PMID: 34690407 PMCID: PMC8528191 DOI: 10.1002/cjs.11581] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2018] [Accepted: 05/04/2020] [Indexed: 11/11/2022]
Abstract
In the group testing procedure, several individual samples are grouped and the pooled samples, instead of each individual sample, are tested for outcome status (e.g., infectious disease status). Although this cost-effectiveness strategy in data collection is both labor and time efficient, it poses statistical challenges to derive statistically and computationally efficient estimators under semiparametric models. We consider semiparametric isotonic regression models for the simultaneous estimation of the conditional probability curve and covariate effects, in which a parametric form for combining the covariate information is assumed and the monotonic link function is left unspecified. We develop an expectation-maximization algorithm to overcome the computational challenge and embed the pool-adjacent violators algorithm in the M-step to facilitate the computation. We establish the large sample behavior of the proposed estimators and examine their finite sample performance in simulation studies. We apply the proposed method to data from the National Health and Nutrition Examination Survey for illustration.
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Affiliation(s)
- Ao Yuan
- Department of Biostatistics, Bioinformatics & Biomathematics, Georgetown University, Washington, DC USA
| | - Jin Piao
- Department of Preventive Medicine, The University of Southern California, Los Angeles, CA USA
| | - Jing Ning
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TX USA
| | - Jing Qin
- Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, Rockville, MD USA
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11
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Mokalled SC, McMahan CS, Tebbs JM, Andrew Brown D, Bilder CR. Incorporating the dilution effect in group testing regression. Stat Med 2021; 40:2540-2555. [PMID: 33598950 DOI: 10.1002/sim.8916] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2020] [Revised: 11/25/2020] [Accepted: 02/03/2021] [Indexed: 11/10/2022]
Abstract
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.
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Affiliation(s)
- Stefani C Mokalled
- School of Mathematical and Statistical Sciences, Clemson University, Clemson, South Carolina, USA
| | - Christopher S McMahan
- School of Mathematical and Statistical Sciences, Clemson University, Clemson, South Carolina, USA
| | - Joshua M Tebbs
- Department of Statistics, University of South Carolina, Columbia, South Carolina, USA
| | - Derek Andrew Brown
- School of Mathematical and Statistical Sciences, Clemson University, Clemson, South Carolina, USA
| | - Christopher R Bilder
- Department of Statistics, University of Nebraska-Lincoln, Lincoln, Nebraska, USA
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12
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Zhang W, Liu A, Li Q, Albert PS. Nonparametric estimation of distributions and diagnostic accuracy based on group-tested results with differential misclassification. Biometrics 2020; 76:1147-1156. [PMID: 32083733 PMCID: PMC8581970 DOI: 10.1111/biom.13236] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2019] [Revised: 12/06/2019] [Accepted: 01/27/2020] [Indexed: 11/30/2022]
Abstract
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.
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Affiliation(s)
- Wei Zhang
- LSC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
| | - Aiyi Liu
- Biostatistics and Bioinformatics Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland
| | - Qizhai Li
- LSC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
| | - Paul S. Albert
- Biostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, National Institutes of Health, Bethesda, Maryland
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13
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Joyner CN, McMahan CS, Tebbs JM, Bilder CR. From mixed effects modeling to spike and slab variable selection: A Bayesian regression model for group testing data. Biometrics 2020; 76:913-923. [PMID: 31729015 PMCID: PMC7944974 DOI: 10.1111/biom.13176] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2019] [Revised: 10/22/2019] [Accepted: 10/29/2019] [Indexed: 12/20/2022]
Abstract
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.
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Affiliation(s)
- Chase N. Joyner
- School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC 29634, U.S.A
| | - Christopher S. McMahan
- School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC 29634, U.S.A
| | - Joshua M. Tebbs
- Department of Statistics, University of South Carolina, Columbia, SC 29208, U.S.A
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14
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Delaigle A, Huang W, Lei S. Estimation of Conditional Prevalence From Group Testing Data With Missing Covariates. J Am Stat Assoc 2020. [DOI: 10.1080/01621459.2019.1566071] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Aurore Delaigle
- School of Mathematics and Statistics and Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), University of Melbourne, Parkville, Australia
| | - Wei Huang
- School of Mathematics and Statistics and Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), University of Melbourne, Parkville, Australia
| | - Shaoke Lei
- Health Services, Murdoch Children’s Research Institute and Health Services Research Unit, The Royal Children’s Hospital, Melbourne, Australia
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15
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16
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Zhang W, Liu A, Li Q, Albert PS. Incorporating retesting outcomes for estimation of disease prevalence. Stat Med 2019; 39:687-697. [PMID: 31758594 DOI: 10.1002/sim.8439] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2019] [Revised: 10/31/2019] [Accepted: 11/03/2019] [Indexed: 11/12/2022]
Abstract
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.
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Affiliation(s)
- Wei Zhang
- LSC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China.,Division of Intramural Population Health Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland
| | - Aiyi Liu
- Division of Intramural Population Health Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland
| | - Qizhai Li
- LSC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
| | - Paul S Albert
- Biostatistics Branch, Division of Cancer Epidemiology and Genetics, National Institutes of Health, Rockville, Maryland
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17
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Lin J, Wang D, Zheng Q. Regression analysis and variable selection for two-stage multiple-infection group testing data. Stat Med 2019; 38:4519-4533. [PMID: 31297869 DOI: 10.1002/sim.8311] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2018] [Revised: 03/03/2019] [Accepted: 06/14/2019] [Indexed: 12/17/2022]
Abstract
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.
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Affiliation(s)
- Juexin Lin
- Department of Statistics, University of South Carolina, South Carolina
| | - Dewei Wang
- Department of Statistics, University of South Carolina, South Carolina
| | - Qi Zheng
- Department of Bioinformatics and Biostatistics, University of Louisville, Kentucky
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18
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Determination of Varying Group Sizes for Pooling Procedure. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2019; 2019:4381084. [PMID: 31065292 PMCID: PMC6466917 DOI: 10.1155/2019/4381084] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/15/2018] [Revised: 01/17/2019] [Accepted: 02/05/2019] [Indexed: 11/17/2022]
Abstract
Pooling is an attractive strategy in screening infected specimens, especially for rare diseases. An essential step of performing the pooled test is to determine the group size. Sometimes, equal group size is not appropriate due to population heterogeneity. In this case, varying group sizes are preferred and could be determined while individual information is available. In this study, we propose a sequential procedure to determine varying group sizes through fully utilizing available information. This procedure is data driven. Simulations show that it has good performance in estimating parameters.
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19
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Gregory KB, Wang D, McMahan CS. Adaptive elastic net for group testing. Biometrics 2019; 75:13-23. [PMID: 30267535 PMCID: PMC7938860 DOI: 10.1111/biom.12973] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2017] [Accepted: 09/14/2018] [Indexed: 11/28/2022]
Abstract
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.
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Affiliation(s)
- Karl B. Gregory
- Department of Statistics, University of South Carolina, Columbia, SC 29208, U.S.A
| | - Dewei Wang
- Department of Statistics, University of South Carolina, Columbia, SC 29208, U.S.A
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20
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Roy S, Banerjee T. Estimation of log-odds ratio from group testing data using Firth correction. Biom J 2019; 61:714-728. [PMID: 30645765 DOI: 10.1002/bimj.201800125] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2018] [Revised: 11/07/2018] [Accepted: 11/09/2018] [Indexed: 11/10/2022]
Abstract
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.
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Affiliation(s)
- Surupa Roy
- Department of Statistics, St Xavier's College, Kolkata, India
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21
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Affiliation(s)
- Juexin Lin
- Department of Statistics, University of South Carolina, Columbia, SC, USA
| | - Dewei Wang
- Department of Statistics, University of South Carolina, Columbia, SC, USA
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22
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Nguyen NT, Bish EK, Aprahamian H. Sequential prevalence estimation with pooling and continuous test outcomes. Stat Med 2018; 37:2391-2426. [PMID: 29687473 DOI: 10.1002/sim.7657] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2017] [Revised: 01/17/2018] [Accepted: 02/15/2018] [Indexed: 01/02/2023]
Abstract
Prevalence estimation is crucial for controlling the spread of infections and diseases and for planning of health care services. Prevalence estimation is typically conducted via pooled, or group, testing due to limited testing budgets. We study a sequential estimation procedure that uses continuous pool readings and considers the dilution effect of pooling so as to efficiently estimate an unknown prevalence rate. Embedded into the sequential estimation procedure is an optimization model that determines the optimal pooling design (number of pools and pool sizes) under a limited testing budget, considering the trade-off between testing cost and estimation accuracy. Our numerical study indicates that the proposed sequential estimation procedure outperforms single-stage procedures, or procedures that use binary test outcomes. Further, the sequential procedure provides robust prevalence estimates in cases where the initial estimate of the unknown prevalence rate is poor, or the assumed distribution of the biomarker load in infected subjects is inaccurate. Thus, when limited and unreliable information is available about the current status of, or biomarker dynamics related to, an infection, the sequential procedure becomes an attractive estimation strategy, due to its ability to mitigate the initial bias.
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Affiliation(s)
- Ngoc T Nguyen
- Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, Virginia, 24061, USA
| | - Ebru K Bish
- Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, Virginia, 24061, USA
| | - Hrayer Aprahamian
- Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, Virginia, 24061, USA
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23
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Affiliation(s)
- Gregory Haber
- Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, Maryland, USA
| | - Yaakov Malinovsky
- Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, Maryland, USA
| | - Paul S. Albert
- Biostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, Rockville, Maryland, USA
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24
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McMahan CS, Tebbs JM, Hanson TE, Bilder CR. Bayesian regression for group testing data. Biometrics 2017; 73:1443-1452. [PMID: 28405965 PMCID: PMC5638690 DOI: 10.1111/biom.12704] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2016] [Revised: 03/01/2017] [Accepted: 03/01/2017] [Indexed: 01/10/2023]
Abstract
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.
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Affiliation(s)
| | - Joshua M. Tebbs
- Department of Statistics, University of South Carolina, Columbia, SC 29208, U.S.A
| | - Timothy E. Hanson
- Department of Statistics, University of South Carolina, Columbia, SC 29208, U.S.A
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25
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Warasi MS, McMahan CS, Tebbs JM, Bilder CR. Group testing regression models with dilution submodels. Stat Med 2017; 36:4860-4872. [PMID: 28856774 DOI: 10.1002/sim.7455] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2017] [Revised: 05/27/2017] [Accepted: 08/11/2017] [Indexed: 12/21/2022]
Abstract
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.
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Affiliation(s)
- Md S Warasi
- Department of Mathematics and Statistics, Radford University, Radford, VA 24142, USA
| | | | - Joshua M Tebbs
- Department of Statistics, University of South Carolina, Columbia, SC 29208, USA
| | - Christopher R Bilder
- Department of Statistics, University of Nebraska-Lincoln, Lincoln, NE 68583, NE, USA
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26
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Liu Y, McMahan C, Gallagher C. A general framework for the regression analysis of pooled biomarker assessments. Stat Med 2017; 36:2363-2377. [PMID: 28349583 PMCID: PMC5484591 DOI: 10.1002/sim.7291] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2016] [Revised: 02/17/2017] [Accepted: 03/06/2017] [Indexed: 11/11/2022]
Abstract
As a cost-efficient data collection mechanism, the process of assaying pooled biospecimens is becoming increasingly common in epidemiological research; for example, pooling has been proposed for the purpose of evaluating the diagnostic efficacy of biological markers (biomarkers). To this end, several authors have proposed techniques that allow for the analysis of continuous pooled biomarker assessments. Regretfully, most of these techniques proceed under restrictive assumptions, are unable to account for the effects of measurement error, and fail to control for confounding variables. These limitations are understandably attributable to the complex structure that is inherent to measurements taken on pooled specimens. Consequently, in order to provide practitioners with the tools necessary to accurately and efficiently analyze pooled biomarker assessments, herein, a general Monte Carlo maximum likelihood-based procedure is presented. The proposed approach allows for the regression analysis of pooled data under practically all parametric models and can be used to directly account for the effects of measurement error. Through simulation, it is shown that the proposed approach can accurately and efficiently estimate all unknown parameters and is more computational efficient than existing techniques. This new methodology is further illustrated using monocyte chemotactic protein-1 data collected by the Collaborative Perinatal Project in an effort to assess the relationship between this chemokine and the risk of miscarriage. Copyright © 2017 John Wiley & Sons, Ltd.
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Affiliation(s)
- Yan Liu
- Department of Mathematical Sciences, Clemson University, Clemson, 29634, SC, U.S.A
| | - Christopher McMahan
- Department of Mathematical Sciences, Clemson University, Clemson, 29634, SC, U.S.A
| | - Colin Gallagher
- Department of Mathematical Sciences, Clemson University, Clemson, 29634, SC, U.S.A
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27
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Huang X, Sarker Warasi MS. Maximum Likelihood Estimators in Regression Models for Error‐prone Group Testing Data. Scand Stat Theory Appl 2017. [DOI: 10.1111/sjos.12282] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Xianzheng Huang
- Department of Statistics, College of Arts & Sciences University of South Carolina
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28
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Abstract
Group testing, introduced by Dorfman (1943), has been used to reduce costs when estimating the prevalence of a binary characteristic based on a screening test of \documentclass[12pt]{minimal}
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}{}$n$\end{document} independent individuals in total. If the unknown prevalence is low and the screening test suffers from misclassification, it is also possible to obtain more precise prevalence estimates than those obtained from testing all \documentclass[12pt]{minimal}
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}{}$n$\end{document} samples separately (Tu et al., 1994). In some applications, the individual binary response corresponds to whether an underlying time-to-event variable \documentclass[12pt]{minimal}
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}{}$T$\end{document} is less than an observed screening time \documentclass[12pt]{minimal}
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}{}$C$\end{document}, a data structure known as current status data. Given sufficient variation in the observed \documentclass[12pt]{minimal}
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}{}$C$\end{document} values, it is possible to estimate the distribution function \documentclass[12pt]{minimal}
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}{}$T$\end{document} nonparametrically, at least at some points in its support, using the pool-adjacent-violators algorithm (Ayer et al., 1955). Here, we consider nonparametric estimation of \documentclass[12pt]{minimal}
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}{}$F$\end{document} based on group-tested current status data for groups of size \documentclass[12pt]{minimal}
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}{}$k$\end{document} where the group tests positive if and only if any individual’s unobserved \documentclass[12pt]{minimal}
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}{}$T$\end{document} is less than the corresponding observed \documentclass[12pt]{minimal}
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}{}$C$\end{document}. We investigate the performance of the group-based estimator as compared to the individual test nonparametric maximum likelihood estimator, and show that the former can be more precise in the presence of misclassification for low values of \documentclass[12pt]{minimal}
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}{}$F(t)$\end{document}. Potential applications include testing for the presence of various diseases in pooled samples where interest focuses on the age-at-incidence distribution rather than overall prevalence. We apply this estimator to the age-at-incidence curve for hepatitis C infection in a sample of U.S. women who gave birth to a child in 2014, where group assignment is done at random and based on maternal age. We discuss connections to other work in the literature, as well as potential extensions.
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Affiliation(s)
- L C Petito
- Division of Biostatistics, School of Public Health, 101 Haviland Hall, University of California, Berkeley, California 94720,
| | - N P Jewell
- Division of Biostatistics, School of Public Health, 101 Haviland Hall, University of California, Berkeley, California 94720,
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29
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Delaigle A, Zhou WX. Nonparametric and Parametric Estimators of Prevalence From Group Testing Data With Aggregated Covariates. J Am Stat Assoc 2016. [DOI: 10.1080/01621459.2015.1054491] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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30
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Delaigle A, Hall P. Nonparametric methods for group testing data, taking dilution into account. Biometrika 2015. [DOI: 10.1093/biomet/asv049] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Wang D, McMahan CS, Gallagher CM. A general regression framework for group testing data, which incorporates pool dilution effects. Stat Med 2015; 34:3606-21. [PMID: 26173957 DOI: 10.1002/sim.6578] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2014] [Revised: 04/21/2015] [Accepted: 06/15/2015] [Indexed: 01/01/2023]
Abstract
Group testing, through the use of pooling, has been widely implemented as a more efficient means to screen individuals for infectious diseases. Typically, in these settings, practitioners are tasked with the complimentary goals of both case identification and estimation. For these purposes, many group testing strategies have been proposed, which address issues such as preserving anonymity in estimation studies, quality control, and classification. In general, these strategies require that a significant number of the individuals be retested, either in pools or individually. In order to provide practitioners with a general methodology that can be used to accurately and precisely analyze data of this form, herein, we propose a binary regression framework that can incorporate data arising from any group testing strategy. Further, we relax previously made assumptions regarding testing error rates by relating the diagnostic testing results to the latent biological marker levels of the individuals being tested. We investigate the finite sample performance of our proposed methodology through simulation and by applying our techniques to hepatitis B data collected as part of a study involving Irish prisoners.
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Affiliation(s)
- Dewei Wang
- Department of Statistics, University of South Carolina, Columbia, SC 29028, U.S.A
| | | | - Colin M Gallagher
- Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, U.S.A
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32
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Komar N, Colborn JM, Horiuchi K, Delorey M, Biggerstaff B, Damian D, Smith K, Townsend J. Reduced West Nile Virus Transmission Around Communal Roosts of Great-Tailed Grackle (Quiscalus mexicanus). ECOHEALTH 2015; 12:144-51. [PMID: 25480320 PMCID: PMC4786297 DOI: 10.1007/s10393-014-0993-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2014] [Revised: 10/14/2014] [Accepted: 10/14/2014] [Indexed: 05/28/2023]
Abstract
West Nile virus has caused several outbreaks among humans in the Phoenix metropolitan area (Arizona, southwest USA) within the last decade. Recent ecologic studies have implicated Culex quinquefasciatus and Culex tarsalis as the mosquito vectors and identified three abundant passerine birds-great-tailed grackle (Quiscalus mexicanus), house sparrow (Passer domesticus), and house finch (Haemorhous mexicanus)-as key amplifiers among vertebrates. Nocturnal congregations of certain species have been suggested as critical for late summer West Nile virus amplification. We evaluated the hypothesis that house sparrow (P. domesticus) and/or great-tailed grackle (Q. mexicanus) communal roost sites (n = 22 and n = 5, respectively) in a primarily suburban environment were spatially associated with West Nile virus transmission indices during the 2010 outbreak of human neurological disease in metropolitan Phoenix. Spatial associations between human case residences and communal roosts were non-significant for house sparrows, and were negative for great-tailed grackle. Several theories that explain these observations are discussed, including the possibility that grackle communal roosts are protective.
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Affiliation(s)
- Nicholas Komar
- Division of Vector-Borne Diseases, Centers for Disease Control and Prevention, 3156 Rampart Road, Fort Collins, CO, 80521, USA,
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33
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Delaigle A, Hall P, Wishart JR. New approaches to nonparametric and semiparametric regression for univariate and multivariate group testing data. Biometrika 2014. [DOI: 10.1093/biomet/asu025] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
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34
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Zhang Z, Liu C, Kim S, Liu A. Prevalence estimation subject to misclassification: the mis-substitution bias and some remedies. Stat Med 2014; 33:4482-500. [PMID: 25043925 DOI: 10.1002/sim.6268] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2013] [Revised: 06/24/2014] [Accepted: 06/30/2014] [Indexed: 11/07/2022]
Abstract
We consider the problem of estimating the prevalence of a disease under a group testing framework. Because assays are usually imperfect, misclassification of disease status is a major challenge in prevalence estimation. To account for possible misclassification, it is usually assumed that the sensitivity and specificity of the assay are known and independent of the group size. This assumption is often questionable, and substitution of incorrect values of an assay's sensitivity and specificity can result in a large bias in the prevalence estimate, which we refer to as the mis-substitution bias. In this article, we propose simple designs and methods for prevalence estimation that do not require known values of assay sensitivity and specificity. If a gold standard test is available, it can be applied to a validation subsample to yield information on the imperfect assay's sensitivity and specificity. When a gold standard is unavailable, it is possible to estimate assay sensitivity and specificity, either as unknown constants or as specified functions of the group size, from group testing data with varying group size. We develop methods for estimating parameters and for finding or approximating optimal designs, and perform extensive simulation experiments to evaluate and compare the different designs. An example concerning human immunodeficiency virus infection is used to illustrate the validation subsample design.
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Affiliation(s)
- Zhiwei Zhang
- Division of Biostatistics, Office of Surveillance and Biometrics, Center for Devices and Radiological Health, Food and Drug Administration, Silver Spring, MA, U.S.A
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35
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Wang D, McMahan CS, Gallagher CM, Kulasekera KB. Semiparametric group testing regression models. Biometrika 2014. [DOI: 10.1093/biomet/asu007] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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Birkner T, Aban IB, Katholi CR. Evaluation of a Frequentist Hierarchical Model to Estimate Prevalence when sampling from a large geographic area using Pool Screening. COMMUN STAT-THEOR M 2013; 42. [PMID: 24347808 DOI: 10.1080/03610926.2011.633732] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Abstract
We present a frequentist Bernoulli-Beta hierarchical model to relax the constant prevalence assumption underlying the traditional prevalence estimation approach based on pooled data. This assumption is called into question when sampling from a large geographic area. Pool screening is a method that combines individual items into pools. Each pool will either test positive (at least one of the items is positive) or negative (all items are negative). Pool screening is commonly applied to the study of tropical diseases where pools consist of vectors (e.g. black flies) that can transmit the disease. The goal is to estimate the proportion of infected vectors. Intermediate estimators (model parameters) and estimators of ultimate interest (pertaining to prevalence) are evaluated by standard measures of merit, such as bias, variance and mean squared error making extensive use of expansions. Using the hierarchical model an investigator can determine the probability of the prevalence being below a prespecified threshold value, a value at which no reemergence of the disease is expected. An investigation into the least biased choice of the α parameter in the Beta (α, β) prevalence distribution leads to the choice of α = 1.
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Affiliation(s)
- Thomas Birkner
- Department of Biostatistics, University of Alabama at Birmingham, Birmingham, Alabama
| | - Inmaculada B Aban
- Department of Biostatistics, University of Alabama at Birmingham, Birmingham, Alabama
| | - Charles R Katholi
- Department of Biostatistics, University of Alabama at Birmingham, Birmingham, Alabama
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37
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Zhang B, Bilder CR, Tebbs JM. Regression analysis for multiple-disease group testing data. Stat Med 2013; 32:4954-66. [PMID: 23703944 PMCID: PMC4301740 DOI: 10.1002/sim.5858] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2012] [Accepted: 04/29/2013] [Indexed: 11/06/2022]
Abstract
Group testing, where individual specimens are composited into groups to test for the presence of a disease (or other binary characteristic), is a procedure commonly used to reduce the costs of screening a large number of individuals. Group testing data are unique in that only group responses may be available, but inferences are needed at the individual level. A further methodological challenge arises when individuals are tested in groups for multiple diseases simultaneously, because unobserved individual disease statuses are likely correlated. In this paper, we propose new regression techniques for multiple-disease group testing data. We develop an expectation-solution based algorithm that provides consistent parameter estimates and natural large-sample inference procedures. We apply our proposed methodology to chlamydia and gonorrhea screening data collected in Nebraska as part of the Infertility Prevention Project and to prenatal infectious disease screening data from Kenya.
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Affiliation(s)
- Boan Zhang
- Department of Statistics, University of Nebraska-Lincoln, Lincoln, NE 68583, USA
| | | | - Joshua M. Tebbs
- Department of Statistics, University of South Carolina, Columbia, SC 29208, USA
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38
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Tebbs JM, McMahan CS, Bilder CR. Two-stage hierarchical group testing for multiple infections with application to the infertility prevention project. Biometrics 2013; 69:1064-73. [PMID: 24117173 PMCID: PMC4371872 DOI: 10.1111/biom.12080] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2013] [Revised: 06/01/2013] [Accepted: 06/01/2013] [Indexed: 11/30/2022]
Abstract
Screening for sexually transmitted diseases (STDs) has benefited greatly from the use of group testing (pooled testing) to lower costs. With the development of assays that detect multiple infections, screening practices now involve testing pools of individuals for multiple infections simultaneously. Building on the research for single infection group testing procedures, we examine the performance of group testing for multiple infections. Our work is motivated by chlamydia and gonorrhea testing for the infertility prevention project (IPP), a national program in the United States. We consider a two-stage pooling algorithm currently used to perform testing for the IPP. We first derive the operating characteristics of this algorithm for classification purposes (e.g., expected number of tests, misclassification probabilities, etc.) and identify pool sizes that minimize the expected number of tests. We then develop an expectation-maximization (EM) algorithm to estimate probabilities of infection using both group and individual retest responses. Our research shows that group testing can offer large cost savings when classifying individuals for multiple infections and can provide prevalence estimates that are actually more efficient than those from individual testing.
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Affiliation(s)
- Joshua M. Tebbs
- Department of Statistics, University of South Carolina, Columbia, SC 29208, U.S.A
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McMahan CS, Tebbs JM, Bilder CR. Regression models for group testing data with pool dilution effects. Biostatistics 2013; 14:284-98. [PMID: 23197382 PMCID: PMC3590921 DOI: 10.1093/biostatistics/kxs045] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2012] [Revised: 10/17/2012] [Accepted: 10/19/2012] [Indexed: 11/13/2022] Open
Abstract
Group testing is widely used to reduce the cost of screening individuals for infectious diseases. There is an extensive literature on group testing, most of which traditionally has focused on estimating the probability of infection in a homogeneous population. More recently, this research area has shifted towards estimating individual-specific probabilities in a regression context. However, existing regression approaches have assumed that the sensitivity and specificity of pooled biospecimens are constant and do not depend on the pool sizes. For those applications, where this assumption may not be realistic, these existing approaches can lead to inaccurate inference, especially when pool sizes are large. Our new approach, which exploits the information readily available from underlying continuous biomarker distributions, provides reliable inference in settings where pooling would be most beneficial and does so even for larger pool sizes. We illustrate our methodology using hepatitis B data from a study involving Irish prisoners.
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Hund L, Pagano M. Estimating HIV prevalence from surveys with low individual consent rates: annealing individual and pooled samples. Emerg Themes Epidemiol 2013; 10:2. [PMID: 23446064 PMCID: PMC3649931 DOI: 10.1186/1742-7622-10-2] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2012] [Accepted: 02/20/2013] [Indexed: 11/30/2022] Open
Abstract
Many HIV prevalence surveys are plagued by the problem that a sizeable number of surveyed individuals do not consent to contribute blood samples for testing. One can ignore this problem, as is often done, but the resultant bias can be of sufficient magnitude to invalidate the results of the survey, especially if the number of non-responders is high and the reason for refusing to participate is related to the individual’s HIV status. One reason for refusing to participate may be for reasons of privacy. For those individuals, we suggest offering the option of being tested in a pool. This form of testing is less certain than individual testing, but, if it convinces more people to submit to testing, it should reduce the potential for bias and give a cleaner answer to the question of prevalence. This paper explores the logistics of implementing a combined individual and pooled testing approach and evaluates the analytical advantages to such a combined testing strategy. We quantify improvements in a prevalence estimator based on this combined testing strategy, relative to an individual testing only approach and a pooled testing only approach. Minimizing non-response is key for reducing bias, and, if pooled testing assuages privacy concerns, offering a pooled testing strategy has the potential to substantially improve HIV prevalence estimates.
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Affiliation(s)
- Lauren Hund
- Department of Family and Community Medicine, University of New Mexico, 2400 Tucker NE, Albuquerque, NM 87106, USA.
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Zhang B, Bilder CR, Tebbs JM. Group testing regression model estimation when case identification is a goal. Biom J 2013; 55:173-89. [PMID: 23401252 DOI: 10.1002/bimj.201200168] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2012] [Revised: 11/16/2012] [Accepted: 12/22/2012] [Indexed: 11/10/2022]
Abstract
Group testing is frequently used to reduce the costs of screening a large number of individuals for infectious diseases or other binary characteristics in small prevalence situations. In many applications, the goals include both identifying individuals as positive or negative and estimating the probability of positivity. The identification aspect leads to additional tests being performed, known as "retests", beyond those performed for initial groups of individuals. In this paper, we investigate how regression models can be fit to estimate the probability of positivity while also incorporating the extra information from these retests. We present simulation evidence showing that significant gains in efficiency occur by incorporating retesting information, and we further examine which testing protocols are the most efficient to use. Our investigations also demonstrate that some group testing protocols can actually lead to more efficient estimates than individual testing when diagnostic tests are imperfect. The proposed methods are applied retrospectively to chlamydia screening data from the Infertility Prevention Project. We demonstrate that significant cost savings could occur through the use of particular group testing protocols.
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Affiliation(s)
- Boan Zhang
- Department of Statistics, University of Nebraska-Lincoln, Lincoln, NE 68583, USA
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Abstract
In situations where individuals are screened for an infectious disease or other binary characteristic and where resources for testing are limited, group testing can offer substantial benefits. Group testing, where subjects are tested in groups (pools) initially, has been successfully applied to problems in blood bank screening, public health, drug discovery, genetics, and many other areas. In these applications, often the goal is to identify each individual as positive or negative using initial group tests and subsequent retests of individuals within positive groups. Many group testing identification procedures have been proposed; however, the vast majority of them fail to incorporate heterogeneity among the individuals being screened. In this paper, we present a new approach to identify positive individuals when covariate information is available on each. This covariate information is used to structure how retesting is implemented within positive groups; therefore, we call this new approach "informative retesting." We derive closed-form expressions and implementation algorithms for the probability mass functions for the number of tests needed to decode positive groups. These informative retesting procedures are illustrated through a number of examples and are applied to chlamydia and gonorrhea testing in Nebraska for the Infertility Prevention Project. Overall, our work shows compelling evidence that informative retesting can dramatically decrease the number of tests while providing accuracy similar to established non-informative retesting procedures.
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Affiliation(s)
- Christopher R Bilder
- Associate Professor of Statistics ( , Website: www.chrisbilder.com ) at the University of Nebraska-Lincoln, Lincoln, NE 68583
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Black MS, Bilder CR, Tebbs JM. Group testing in heterogeneous populations by using halving algorithms. J R Stat Soc Ser C Appl Stat 2011; 61:277-290. [PMID: 25035521 DOI: 10.1111/j.1467-9876.2011.01008.x] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Group (pooled) testing is often used to reduce the total number of tests that are needed to screen a large number of individuals for an infectious disease or some other binary characteristic. Traditionally, research in group testing has assumed that each individual is independent with the same risk of positivity. More recently, there has been a growing set of literature generalizing previous work in group testing to include heterogeneous populations so that each individual has a different risk of positivity. We investigate the effect of acknowledging population heterogeneity on a commonly used group testing procedure which is known as 'halving'. For this procedure, positive groups are successively split into two equal-sized halves until all groups test negatively or until individual testing occurs. We show that heterogeneity does not affect the mean number of tests when individuals are randomly assigned to subgroups. However, when individuals are assigned to subgroups on the basis of their risk probabilities, we show that our proposed procedures reduce the number of tests by taking advantage of the heterogeneity. This is illustrated by using chlamydia and gonorrhoea screening data from the state of Nebraska.
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Abstract
Since the early 1940s, group testing (pooled testing) has been used to reduce costs in a variety of applications, including infectious disease screening, drug discovery, and genetics. In such applications, the goal is often to classify individuals as positive or negative using initial group testing results and the subsequent process of decoding of positive pools. Many decoding algorithms have been proposed, but most fail to acknowledge, and to further exploit, the heterogeneous nature of the individuals being screened. In this article, we use individuals' risk probabilities to formulate new informative decoding algorithms that implement Dorfman retesting in a heterogeneous population. We introduce the concept of "thresholding" to classify individuals as "high" or "low risk," so that separate, risk-specific algorithms may be used, while simultaneously identifying pool sizes that minimize the expected number of tests. When compared to competing algorithms which treat the population as homogeneous, we show that significant gains in testing efficiency can be realized with virtually no loss in screening accuracy. An important additional benefit is that our new procedures are easy to implement. We apply our methods to chlamydia and gonorrhea data collected recently in Nebraska as part of the Infertility Prevention Project.
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Affiliation(s)
- Christopher S McMahan
- Department of Statistics, University of South Carolina, Columbia, South Carolina 29208, USA
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Pritchard NA, Tebbs JM. Estimating Disease Prevalence Using Inverse Binomial Pooled Testing. JOURNAL OF AGRICULTURAL, BIOLOGICAL, AND ENVIRONMENTAL STATISTICS 2011; 16:70-87. [PMID: 21743789 PMCID: PMC3131210 DOI: 10.1007/s13253-010-0036-4] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Monitoring populations of hosts as well as insect vectors is an important part of agricultural and public health risk assessment. In applications where pathogen prevalence is likely low, it is common to test pools of subjects for the presence of infection, rather than to test subjects individually. This technique is known as pooled (group) testing. In this paper, we revisit the problem of estimating the population prevalence p from pooled testing, but we consider applications where inverse binomial sampling is used. Our work is unlike previous research in pooled testing, which has largely assumed a binomial model. Inverse sampling is natural to implement when there is a need to report estimates early on in the data collection process and has been used in individual testing applications when disease incidence is low. We consider point and interval estimation procedures for p in this new pooled testing setting, and we use example data sets from the literature to describe and to illustrate our methods.
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Affiliation(s)
- Nicholas A. Pritchard
- Department of Mathematics and Statistics, Coastal Carolina University, Conway, SC 29528, USA
| | - Joshua M. Tebbs
- Department of Statistics, University of South Carolina, Columbia, SC 29208, USA
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Abstract
Group testing, where subjects are tested in pools rather than individually, has a long history of successful application in infectious disease screening. In this article, we develop group testing regression models to include covariate effects that are best regarded as random. We present approaches to fit mixed effects models using maximum likelihood, investigate likelihood ratio and score tests for variance components, and evaluate small sample performance using simulation. We illustrate our methods using chlamydia and gonorrhea data collected by the state of Nebraska as part of the Infertility Prevention Project.
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Affiliation(s)
- Peng Chen
- Department of Statistics, University of South Carolina, Columbia, South Carolina 29208, USA
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Chen P, Tebbs JM, Bilder CR. Global goodness-of-fit tests for group testing regression models. Stat Med 2009; 28:2912-28. [PMID: 19610130 DOI: 10.1002/sim.3678] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
In a variety of biomedical applications, particularly those involving screening for infectious diseases, testing individuals (e.g. blood/urine samples, etc.) in pools has become a standard method of data collection. This experimental design, known as group testing (or pooled testing), can provide a large reduction in testing costs and can offer nearly the same precision as individual testing. To account for covariate information on individual subjects, regression models for group testing data have been proposed recently. However, there are currently no tools available to check the adequacy of these models. In this paper, we present various global goodness-of-fit tests for regression models with group testing data. We use simulation to examine the small-sample size and power properties of the tests for different pool composition strategies. We illustrate our methods using two infectious disease data sets, one from an HIV study in Kenya and one from the Infertility Prevention Project.
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Affiliation(s)
- Peng Chen
- Takeda Global Research and Development Center, Inc., 675 North Field Drive, Lake Forest, IL 60045, USA
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Huang X. An improved test of latent-variable model misspecification in structural measurement error models for group testing data. Stat Med 2009; 28:3316-27. [DOI: 10.1002/sim.3698] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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