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@Article{Malinovsky2016,
  author   = {{Malinovsky, Y.} and {Albert, P.} and {Roy, A.}},
  title    = {Reader reaction: A note on the evaluation of group testing algorithms in the presence of misclassification},
  journal  = {Biometrics},
  year     = {2016},
  volume   = {72},
  pages    = {299--302},
  doi      = {10.1111/biom.12385},
  keywords = {Dorfman two-stage procedure,Group testing,Optimum group size,Sensitivity,Specificity},
}

@Article{McMahan2012b,
  author   = {{McMahan, C.} and {Tebbs, J.} and {Bilder, C.}},
  title    = {Two-Dimensional Informative Array Testing},
  journal  = {Biometrics},
  year     = {2012b},
  volume   = {68},
  pages    = {793--804},
  abstract = {Array-based group-testing algorithms for case identification are widely$\backslash$nused in infectious disease testing, drug discovery, and genetics. In$\backslash$nthis article, we generalize previous statistical work in array testing$\backslash$nto account for heterogeneity among individuals being tested. We first$\backslash$nderive closed-form expressions for the expected number of tests$\backslash$n(efficiency) and misclassification probabilities (sensitivity,$\backslash$nspecificity, predictive values) for two-dimensional array testing in a$\backslash$nheterogeneous population. We then propose two informative array$\backslash$nconstruction techniques which exploit population heterogeneity in ways$\backslash$nthat can substantially improve testing efficiency when compared to$\backslash$nclassical approaches that regard the population as homogeneous.$\backslash$nFurthermore, a useful byproduct of our methodology is that$\backslash$nmisclassification probabilities can be estimated on a per-individual$\backslash$nbasis. We illustrate our new procedures using chlamydia and gonorrhea$\backslash$ntesting data collected in Nebraska as part of the Infertility Prevention$\backslash$nProject.},
  doi      = {10.1111/j.1541-0420.2011.01726.x},
  isbn     = {1541-0420 (Electronic)$\backslash$r0006-341X (Linking)},
  keywords = {Disease screening,Efficiency,Group testing,Infertility Prevention Project,Matrix pooling,Pooled testing},
  pmid     = {22212007},
}

@Article{McMahan2012a,
  author   = {{McMahan, C.} and {Tebbs, J.} and {Bilder, C.}},
  title    = {Informative {D}orfman Screening},
  journal  = {Biometrics},
  year     = {2012a},
  volume   = {68},
  pages    = {287--296},
  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.},
  doi      = {10.1111/j.1541-0420.2011.01644.x},
  isbn     = {1541-0420 (Electronic)$\backslash$r0006-341X (Linking)},
  keywords = {Dorfman retesting,Group testing,Infertility Prevention Project,Pooled testing,Sensitivity,Specificity},
  pmid     = {21762119},
}

@Article{Graff1972,
  author   = {{Graff, L.} and {Roeloffs, R.}},
  title    = {Group testing in the presence of test error; an extension of the {D}orfman procedure},
  journal  = {Technometrics},
  year     = {1972},
  volume   = {14},
  pages    = {113--122},
  doi      = {10.1080/00401706.1972.10488888},
  keywords = {Binomial distribution,Group testing,Screening},
}

@Article{Black2015,
  author   = {{Black, M.} and {Bilder, C.} and {Tebbs, J.}},
  title    = {Optimal retesting configurations for hierarchical group testing},
  journal  = {Journal of the Royal Statistical Society. Series C: Applied Statistics},
  year     = {2015},
  volume   = {64},
  pages    = {693--710},
  abstract = {Hierarchical group testing is widely used to test individuals for diseases. This testing procedure works by first amalgamating individual specimens into groups for testing. Groups testing negatively have their members declared negative. Groups testing positively are subsequently divided into smaller subgroups and are then retested to search for positive individuals. We propose a new class of informative retesting procedures for hierarchical group testing that acknowledges heterogeneity among individuals. These procedures identify the optimal number of groups and their sizes at each testing stage to minimize the expected number of tests. We apply our proposals in two settings: human immunodeficiency virus testing programmes that currently use three‐stage hierarchical testing and chlamydia and gonorrhoea screening practices that currently use individual testing. For both applications, we show that substantial savings can be realized by our new procedures. (PsycINFO Database Record (c) 2016 APA, all rights reserved)},
  doi      = {10.1111/rssc.12097},
  isbn     = {0035-9254 1467-9876},
  keywords = {Classification,Human immunodeficiency virus,Infertility prevention project,Informative retesting,Pooled testing,Retesting},
}

@Article{Black2012,
  author   = {{Black, M.} and {Bilder, C.} and {Tebbs, J.}},
  title    = {Group testing in heterogeneous populations by using halving algorithms},
  journal  = {Journal of the Royal Statistical Society. Series C: Applied Statistics},
  year     = {2012},
  volume   = {61},
  pages    = {277--290},
  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. (PsycINFO Database Record (c) 2016 APA, all rights reserved)},
  doi      = {10.1111/j.1467-9876.2011.01008.x},
  isbn     = {0035-9254 1467-9876},
  keywords = {Binary response,Classification,Identification,Pooled testing,Retesting,Screening},
}

@Article{Bilder2010a,
  author   = {{Bilder, C.} and {Tebbs, J.} and {Chen, P.}},
  title    = {Informative retesting},
  journal  = {Journal of the American Statistical Association},
  year     = {2010},
  volume   = {105},
  pages    = {942--955},
  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.},
  doi      = {10.1198/jasa.2010.ap09231},
  keywords = {Binary response,Chlamydia,Gonorrhea,Group testing,Identification,Pooled testing},
}

@Article{Altman1994a,
  author  = {{Altman, D.} and {Bland, J.}},
  title   = {Diagnostic tests 1: Sensitivity and specificity},
  journal = {BMJ},
  year    = {1994},
  volume  = {308},
  pages   = {1552},
}

@Article{Altman1994b,
  author  = {{Altman, D.} and {Bland, J.}},
  title   = {Diagnostic tests 2: Predictive values},
  journal = {BMJ},
  year    = {1994},
  volume  = {309},
  pages   = {102},
}

@Article{Hitt2019,
  author  = {{Hitt, B.} and {Bilder, C.} and {Tebbs, J.} and {McMahan, C.}},
  title   = {The objective function controversy for group testing: Much ado about nothing?},
  journal = {Statistics in Medicine},
  year    = {2019},
  volume  = {38},
  pages   = {4912--4923},
  doi     = {10.1002/sim.8341},
}

@Article{Vansteelandt2000,
  author  = {{Vansteelandt, S.} and {Goetghebeur, E.} and {Verstraeten, T.}},
  title   = {Regression models for disease prevalence with diagnostic tests on pools of serum samples},
  journal = {Biometrics},
  year    = {2000},
  volume  = {56},
  pages   = {1126--1133},
  doi     = {10.1111/j.0006-341x.2000.01126.x},
}

@Article{Biggerstaff2008,
  author  = {{Biggerstaff, B.}},
  title   = {Confidence intervals for the difference of proportions estimated from pooled samples},
  journal = {Journal of Agricultural, Biological, and Environmental Statistics},
  year    = {2008},
  volume  = {13},
  pages   = {478--496},
  doi     = {10.1198/108571108X379055},
}

@Article{Hepworth1996,
  author  = {{Hepworth, G.}},
  title   = {Exact confidence intervals for proportions estimated by group testing},
  journal = {Biometrics},
  year    = {1996},
  volume  = {52},
  pages   = {1134--1146},
}

@Article{Schaarschmidt2007,
  author  = {{Schaarschmidt, F.}},
  title   = {Experimental design for one-sided confidence intervals or hypothesis tests in binomial group testing},
  journal = {Communications in Biometry and Crop Science},
  year    = {2007},
  volume  = {2},
  pages   = {32--40},
  issn    = {1896-0782},
}

@Article{Swallow1985,
  author  = {{Swallow, W.}},
  title   = {Group testing for estimating infection rates and probabilities of disease transmission},
  journal = {Phytopathology},
  year    = {1985},
  volume  = {75},
  pages   = {882--889},
  doi     = {10.1094/Phyto-75-882},
}

@Article{Tebbs2004,
  author  = {{Tebbs, J.} and {Bilder, C.}},
  title   = {Confidence interval procedures for the probability of disease transmission in multiple-vector-transfer designs},
  journal = {Journal of Agricultural, Biological, and Environmental Statistics},
  year    = {2004},
  volume  = {9},
  pages   = {75--90},
  doi     = {10.1198/1085711043127},
}

@Article{Xie2001,
  author  = {{Xie, M.}},
  title   = {Regression analysis of group testing samples},
  journal = {Statistics in Medicine},
  year    = {2001},
  volume  = {20},
  pages   = {1957--1969},
  doi     = {10.1002/sim.817},
}

@Unpublished{Hou2019,
  author = {{Hou, P.} and {Tebbs, J.} and {Wang, D.} and {McMahan, C.} and {Bilder, C.}},
  title  = {Array testing with multiplex assays},
  note   = {To appear in \emph{Biostatistics}},
  year   = {2020},
}

@Article{Bilder2019,
  author  = {{Bilder, C.} and {Tebbs, J.} and {McMahan, C.}},
  title   = {Informative group testing for multiplex assays},
  journal = {Biometrics},
  year    = {2019},
  volume  = {75},
  pages   = {278--288},
  doi     = {10.1111/biom.12988},
}

@Article{Hepworth2017,
  author  = {{Hepworth, G.} and {Biggerstaff, B.}},
  title   = {Bias correction in estimating proportions by pooled testing},
  journal = {Journal of Agricultural, Biological, and Environmental Statistics},
  year    = {2017},
  volume  = {22},
  pages   = {602--614},
  month   = dec,
  doi     = {10.1007/s13253-017-0297-2},
}

@Article{Bilder2019est,
  author   = {{Bilder, C.}},
  title    = {Group Testing for Estimation},
  journal  = {Wiley StatsRef: Statistics Reference Online},
  year     = {2019a},
  abstract = {Abstract Group (pooled) testing involves combining a set number of items together and performing one test for a binary trait (e.g., positive or negative for a disease) on that combination. While testing is performed on the group, the purpose is still to understand this trait relative to each individual item. When compared to testing a large number of items separately, testing instead via groups can result in a significant reduction in the total number of tests, provided that the prevalence of a particular level of the trait (e.g., positive for a disease) is small. Furthermore, group testing can lead to more efficient estimators than individual testing if testing error is possible. The purpose of this article is to introduce how estimation can be performed with data arising through group testing. Focus is on estimating the probability an item has a particular level of the trait rather than determining the trait status of individual items.},
  doi      = {10.1002/9781118445112.stat08231},
  keywords = {binary response, infectious disease, pooled testing, R, regression, screening, sensitivity, specificity, testing},
}

@Article{Bilder2019id,
  author   = {{Bilder, C.}},
  title    = {Group Testing for Identification},
  journal  = {Wiley StatsRef: Statistics Reference Online},
  year     = {2019b},
  abstract = {Abstract Grouping (pooling) items together and testing them as one unit for a binary trait is the process known concurrently as group testing and pooled testing. As long as trait prevalence is small, group testing can lead to significant reductions in the number of tests when compared to testing each item individually. The purpose of this article is to outline commonly used group-testing algorithms and describe how to calculate their corresponding operating characteristics. Focus is on using group testing to identify whether an item has a particular trait rather than estimating the probability an item has this trait.},
  doi      = {10.1002/9781118445112.stat08227},
  keywords = {binary response, infectious disease, pooled testing, R , screening, sensitivity, specificity, testing},
}

@Article{Verstraeten1998,
  author  = {{Verstraeten, T.} and {Farah, B.} and {Duchateau, L.} and {Matu, R.}},
  title   = {Pooling sera to reduce the cost of {HIV} surveillance: a feasibility study in a rural {K}enyan district},
  journal = {Tropical Medicine \& International Health},
  year    = {1998},
  volume  = {3},
  pages   = {747--750},
  doi     = {10.1046/j.1365-3156.1998.00293.x},
}

@Comment{jabref-meta: databaseType:bibtex;}
