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Robustness of Group Testing in the Estimation of Proportions
Author(s) -
Hung M.,
Swallow William H.
Publication year - 1999
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.1999.00231.x
Subject(s) - group testing , statistics , group tests , mathematics , robustness (evolution) , binomial distribution , independent and identically distributed random variables , group (periodic table) , estimator , bernoulli's principle , correlation , negative binomial distribution , standard error , statistical hypothesis testing , random variable , econometrics , combinatorics , poisson distribution , biochemistry , chemistry , geometry , organic chemistry , engineering , gene , aerospace engineering
Summary. In binomial group testing, unlike one‐at‐a‐time testing, the test unit consists of a group of individuals, and each group is declared to be defective or nondefective. A defective group is one that is presumed to include one or more defective (e.g., infected, positive) individuals and a nondefective group to contain only nondefective individuals. The usual binomial model considers the individuals being grouped as independent and identically distributed Bernoulli random variables. Under the binomial model and presuming that groups are tested and classified without error, it has been shown that, when the proportion of defective individuals is low, group testing is often preferable to individual testing for identifying infected individuals and for estimating proportions of defectives. We discuss the robustness of group testing for estimating proportions when the underlying assumptions of (i) no testing errors and (ii) independent individuals are violated. To evaluate the effect of these model violations, two dilution‐effect models and a serial correlation model are considered. Group testing proved to be quite robust to serial correlation. In the presence of a dilution effect, smaller group sizes should be used, but most of the benefits of group testing can still be realized.