An Empirical Bayes Group-Testing Approach to Estimating Small Proportions

Group testing has long been recognized as a safe and sensible alternative to one-at-a-time testing in applications wherein the prevalence rate p is small. In this article, we develop an empirical Bayes (EB) procedure to estimate p using a beta-type prior distribution and a squared-error loss functio...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2003-01, Vol.32 (5), p.983-995
Main Authors: Tebbs, Joshua M., Bilder, Christopher R., Moser, Barry K.
Format: Article
Language:English
Subjects:
Applications
Composite sampling
Decision theory
Empirical Bayes estimation
Exact sciences and technology
Hepatitis C virus
Mathematics
Medical sciences
Pooling designs
Probability and statistics
Sciences and techniques of general use
Screening experiments
Statistics
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Summary:Group testing has long been recognized as a safe and sensible alternative to one-at-a-time testing in applications wherein the prevalence rate p is small. In this article, we develop an empirical Bayes (EB) procedure to estimate p using a beta-type prior distribution and a squared-error loss function. We show that the EB estimator is preferred over the usual maximum likelihood estimator (MLE) for small group sizes and small p. In addition, we also discuss interval estimation and consider the use of other loss functions perhaps more appropriate in public health studies. The proposed methods are illustrated using group-testing data from a prospective hepatitis C virus study conducted in Xuzhou City, China.
ISSN:0361-0926
1532-415X
DOI:10.1081/STA-120019957