Journal
BIOMETRICAL JOURNAL
Volume 48, Issue 5, Pages 792-804Publisher
AKADEMIE VERLAG GMBH
DOI: 10.1002/bimj.200510261
Keywords
arc-sin square-root transformation; Erwinia stewartii; group testing; HIV prevalence; isotonic regression; likelihood ratio test; order-restricted inference; Stewart's wilt rating; vector-transfer design
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The use of pooled testing as a means of estimating the prevalence of rare traits has received considerable attention in recent years, particularly in the areas of public health, genetics, animal-disease assessment, and plant pathology. In pooled-testing applications, observations are made on pools of individuals amalgamated together. In this paper, we examine order-restricted hypothesis tests involving k > 2 binomial proportions estimated by pooled testing, extending the earlier work of Tebbs and Swallow (2003, Biometrika, 90, 471-477 and Biometrical Journal, 45, 618-630). In particular, we focus on (i) testing the equality of proportions versus an isotonic alternative and (ii) testing for a violation of isotonicity. We propose new tests for each scenario and provide results which characterize the small-sample performance of our procedures. We illustrate our methods using two data sets; one from an observational HIV study and one from an agricultural experiment.
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