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Confidence interval procedures for proportions estimated by group testing with groups of unequal size adjusted for overdispersion
Authors:Shih-Chia Liu  Cheng-Hsiang Lin  Ting-Chin Deng
Institution:1. Department of Statistics , Tunghai University , Taichung, Taiwan, Republic of China;2. Department of Statistics and Department of Finance , Tunghai University , Taichung, Taiwan, Republic of China;3. Plant Pathology Division , Agricultural Research Institute , Wufeng, Taichung, Taiwan, Republic of China
Abstract:Group testing is a method of pooling a number of units together and performing a single test on the resulting group. Group testing is an appealing option when few individual units are thought to be infected and the cost of the testing is non-negligible. Overdispersion is the phenomenon of having greater variability than predicted by the random component of the model; this is common in the modeling of binomial distribution for group testing. The purpose of this paper is to provide a comparison of several established methods of constructing confidence intervals after adjusting for overdispersion. We evaluate and investigate each method in six different cases of group testing. A method based on the score statistic with correction for skewness is recommended. We illustrate the methods using two data sets, one from the detection of seed transmission and the other from serological testing for malaria.
Keywords:group testing  confidence interval  quasi-likelihood  overdispersion  seed health assays
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