Group testing occurs when units from a population are pooled and tested as a group for the presence of a particular attribute, such as a disease. It is assumed that if the test result is positive, at least one of the units in the group is positive, and if the result is negative, all the units are negative. Group testing has been applied in many fields of study since its first appearance in the statistical literature, Dorfman (Ref. 1). These fields include plant disease assessment, Fletcher, Russell and Butler (Ref. 2), fisheries, Worlund and Taylor (Ref. 3), and transmission of viruses by insect vectors, Swallow (Ref. 4). Group testing has also appeared under other names, such as 'batch sampling' and 'pooled testing'. Its main benefit is the saving of resources due to the fact that many units are not individually tested. Group testing has one of the following two aims, which in practice are almost mutually exclusive either to identify the positive units in the groups tested or to estimate the proportion of positives (p) in the wider population. Two assumptions will be made about group testing in this article: The outcomes for the units in each group follow independent, identically distributed (iid) binomial distributions with parameter p. The testing is conducted without error, that is, there are no false negatives (perfect sensitivity) and no false positives (perfect specificity). Section 2 examines interval estimation methods based on functions of the MLE of p, looking first at the identity function, which is shown to be unsatisfactory. The logit and complementary log-log functions are then considered and are shown to warrant further investigation. Section 3 examines methods based on the score and finds a correction for skewness to provide the substantial improvement necessary to consider the method further. Section 4 considers intervals based on the likelihood ratio, which also prove to be satisfactory. Section 5 compares the four promising methods using five realistic group testing procedures involving unequal group sizes. A brief comparison is also made with exact interval estimation methods. The main assessment criterion used in the comparisons is the coverage probability achieved by nominal 95 percent CIs, though interval width is also considered. Section 6 concludes the article with a discussion.
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