Exact Confidence Intervals for Proportions Estimated by Group Testing with Different Group Sizes

Group testing is the process of combining individual samples and testing them as a group for the presence of an attribute. The use of such testing to estimate proportions is an important statistical tool in many applications. When samples are collected and tested in groups of different size, complications arise in the construction of exact confidence intervals. In this case, the numbers of positive groups has a multivariate distribution, and the difficulty stems from a lack of a natural ordering of the sample points. Exact two‐sided intervals such as the equal‐tail method based on maximum likelihood estimation, and those based on joint probability or likelihood ratio statistics, have been previously considered. In this paper several new estimators are developed and assessed. We show that the combined tails (or Blaker) method based on a suitable ordering statistic, is the best choice in this setting. The methods are illustrated using a study involving the infection prevalence of Myxobolus cerebralis among free‐ranging fish.