Confidence intervals for proportions estimated by group testing with groups of unequal size

Group testing, in which units are pooled together and tested as a group for the presence of an attribute, has been used in many fields of study, including blood testing, plant disease assessment, fisheries, and vector transmission of viruses. When groups are of unequal size, complications arise in the derivation of confidence intervals for the proportion of units in the population with the attribute. We evaluate several asymptotic interval estimation methods for problems in which groups are of different size. Each method is examined for its theoretical properties, and adapted or developed for group testing. In an initial assessment using a study of virus prevalence in carnations, four methods are found to be satisfactory, and are considered further—two based on the distribution of the MLE, one on the score statistic, and one on the likelihood ratio. The performance of each method is then tested empirically on five realistic group testing procedures, with the evaluation focusing on the coverage probability provided by the confidence intervals. A method based on the score statistic with a correction for skewness is recommended, followed by a method in which the logit function is applied to the MLE.