Mid-P confidence intervals for group testing based on the total number of positive groups

In the estimation of proportions by group testing, unequal sized groups results in an ambiguous ordering of the sample space, which complicates the construction of exact confidence intervals. The total number of positive groups is shown to be a suitable statistic for ordering outcomes, provided its ties are broken by the MLE. We propose an interval estimation method based on this quantity, with a mid-P correction. Coverage is evaluated using group testing problems in plant disease assessment and virus transmission by insect vectors. The proposed method provides good coverage in a range of situations, and compares favorably with existing exact methods.