Mid-P confidence intervals based on the likelihood ratio for proportions estimated by group testing

Group testing has been used in many fields of study to estimate proportions. When groups are of different size, the derivation of exact confidence intervals is complicated by the lack of a unique ordering of the event space. An exact interval estimation method is described here, in which outcomes are ordered according to a likelihood ratio statistic. The method is compared with another exact method, in which outcomes are ordered by their associated MLE. Plots of the P-value against the proportion are useful in examining the properties of the methods. Coverage provided by the intervals is assessed using several realistic grouptesting procedures. The method based on the likelihood ratio, with a mid-P correction, is shown to give very good coverage in terms of closeness to the nominal level, and is recommended for this type of problem.