Improved Estimation of Proportions Using Inverse Binomial Group Testing

Inverse sampling for proportions is useful when there is a need to estimate the prevalence of a disease without delay. This can be combined with group (pooled) testing, in which individuals are pooled together and tested as a group for the disease. Pritchard and Tebbs (in Journal of Agricultural, Biological, and Environmental Statistics 16, 70-87, 2011a) introduced this combination to the statistical literature, and we have addressed some of the key problems raised, for groups of equal size. Most point estimators of the proportion are biased, especially the MLE, but by applying a suitable correction we have developed an estimator which is almost unbiased in the region of interest. We propose two interval estimators which improve on existing methods and have excellent coverage properties. Our recommendation is a score-based method with a correction for skewness, but a good alternative is an exact method with a mid-P correction.