Pooled testing (or group testing) arises when units are pooled together and tested as a group for the presence of an attribute, such as a disease. We have encountered pooled testing problems in plant disease assessment and prevalence estimation of mosquito-borne viruses.

In the estimation of proportions by pooled testing, the MLE is biased, and several methods of correcting the bias have been presented in previous studies. We propose a new estimator based on the bias correction method introduced by Firth (1993), which uses a modification of the score function. Our proposed estimator is almost unbiased across a range of problems, and superior to existing methods. We show that for equal pool sizes the new estimator is equivalent to the estimator proposed by Burrows (1987), which has been used by many practitioners.