Bias correction of estimated proportions using inverse binomial group testing

Abstract

SummaryGroup testing, in which individuals are pooled together and tested as a group, can be combined with inverse sampling to estimate the prevalence of a disease. Alternatives to the MLE are desirable because of its severe bias. We propose an estimator based on the bias correction method of Firth (1993), which is almost unbiased across the range of prevalences consistent with the group testing design. For equal group sizes, this estimator is shown to be equivalent to that derived by applying the correction method of Burrows (1987), and better than existing methods. For unequal group sizes, the problem has some intractable elements, but under some circumstances our proposed estimator can be found, and we show it to be almost unbiased. Calculation of the bias requires computer‐intensive approximation because of the infinite number of possible outcomes.