Bias Correction in Estimating Proportions by Pooled Testing

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 (Biometrika 80: 27-38, 1993), which uses a modification of the score function, and we provide an easily computable, Newton-Raphson iterative formula for its computation. Our proposed estimator is almost unbiased across a range of problems, and superior to existing methods. We showthat for equal pool sizes the newestimator is equivalent to the estimator proposed by Burrows (Phytopathology 77: 363-365, 1987). The performance of our estimator is examined using pooled testing problems encountered in plant disease assessment and prevalence estimation of mosquito-borne viruses. Supplementary materials accompanying this paper appear online.