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 show that for equal pool sizes the new estimator 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.

中文翻译：

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通过合并测试估计比例的偏差校正

在通过合并检验估计比例时，MLE 是有偏差的，以前的研究中已经提出了几种纠正偏差的方法。我们提出了一种基于 Firth (Biometrika 80:27–38, 1993) 引入的偏差校正方法的新估计器，它使用了分数函数的修改，并且我们提供了一个易于计算的 Newton-Raphson 迭代公式来计算。我们提出的估计器在一系列问题上几乎是无偏的，并且优于现有方法。我们表明，对于相同的池大小，新的估计量相当于 Burrows 提出的估计量 (Phytopathology 77:363–365, 1987)。使用在植物疾病评估和蚊媒病毒流行率估计中遇到的汇总测试问题来检查我们的估计器的性能。