In the estimation of proportions by pooled testing, the MLE is biased. Hepworth and Biggerstaff (JABES, 22:602–614, 2017) proposed an estimator based on the bias correction method of Firth (Biometrika 80:27–38, 1993) and showed that it is almost unbiased across a range of pooled testing problems involving no misclassification. We now extend their work to allow for imperfect testing. We derive the estimator, provide a Newton–Raphson iterative formula for its computation and test it in situations involving equal or unequal pool sizes, drawing on problems encountered in plant disease assessment and prevalence estimation of mosquito-borne viruses. Our estimator is highly effective at reducing the bias for prevalences consistent with the pooled testing procedure employed.

中文翻译：

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通过不完善的合并测试估计比例的偏差校正

在通过合并测试估计比例时，MLE 是有偏差的。Hepworth 和 Biggerstaff (JABES, 22:602–614, 2017) 提出了一个基于 Firth (Biometrika 80:27–38, 1993) 偏差校正方法的估计器，并表明它在涉及一系列集合测试问题时几乎是无偏差的。没有错误分类。我们现在扩展他们的工作以允许不完美的测试。我们推导出估计量，提供用于计算的 Newton-Raphson 迭代公式，并利用在植物疾病评估和蚊媒病毒流行率估计中遇到的问题，在涉及相等或不等池大小的情况下对其进行测试。我们的估计器非常有效地减少了与所采用的汇总测试程序一致的流行率偏差。