引用本文: 李一鸣, 张洪, 刘爱义. 组检验在差异化误分类下的最优性[J]. 应用概率统计, 2024, 40(4): 644-662.
LI Y M, ZHANG H, LIU A Y. Optimality of group testing with differential misclassification [J]. Chinese J Appl Probab Statist, 2024, 40(4): 644−662.
 Citation: LI Y M, ZHANG H, LIU A Y. Optimality of group testing with differential misclassification [J]. Chinese J Appl Probab Statist, 2024, 40(4): 644−662.

## Optimality of Group Testing with Differential Misclassification

• 摘要: 组检验是可以用来估计罕见传染疾病发病率的一种方法, 相比于样本单独检测的方法来说, 它可以有效地节省时间和降低成本. 然而, 以往的文献中只证明了用组检验策略估计发病率在一些较强假设下的最优性质. 本文弱化了以往文献中对误分类率条件的假定, 把检测对样本染病状态的误分类率当成样本池中样本数的可微函数, 探讨了组检验程序在存在符合该假定的差异化误分类的情况下, 估计疾病发病率时的一些最优性质. 本文从理论上证明了, 当给定样本池总数或检测群体规模确定时, 在估计疾病发病率方面组检验策略表现更优于逐个样本检测程序. 本文还通过数值模拟实验, 探讨了当稀释作用存在时, 用组检验估计发病率的表现.

Abstract: Group testing is a method that can be used to estimate the prevalence of rare infectious diseases, which can effectively save time and reduce costs compared to the method of random sampling. However, previous literature only demonstrated the optimality of group testing strategy while estimating prevalence under some strong assumptions. This article weakens the assumption of misclassification rate in the previous literature, considers the misclassification rate of the infected samples as a differentiable function of the pool size, and explores some optimal properties of group testing for estimating prevalence in the presence of differential misclassification conforming to this assumption. This article theoretically demonstrates that the group testing strategy performs better than the sample by sample procedure in estimating disease prevalence when the total number of sample pools is given or the size of the test population is determined. Numerical simulation experiments were conducted to evaluate the performance of group tests in estimating prevalence in the presence of dilution effect.

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