组间有重叠的分组检测算法的设计及统计推断

Group testing is applied to projects that screen a large scale of samples. For example, the American Red Cross uses group testing to screen millions of blood samples; the state of Iowa uses group testing to screen chlamydia and gonorrhea in the infertility prevention project. A key step of conducting group testing is the design of the group testing algorithm. A good algorithm is expected to have excellent performance in cost saving, precision of parameter estimation and test results. This research mainly focuses on three points: (1) derive a more efficient array-based group testing algorithm and also provide estimator of parameters; (2) improve the algorithms through incorporating individual information; (3) obtain optimal overlapping ratio of groups and group size for the design of group testing algorithms by balancing cost saving and the precision of estimators. This research plans to study the design and optimization strategies of group testing algorithms by means of overlapping ratio, in order to obtain a more efficient and precise group testing algorithm. The outcomes of this research could be directly used in screening diseases in human and agriculture, and provide theoretical support for the practical application.

分组检测方法适用于大规模群体检测项目，例如，美国红十字会将分组检测方法用于筛选血液样本，俄亥俄州将该方法用于性病（淋病和衣原体感染）的检测。实施分组检测方法的一个关键步骤是设计检测算法，优良的分组检测算法在经济效益、参数估计和检测精度三个方面都应有良好的表现。本课题主要研究：(1) 更加高效的阵列分组检测算法并给出相应的参数估计方法；（2）结合个体信息进一步优化（1）中的算法；(3) 综合考虑检测成本和估计精度，由此获得最优的重叠率和组大小，进而设计检测算法。本课题从重叠率的角度来研究分组检测算法的设计和优化，以期获得更加高效、精确的分组检测算法。本课题的成果可以直接应用于传染病、农业虫害等大规模检测项目，为实际应用提供理论支持。

分组检测算法的设计与优化对于实施与推广分组检测方法有重要意义。优良的分组检测算法在经济效益、参数估计和检测精度三个方面都应有良好的表现。本课题从重叠率、检测精度的角度研究分组检测算法的设计和优化。首先，我们提出了一种高效的嵌套分组检测算法，并从理论上证明了该方法能够降低假阴性，提高阳性检出率。该方法适用于大规模群体筛查，有效控制危害性大的传染性疾病（例如新冠肺炎）的传播。 其次，基于个体信息进一步优化算法，给出了确定最优不等组大小的方法，在检测成本和精度两方面均有良好表现。针对不同的群体根据其患病率可采用不同的组大小，更高效地实施分组检测方法。