Choosing an optimal strategy for hierarchical group testing is an important problem for practitioners who are interested in disease screening with limited resources. For example, when screening for infectious diseases in large populations, it is important to use algorithms that minimize the cost of potentially expensive assays. Black and co‐workers described this as an intractable problem unless the number of individuals to screen is small. They proposed an approximation to an optimal strategy that is difficult to implement for large population sizes. We develop an optimal design with respect to the expected total number of tests that can be obtained by using a novel dynamic programming algorithm. We show that this algorithm is substantially more efficient than the approach that was proposed by Black and co‐workers. In addition, we compare the two designs for imperfect tests. R code is provided for practitioners.

中文翻译：

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分层广义组测试的最佳设计

对于对有限资源进行疾病筛查感兴趣的从业者，选择最佳策略进行分层组检测是一个重要问题。例如，在筛查大量人群的传染病时，重要的是要使用算法，以尽量减少可能昂贵的测定的成本。布莱克及其同事将其描述为一个棘手的问题，除非要筛选的人数很少。他们提出了一种最佳策略的近似方法，该策略很难对大量人口实施。我们针对预期的测试总数（使用新颖的动态编程算法可以获得）进行了优化设计。我们证明该算法比Black和同事提出的方法有效得多。此外，我们比较两种设计的不完善测试。R代码是为从业人员提供的。