论文标题
二进制分类测试，不完善的标准和模棱两可的信息
Binary Classification Tests, Imperfect Standards, and Ambiguous Information
论文作者
论文摘要
通常相对于预先建立的测试评估新的二元分类测试。例如，相对于更确定的PCR检测，评估了用于检测SARS-COV-2的快速抗原测试。在本文中，我认为新测试可以描述为当预先建立的不完美时产生模棱两可的信息。这允许一种称为扩张的现象 - 一种非信息性的极端形式。例如，我提供了假设的测试数据，这些数据满足了WHO的最低质量需求，以便快速抗原测试导致扩张。信息的歧义是由于已建立的测试不完美而导致的数据问题引起的：未观察到真正感染和测试结果的联合分布。利用Copula理论的结果，我构建了所有这些可能的联合分布的（通常是非辛格尔顿）集，这使我能够评估新的测试的信息。该分析导致一个简单的条件，以确保新的测试不是扩张。我说明了我对三个COVID-19相关测试数据的应用程序的方法。两项快速的抗原测试很容易满足我的足够条件，因此具有丰富的信息。但是，较少准确的程序，例如胸部CT扫描，可能表现出扩张。
New binary classification tests are often evaluated relative to a pre-established test. For example, rapid Antigen tests for the detection of SARS-CoV-2 are assessed relative to more established PCR tests. In this paper, I argue that the new test can be described as producing ambiguous information when the pre-established is imperfect. This allows for a phenomenon called dilation -- an extreme form of non-informativeness. As an example, I present hypothetical test data satisfying the WHO's minimum quality requirement for rapid Antigen tests which leads to dilation. The ambiguity in the information arises from a missing data problem due to imperfection of the established test: the joint distribution of true infection and test results is not observed. Using results from Copula theory, I construct the (usually non-singleton) set of all these possible joint distributions, which allows me to assess the new test's informativeness. This analysis leads to a simple sufficient condition to make sure that a new test is not a dilation. I illustrate my approach with applications to data from three COVID-19 related tests. Two rapid Antigen tests satisfy my sufficient condition easily and are therefore informative. However, less accurate procedures, like chest CT scans, may exhibit dilation.
