A population-based paired design is often used for comparing the diagnostic likelihood ratios of two binary diagnostic tests. However, a case-control paired design, which involves the application of both diagnostic tests to two independent samples, is a good alternative study design especially when the disease is rare. Existing methods for comparing two diagnostic likelihood ratios have been mainly focused on the population-based paired design with little attention paid to the case-control paired design. In this paper, we derive a confidence interval formula for the relative diagnostic likelihood ratio (the ratio of two diagnostic likelihood ratios), which can be used for the comparison of two positive or negative diagnostic likelihood ratios separately. We also derive a confidence region formula for the two relative positive and negative diagnostic likelihood ratios, which allows simultaneous comparison of two positive and negative diagnostic likelihood ratios. The proposed confidence interval and region formulas are simple to compute and can be used for both population-based paired design and case-control paired designs. Simulation studies are used to assess the finite sample performance of the confidence interval and region formulas. The proposed methods are applied to a real data set on coronary artery disease and two diagnostic tests.

中文翻译：

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用于比较配对设计下诊断似然比的简单置信区间和区域公式

基于人群的配对设计通常用于比较两个二元诊断测试的诊断似然比。然而，病例对照配对设计涉及对两个独立样本应用两种诊断测试，是一种很好的替代研究设计，尤其是在疾病罕见时。现有的比较两种诊断似然比的方法主要集中在基于人群的配对设计上，很少关注病例对照配对设计。在本文中，我们推导出相对诊断似然比（两个诊断似然比之比）的置信区间公式，可分别用于两个阳性或阴性诊断似然比的比较。我们还推导出两个相对阳性和阴性诊断似然比的置信区域公式，它允许同时比较两个阳性和阴性诊断似然比。建议的置信区间和区域公式易于计算，可用于基于人群的配对设计和病例对照配对设计。模拟研究用于评估置信区间和区域公式的有限样本性能。所提出的方法应用于冠状动脉疾病的真实数据集和两个诊断测试。建议的置信区间和区域公式易于计算，可用于基于人群的配对设计和病例对照配对设计。模拟研究用于评估置信区间和区域公式的有限样本性能。所提出的方法应用于冠状动脉疾病的真实数据集和两个诊断测试。建议的置信区间和区域公式易于计算，可用于基于人群的配对设计和病例对照配对设计。模拟研究用于评估置信区间和区域公式的有限样本性能。所提出的方法应用于冠状动脉疾病的真实数据集和两个诊断测试。