Samuelson Frank, Abbey Craig
Int J Biostat. 2016 Nov 1;12(2). doi: 10.1515/ijb-2016-0017.
Schatzkin et al. and other authors demonstrated that the ratios of some conditional statistics such as the true positive fraction are equal to the ratios of unconditional statistics, such as disease detection rates, and therefore we can calculate these ratios between two screening tests on the same population even if negative test patients are not followed with a reference procedure and the true and false negative rates are unknown. We demonstrate that this same property applies to an expected utility metric. We also demonstrate that while simple estimates of relative specificities and relative areas under ROC curves (AUC) do depend on the unknown negative rates, we can write these ratios in terms of disease prevalence, and the dependence of these ratios on a posited prevalence is often weak particularly if that prevalence is small or the performance of the two screening tests is similar. Therefore we can estimate relative specificity or AUC with little loss of accuracy, if we use an approximate value of disease prevalence.
沙茨金等人及其他作者证明，某些条件统计量（如真阳性率）的比率等于无条件统计量（如疾病检测率）的比率，因此，即使未对检测结果为阴性的患者采用参考程序进行随访，且真阴性率和假阴性率未知，我们也能够计算同一人群中两种筛查试验之间的这些比率。我们证明，这一特性同样适用于预期效用指标。我们还证明，虽然相对特异性和ROC曲线下相对面积（AUC）的简单估计确实依赖于未知的阴性率，但我们可以根据疾病患病率来表示这些比率，而且这些比率对假定患病率的依赖性通常较弱，尤其是当患病率较低或两种筛查试验的性能相似时。因此，如果我们使用疾病患病率的近似值，就能够在几乎不损失准确性的情况下估计相对特异性或AUC。
