成對部分ROC曲線下面積差之非劣性檢定

Abstract

在診斷試驗中，比較新診斷工具與舊(標準)診斷工具的準確性是一項重要的課題。當新的診斷工具其準確性不比舊的診斷工具差， 同時使用上更為安全、相關費用較為經濟亦或是較少侵入性等。這類型的臨床試驗稱之為非劣性試驗 (non-inferiority test)。 接受者操作特徵曲線(receiver operating characteristic curve)簡稱ROC曲線，是用來評估診斷工具準確性的統計方法。ROC 曲線下面積(AUROC)則是用來評估診斷性的方法之一。當考慮兩個診斷工具時，在相同的AUROC之下，可能有部分的區域是具有臨床相關性，但容易被忽略。 而ROC曲線下部分面積(PAUROC)則是更能全面性的評估其精確性，並克服AUROC面臨的難題。

當黃金標準試驗(gold standard test； GS)存在時，一般常以ROC曲線下部分面積(PAUROC)作為評估兩個診斷工具準確性的指標。 然而在某些情況下，黃金標準試驗容易因執行費用太昂貴或是不易取得而不存在(no-gold standard test； NGS)。 本篇論文討論在常態性假設之下，利用EM演算法及拔靴法(bootstrap method)，提出以最大概似法為基礎(maximum likelihood based method； ML-based method)的統計程序， 討論當黃金標準不存在(NGS)，針對成對部分ROC曲線(PAUROC)下面積的非劣性檢定。 經由模擬研究可驗證，當黃金標準試驗不存在時， ML-based方法足以將Emipirical size控制在0.05左右，同時針對新診斷方法的非劣性檢定也提供的充分的檢定力。 最後利用提出之方法針對胰臟癌(Pancreatic cancer)的實際診斷資料進行分析。

The non-inferiority test is an approach to assess the accuracy of a new diagnostic test if it reduces the cost. Receiver operating characteristic (ROC) curves can be used to assess the accuracy of tests measured on ordinal or continuous scales. The area under ROC curve (AUROC) is widely applied in many kinds of field and is used as a tool to decide the accuracy of diagnositic tests. However, it may not differentiate the various shapes of the ROC curves with different diagnostic significances. The partial area under ROC curve (PAUROC) is an attractive alternative that can provide additional and complimentary information for some diagnostic procedures which require the false-positive rate (FPR) to be within a range of clinical interest. A gold standard (GS) test on the true disease status is required to estimate the PAUROC. However, a GS test may be too expensive or infeasible. In many medical researches, the true disease status of the subjects may remain unknown. Under the normality assumption on test results from each disease group of subjects, we propose the maximum likelihood-based (ML-based) method to construct a non-inferiority test for diagnostic accuracy based on the difference in paired PAUROCs in the absence of a GS test (NGS). Simulation results shows that the proposed method for non-inferiority under the NGS case controls the size at the nominal level, and the performance in empirical power is similar to GS case. The proposed method is illustrated with an example.