尋求連續型診斷試劑之參數 ROC 曲線的最適門檻值

Finding the Optimal Threshold of the Parametric ROC Curve under Continuous Diagnostic Measurement

洪郁涵(Yu-Han Hung)

指導教授 ： 黃怡婷

共同指導教授 ： 汪群超(Chun-Chao Wang)

國立臺北大學/商學院/統計學系/碩士(2012年)

摘要

若診斷試劑判定結果為二元陽性或陰性時, 只要將判定結果與病患的實際身體狀況做連結即可得知判定診斷試劑的優劣, 即衡量診斷試劑的敏感度及特異度, 但若檢測結果為連續數值時, 則判定罹病與否的標準會因不同的門檻值 (Threshold) 而有不同, 因此, 要衡量診斷試劑的精確度需藉由設定多個門檻值來獲得多組敏感度與特異度,而 ROC 曲線則將所有可能的組合結果整合在圖形上。 診斷試劑的精確度雖然可以利用 ROC 曲線來衡量, 但為了實務判讀結果方便, 其在應用上仍需提供一個門檻值。 最適門檻值則會因使用者所希望得到診斷試劑精確度的情況, 而得到不同的結果。
實務應用上因成本的考量, 使用者對於診斷試劑的敏感度與特異度之要求可能因而有所不同。為方便使用者找出其要求之診斷試劑的敏感度及特異度組合的最適門檻值, 在給定可能的精確度要求下, 本論文提供兩種診斷試劑之常用參數分配 (Binormal 分配與邏輯斯分配) 之最適門檻值。 因最適門檻值無法求得封閉解, 本研究考慮數種參數設定情況, 利用數值方式求得最適門檻值, 以方便使用者日後選擇診斷試劑的合適門檻值。

關鍵字

敏感度 ； 特異度 ； 最適門檻值 ； Binormal 模型 ； 雙邏輯斯模型

並列摘要

The accuracy of a binary diagnostic test can be assessed easily through comparing the results with the status of respondents. That is, the sensitivity and specificity are evaluated. However, when the diagnostic test is resulted in
a continuous version, the accuracy depends upon the specified threshold. The ROC curve (receiver operating characteristic curve) that includes all possible
combinations of sensitivity and specificity, provides a way to evaluate an overall evaluation of the diagnostic test. Nevertheless, in practice, a threshold is still needed to have an easier clinical representation. The determination of
a proper threshold depends upon the definition of accuracy.
The determination of the accuracy depends on how important the practitioner views the specificity and sensitivity. Given a particular concern of specificity and sensitivity, this thesis derives the optimal threshold under two commonly used parametric assumptions on the diagnostic test (Binormal model and Bilogistic model). Since the optimal threshold does not have a closed form, the numerical results are given in tables for many parameter settings, so the practitioner can easily find the optimal threshold for their studies.

並列關鍵字

sensitivity ； specificity ； optimal threshold ； Binormal model ； Bilogistic model

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