癌症篩檢上，不僅是得病與否受人關注，腫瘤位置也十分重要，因此Lim et al. (2018)提出半陽性預測值(Semi-Positive Prediction Value)與半敏感度(Semi-Sensitivity)兩個新指標，並且在成對設計下以聯合分配為基礎，使用Bennett (1972)的統計方法，提出了比較兩個篩檢的半陽性預測值與半敏感度的卡方檢定統計量。 本文提出比較兩個篩檢的半陽性預測值的強韌化概似函數的方法。相較於上述的聯合分配，我們假設資料獨立，也就是忽略相關性，使用獨立下的實作模型。針對感興趣的參數，即兩個篩檢的半陽性預測值之差異，我們將實作概似函數強韌化，提出強韌的，基於正確的概似函數的統計量。我們以模擬的方式來比較我們的強韌統計量與其他現有的檢定統計量的表現。 ;Robust likelihood inferences for comparing the semi-positive values of diagnostic procedures in paired designs
Abstract
In cancer screening, not only the disease is concerned, but also the location of the tumor is very important. Therefore, Lim et al. (2018) proposed semi-positive predictive value and semi-sensitivity two new indicators, and based on joint distribution in paired designs, using the statistical method of Bennett (1972), a chi-square test statistic comparing the semi-positive predictive values and semi-sensitivity of the two screening tests was proposed. This paper presents a method for comparing the semi-positive predictive values of two screens with a robust likelihood function. Compared with the above-mentioned joint distribution, we assume data independence, that is, ignore the correlation, and use the working model under independence. For the parameter of interest, that is, the difference between the semi-positive predictive values of the two screens, we robustify the actual likelihood function and propose a robust statistic based on the correct likelihood function. We utilize simulations to compare our statistic and other current existing test statistics.
