疾病篩檢用於診斷個體疾病的存在。其中敏感度（Sensitivity）與陽性預測值（Positive Predictive Value）是評估篩檢效能的常用指標。然而，在癌症篩檢上，除了正確診斷個體患病與否外，亦需準確判斷腫瘤之位置。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）兩種新指標，針對在成對設計下的資料，參照 Bennett (1972) 的統計方法，以多項聯合分配為基礎提出漸近卡方檢定統計量，以比較兩種篩檢的半陽性預測值或半敏感度之優劣，卻在估計量漸近變異數上具有計算上的困難。 本研究中，我們基於 Royall and Tsou (2003) 提出的方法，假設同個人的兩種篩檢資料之間獨立，也就是忽略兩種篩檢結果來自同個個體的相關性，使用獨立假設下的實作模型。接著針對兩種篩檢的半敏感度差異，進行概似函數的強韌化，提出強韌化的華德統計量、分數統計量和概似比統計量，並提供估計量漸近變異數與信賴區間。以模擬研究與實例分析比較上述的強韌統計量與 Lim et al. (2018) 提出的兩半敏感度差異之卡方檢定統計量的檢定表現。 ;Sensitivity and positive predictive value are widely used metrics to evaluate screening performance in disease diagnosis. In cancer screening, however, accurate localization of tumors is equally critical. To address this, Lim et al. (2018) introduced semi-positive predictive value and semi-sensitivity as novel indices, applying Bennett’s (1972) chisquare method based on multinomial distributions in paired designs. Nevertheless, this method leads to difficulties in the calculation of the asymptotic variance of the estimators. In this study, we base our approach on the method proposed by Royall and Tsou (2003), assuming that the two types of screening data from the same individual are independent; that is, the correlation between the two screening results from the same individual is ignored, and use the working model under the assumption of independence. Then, we focus on the difference in semi-sensitivities between the two screenings, perform a robustification of the approximate function, propose a robust Wald test statistic, score test statistic and likelihood ratio test statistic, while providing asymptotic variances and confidence intervals for the estimators. Through simulation studies and practical examples, we compare the performance of the proposed robust statistics with the chi-square statistic proposed by Lim et al. (2018).
