Analysis of the Optimal Critical Points on ROC Curves with Disproportionately-Sampled Data

• Main Authors: Wang, Shu-Han, 王舒涵
• Other Authors: Huang, Yu-Min
• Format: Others
• Language: zh-TW
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/93548854602394269867

碩士 === 東海大學 === 統計學系 === 104 === In medical applications, we need to invent diagnostic devices that can generate references to detect disease status as soon as possible. In addition to cost considerations, the diagnostic device must have a certain degree of accuracy for determining such reference, and therefore the accuracy of the diagnostic device is an important issue. Typically, the outcomes of diagnostic devices are binary, with positive/negative signs based on a critical value of the quantity of a continuous variable, usually a biomarker which originally measures the medical status. In this work, we perform ROC curve (Receiver Operating Characteristic Curve) analysis to obtain the optimum critical value that has a lowest misclassification rate. In real practices, we may conduct disproportionately stratified sampling to collect data for improving the accuracy of critical value analysis. With such disproportionately stratified samples, we first estimated the distribution of the biomarker with conditional maximum likelihood under some parametrical assumptions. Then, we used the estimated probabilities as adjustments to calculate the ROC curve. Simulation analysis showed that our method can provide good estimators, and ROC curve analysis can objectively provide the best critical value. We also present an empirical study on blood samples of a type of glucose (a biomarker), tested with a newly invented test kit. A preliminary investigation found that the population distribution of such blood data is moderately skewed to the right. Therefore, we suggest a gamma distribution for this biomarker. We performed our method to analyze this data and also analyze questionnaires related to the operations of the test kit.