| Summary: | 碩士 === 國立臺北大學 === 統計學系 === 101 === In preventive medical science, diagnostic tests have been developed to detect the diseases. A diagnostic test that can detect the disease early and correctly is preferred. In general, the consistency of true disease status and test results is used to assessed the accuracy of the diagnostic test. For binary outcomes, the accuracy of the diagnostic test can be summarized by two basic indices, sensitivity and specificity. For continuous or ordinal outcomes, choose the threshold to set up the criteria of tests. However, as the threshold changes, the criteria will also be different. The receiver operating characteristic (ROC) curve is used to assess the performance of the diagnostic test when the test results are continuous or ordinal. This paper use parametric approaches to construct the ROC curve. We assume that the distributions of the test results are from a parametric family. Under this assumption,the ROC curve can be described by two parameters, a and b, which are the functions of location and scale parameters. When the participants of two diagnostic tests are independent, we use the signal detection theory proposed by Green and Swet (1966) to construct the likelihood function and obtain the maximum likelihood estimators of a and b. Furthermore, we can use the distribution of test results to construct the likelihood function. Zhou et al (2002) propose the corresponding formula of estimators of a and b. When two test results are paired, we use the bivariate binomial distribution proposed by Biswas and Hwang (2002) to construct the likelihood function. In this paper, we derive the estimators of a and b and their asymptotic distributions. When there are two diagnostic tests can be used to detect the disease, comparing their accuracies can help us to figure out which test is better. This paper compare the accuracy of two diagnostic tests and test if the parameters of two ROC curves are equal or not.
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