Study 1: Estimating diagnostic accuracy of a multi-stage screening procedure. Summary: In studies to ascertain true disease status, a definitive diagnostic test often is too invasive or expensive to be applied to all subjects, in which case a two-phase design is often used. The results for all subjects from the Phase 1 test, which is inexpensive and non-invasive, are used to determine which subjects will receive the gold standard test in a later phase. Analysis restricted only to verified cases leads to verification bias. The multiple phase design has been used in studies of dementia and in the diagnosis and screening of many other diseases, e.g., colorectal and breast cancer. The design usually involves more than two phases. For example, in a three-phase study the prevalent test in Phase 1 usually has high sensitivity, but relatively low specificity;Phase 2 consists of a second application of the screening test or a more confirmatory test;and the test in the final phase is the gold standard. In this paper, we proposed a method of estimating the parameters of test efficacy and the ROC curves for continuous screening tests in a multiple-phase study in the presence of verification bias. The verification process and efficacy of the screening test could also depend on covariates. We evaluated estimates of parameters of test efficacy after adjusting for verification bias, and we compared different schemes for combining the sequential tests using empirical studies. If we assume the people with unverified dementia status as non-demented, we tend to be optimistic about the ROC curve. For example for a subject who is 70 years old with no education, using a cut-off at 75 yields FPR=0.42 and TPR=0.64. If we ignore the verification bias, then FPR=0.39 and TPR=0.96, which over-estimates the specificity. Comparing Figure4 a-d, we see that education level has a remarkable impact on test accuracy if the cut-off of 75 is used, but there is not much difference for different ages. For the subject who is 70 years old and has 10 years of education, the FPR is 0.05 and TPR is 0.30 for the cut-off of 75. So the screening test using the cut-off of 75 has a high sensitivity and relatively low specificity for subjects with a 10-year education. For subjects with low education, both sensitivity and specificity are moderate. In terms of AUC under the ROC curve, the CASI test performed better for subjects with higher education. Study 2. Estimating the diagnostic accuracy of composite decision rules Screening is a very important step to reduce morbidity or mortality from the disease by detecting diseases in their earliest stages. It is not unusual that several diagnostic tests are performed or multiple disease markers are available for the same individuals. There has been extensive work on the development of methodology for combining information from multiple tests to optimize diagnostic accuracy. Linear combination is a popular method of combining multiple tests by creating a risk score. In clinical settings, the decision rules used in diagnosis are usually more complicated. For example, if the disease is identified by a sequential multi-phase screening procedure, a subject who is screened negative by an initial test in early phase does not go through another screening test in the next phase. In a combined screening for breast cancer with ultrasound and mammography, the screening result is positive if either the ultrasound or the mammogram is positive. In such scenarios, the believe-the-positive (BP) and believe-the-negative (BN) rules, instead of the linear combination, are commonly used by physicians and clinicians. Our goal is to develop a technique to estimate the overall accuracy of a diagnostic procedure as well as the accuracy of each single test when composite decision rules are used to determine disease status. Copula is a popular multivariate modeling tool when the assumption of joint normality is not satisfied. The copula model has found many successful applications in various fields, e.g., actuarial science and survival analysis. We extend the use of semiparametric copula models (SCM) to multiple tests in disease diagnosis. We assume that the marginal distributions of the diagnostic tests are related to the covariates by regression and the associations among the tests are parameterized separately from the marginal distribution by a copula.