In many applications, it is common to have multiple diagnostic tests on each subject. When there are multiple tests available, combining tests to incorporate information from various aspects in subjects may be necessary in order to obtain a better diagnostic. For continuous tests, in the presence of a gold standard, we could combine the tests linearly (Su and Liu, 1993) or sequentially (Thompson, 2003), or using the risk score as studied by McIntosh and Pepe (2002). The gold standard, however, is not always available in practice. This dissertation concentrates on deriving classification methods based on multiple tests in the absence of a gold standard.

Motivated by a lab data set consisting of two tests testing for an antibody in 100 blood samples, we first develop a mixture model of four bivariate normal distributions with the mixture probabilities depending on a two-stage latent structure. The proposed two-stage latent structure is based on the biological mechanism of the tests. A Bayesian classification method incorporating the available prior information is derived utilizing Bayesian decision theory. The proposed method is illustrated by the motivating example, and the properties of the estimation and the classification are described via simulation studies. Sensitivity to the choice of the prior distribution is also studied.

We also investigate a general problem of combining multiple continuous tests without any gold standard or a reference test. We thoroughly study the existing methods for combining multiple tests and develop optimal classification rules corresponding to the methods accommodating the situation without a gold standard. We justify the proposed methods both theoretically and numerically through extensive simulation studies and illustrate the methods with the motivating example. In the end, we conclude the thesis with remarks and some interesting open questions extended from the dissertation.