A sequential classification rule based on multiple quantitative tests in the absence of a gold standard

In many medical applications, combining information from multiple biomarkers could yield a better diagnosis than any single one on its own. When there is a lack of a gold standard, an algorithm of classifying subjects into the case and non-case status is necessary for combining multiple markers. The aim of this paper is to develop a method to construct a composite test from multiple applicable tests and derive an optimal classification rule under the absence of a gold standard. Rather than combining the tests, we treat the tests as a sequence. This sequential composite test is based on a mixture of two multivariate normal latent models for the distribution of the test results in case and non-case groups, and the optimal classification rule is derived returning the greatest sensitivity at a given specificity. This method is applied to a real-data example and simulation studies have been carried out to assess the statistical properties and predictive accuracy of the proposed composite test. This method is also attainable to implement nonparametrically.