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

Solutions of GSQQ Front Problems

We consider a family of patch-like solutions of generalized surface quasi-geostrophic (GSQG) equation, where the patch may be unbounded. We derive the equations of the contour dynamics under different geometrical situations and prove that the initial value problems have unique local smooth solutions. Under a smallness assumption on the initial data, with the help of the dispersive estimate, we are able to prove the global existence of the solutions for SQG front problem. This is a joint work with John Hunter and Jingyang Shu