Diagnostic Tests

When it comes to making medical decisions, sometimes even our tests need to be tested. Ying-Ju Tessa Chen, Ph.D., assistant professor in the Department of Mathematics at the University of Dayton, in collaboration with former advisor Wei Ning, Ph.D., at the Bowling Green State University, is studying the effectiveness of the receiver operating characteristics (ROC) curve analysis using their proposed method: the Adjusted Jackknife Empirical Likelihood (AJEL) method. Chen’s research is accelerated through the use of the Ohio Supercomputer Center services to process huge datasets.

In the medical world, the ROC curve analysis is the gold standard for measuring the effectiveness of various diagnostic tests. It provides a graphical display showing the relationship between the true positive rate and false positive rate of test results as the criterion changes. The ROC curve has been widely applied in epidemiology, biometrics, medical research, diagnostic medicine and material testing and model performance assessments.

While the ROC curve effectiveness has been explored previously by other researchers in the field, Chen hopes the AJEL method will be easier to implement and have fewer complications than previous methods.

 “There are some computational difficulties in practice while using (previous methods),” Chen said. “To obtain the statistic based on the empirical likelihood, the procedure involves the maximization of the nonparametric likelihood through the calculation of Lagrange multiplier subject to given constraints. When the constraints are either linear or can be switched to be linear, the maximization process of EL method is easy to be accomplished. However, when the constraints are nonlinear, there are some computational challenges. In addition, the convex hull of the estimating equation might not contain the zero vector and then the estimate of interest parameter does not exist. In short, the maximum likelihood estimator of the ROC curve may not exist due to such difficulty”.

To test her proposed method, Chen needed to perform an extensive simulation study with a high number of repetitions and large sample sizes to compare the performance of the proposed method against several existing methods. Using R programming language, Chen wrote parallel algorithms to run the simulations.

“The computing resources in the Ohio Supercomputer Center helped us to speed up the progress of completing this project tremendously,” Chen said.

The AJEL method and the corresponding properties were developed based on U-statistics. In future work, Chen and colleagues are interested in extending a similar idea to more general class of statistics than U-statistics and investigate the properties of AJEL method beyond the ROC curve.

“If we didn’t have access to OSC, it would be very difficult to complete this project,” Chen said. "The project would only include the simulation study with some simple comparison.”