Nonparametric Predictive Inference
for Ordinal Data and Accuracy of
Diagnostic Tests

Abstract

This thesis considers Nonparametric Predictive Inference (NPI) for ordinal data and
accuracy of diagnostic tests. We introduce NPI for ordinal data, which are categor-
ical data with an ordering of the categories. Such data occur in many application
areas, for example medical and social studies. The method uses a latent variable
representation of the observations and categories on the real line. Lower and upper
probabilities for events involving the next observation are presented, with specic
attention to comparison of multiple groups of ordinal data.
We introduce NPI for accuracy of diagnostic tests with ordinal outcomes, with
the inferences based on data for a disease group and a non-disease group. We intro-
duce empirical and NPI lower and upper Receiver Operating Characteristic (ROC)
curves and the corresponding areas under the curves. We discuss the use of the
Youden index related to the NPI lower and upper ROC curves in order to deter-
mine the optimal cut-o point for the test. Finally, we present NPI for assessment
of accuracy of diagnostic tests involving three groups of real-valued data. This is
achieved by developing NPI lower and upper ROC surfaces and the corresponding
volumes under these surfaces, and we also consider the choice of cut-o points for
classications based on such diagnostic tests.