Nonparametric predictive inference
for diagnostic test thresholds

Abstract

Nonparametric Predictive Inference (NPI) is a frequentist statistical method that is
explicitly aimed at using few modelling assumptions, with inferences in terms of one
or more future observations. NPI has been introduced for diagnostic test accuracy, yet
mostly restricting attention to one future observation. In this thesis, NPI for the accuracy
of diagnostic tests will be developed for multiple future observations. The present thesis
consists of three main contributions related to studying the accuracy of diagnostic tests.
We introduce NPI for selecting the optimal diagnostic test thresholds for two-group
and three-group classification, and we compare two diagnostic tests for multiple future
individuals.
For the two- and three-group classification problems, we present new NPI approaches
for selecting the optimal diagnostic test thresholds based on multiple future observations.
We compare the proposed methods with some classical methods, including the two-group
and three-group Youden index and the maximum area (volume) methods. The results of
simulation studies are presented to investigate the predictive performance of the proposed
methods along with the classical methods, and example applications using data from the
literature are used to illustrate and discuss the methods.
NPI for comparison of two diagnostic tests is presented, assuming the tests are applied
on the same individuals from two groups, namely healthy and diseased individuals. We
also introduce weights to reflect the relative importance of the two groups.