Nonparametric ROC Analysis for Diagnostic Trials
The aim of diagnostic trials is to investigate whether a diagnostic test is appropriate to distinguish different groups, in general to separate diseased and nondiseased individuals.
In early phase studies the primary aim is usually to evaluate the overall accuracy of a diagnostic test. One possibility is to draw the receiver operating characteristic (ROC) curve, which for each possible threshold displays sensitivity as true positive fraction against 1 – specificity as false positive fraction. Thereby the test result can, depending on the diagnostic procedure, be binary, ordinal like a rating scale or numeric. It is a prerequisite that the true disease state is known. In general it is defined by an independent gold standard. The gold standard should be the most reliable method to classify the patients as “diseased” and “non-diseased” . Sometimes the true disease state is unknown or given only for a subgroup of patients, also called differential verification, which leads to an overestimation of sensitivity and specificity (see References  and ). There are various approaches to solve this problem, like latent class models. However, Albert and Dodd , for example, demonstrated that model misspecifications can lead to biased estimators.
The ROC curve of a diagnostic test without any accuracy would be the diagonal in the sensitivity × (1 – specificity) unit square. ...