Diagnostic accuracy analysis for multiple raters using probit hierarchical model for ordinal ratings

This paper delves into the realm of ordinal classification processes for multiple raters. A Probit hierarchical model is proposed linking rater's ordinal ratings with rater diagnostic skills (bias and magnifier) and patient latent disease severity, where patient latent disease severity is assumed to follow a latent class normal mixture distribution. This model specification provides closed-form expressions for both overall and individual rater receiver operator characteristic (ROC) curves and the area under these ROC curves (AUC). We further extend the model by incorporating covariate information and adding a regression layer for rater diagnostic skill parameters and/or for patient latent disease severity. The extended covariate models also offer closed-form solutions for covariate-specific ROCs and AUCs. These analytical tools greatly facilitate traditional diagnostic accuracy analysis. We demonstrate our methods thoroughly with a practical mammography example.