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

Yun Yang1, Xiaoyan Lin1, Kerrie P Nelson2

  • 1Department of Statistics, University of South Carolina, USA.

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Summary

This study introduces a Probit hierarchical model for ordinal classification with multiple raters, enhancing diagnostic accuracy analysis. The model provides analytical solutions for receiver operator characteristic (ROC) curves and area under the ROC curves (AUC).

Keywords:
AUCROCdiagnostic biasdiagnostic magnifierdiagnostic scoredisease classdisease severity

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Area of Science:

  • Statistics
  • Medical Informatics
  • Biostatistics

Background:

  • Ordinal classification is crucial in medical diagnosis.
  • Accurate assessment of rater performance and disease severity is challenging with multiple raters.
  • Existing methods often lack closed-form solutions for diagnostic accuracy metrics.

Purpose of the Study:

  • To develop a hierarchical model for ordinal classification with multiple raters.
  • To provide closed-form expressions for receiver operator characteristic (ROC) curves and area under the ROC curves (AUC).
  • To extend the model with covariates for enhanced diagnostic accuracy analysis.

Main Methods:

  • A Probit hierarchical model is proposed, linking rater ratings to diagnostic skills (bias, magnifier) and latent disease severity.
  • Latent disease severity is modeled using a latent class normal mixture distribution.
  • Covariate information is incorporated via a regression layer for diagnostic skills and/or disease severity.

Main Results:

  • The proposed model yields closed-form expressions for overall and individual rater ROC curves and AUC.
  • Extended covariate models provide closed-form solutions for covariate-specific ROCs and AUCs.
  • The methods are demonstrated effectively using a mammography dataset.

Conclusions:

  • The developed analytical tools significantly simplify traditional diagnostic accuracy analysis.
  • The hierarchical model offers a robust framework for understanding rater performance and disease severity.
  • This approach facilitates more precise evaluation in multi-rater ordinal classification tasks.