A Bayesian Model to Assess a Binary Measurement System When No Gold Standard System Is Available

Abstract

A repeated binary testing framework is implemented when quality inspections fallibly classify units as either conforming or not conforming to quality standards. We develop a Bayesian approach to the statistical analysis of repeated binary testing data. Our approach allows an investigator to characterize and incorporate prior information on the unknown conforming rate and misclassification parameters. Our model assumes beta density priors and we develop a Markov chain Monte Carlo approach for representing posterior densities. In addition, we propose methods for the determination of necessary sample sizes based on average posterior variance criteria and average credible interval length criteria.

• Bayesian Inference
• Beta Prior
• Misclassification
• Pass–Fail
• Sample-Size Determination

Additional information

Notes on contributors

Daniel P. Beavers

Dr. Beavers is Assistant Professor of Biostatistics in the Department of Biostatistics at Wake Forest University Health Sciences. His email address is [email protected].

James D. Stamey

Dr. Stamey is Associate Professor of Statistics at the Department of Statistical Science, Baylor University. His email address is [email protected].

B. Nebiyou Bekele

Dr. Bekele is Associate Professor of Biostatistics at the Department of Biostatistics, University of Texas M. D. Anderson Cancer Center. His email address is [email protected].