Disease Diagnosis from Immunoassays with Plate to Plate Variability: A Hierarchical Bayesian Approach

• Published in: Statistics in biosciences Vol. 7; no. 2; pp. 206 - 224
• Main Authors: A. Entine, Oliver, Small, Dylan S., Jensen, Shane T., Sanchez, Gerardo, Bastos, Milagros, R. Verastegui, Manuela, Levy, Michael Z.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2015
• Subjects: Biostatistics; Health Sciences; Mathematics and Statistics; Medicine; Statistics; Statistics for Life Sciences; Theoretical Ecology/Statistics; Conditional Posterior Distribution; Markov Chain Monte Carlo; Posterior Distribution; Markov Chain Monte Carlo Procedure; Probability Cutoff
• ISSN: 1867-1764; 1867-1772
• DOI: 10.1007/s12561-014-9113-5

The standard methods of diagnosing disease based on antibody microtiter plates are quite crude. Few methods create a rigorous underlying model for the antibody levels of populations consisting of a mixture of positive and negative subjects, and fewer make full use of the entirety of the available data for diagnoses. In this paper, we propose a Bayesian hierarchical model that provides a systematic way of pooling data across different plates, and accounts for the subtle sources of variations that occur in the optical densities of typical microtiter data. In addition to our Bayesian method having good frequentist properties, we find that our method outperforms one of the standard crude approaches (the “3 SD Rule”) under reasonable assumptions, and provides more accurate disease diagnoses in terms of both sensitivity and specificity.