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Abstract:
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This work is motivated by reconciling two quantitative enzyme-linked immunosorbent assay tests for an antibody to an RNA virus, in a situation without a gold standard and where false negatives may occur. False negatives occur when access of the antibody to the binding site is blocked. Based on the mechanism of the assay, a mixture of four bivariate normal distributions is proposed with the mixture probabilities depending on a two-stage latent variable model including the prevalence of the antibody in the population and the probabilities of blocking on each test. A Bayesian approach is adopted for parameter estimation and the priors is elicited from the historical information and to be consistent with the biological mechanism. Bayesian decision theory is utilized for classification. The proposed method is applied to the motivating data set to classify the data into two groups: those with and those without the antibody. The properties of the estimation and the classification, and sensitivity to the choice of the prior distribution are illustrated by simulation studies.
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