A Dirichlet-Multinomial Gibbs Algorithm for Assessing the Accuracy of Binary Tests in the Absence of a Gold Standard.

Each patient is simultaneously given several binary tests for a disease. The tests are partitioned into disjoint groups, assumed to be conditionally independent between groups, but allowed to have arbitrary dependence within a group. The groups are intended to capture similar biological features of the tests. A Dirichlet-multinomial model is employed with a Gibbs Sampler to estimate the sensitivity and specificity of the tests. The model is exemplified by data on four tests for Chlamydia, both with complete data and with a random 10% of the data treated as missing.