Evaluation of a new diagnostic test against a reference test less than perfect in accuracy

An EM algorithm is developed for computing the maximum likelihood estimates, along with their standard errors, of the accuracy rates of a new medical diagnostic test, as well as for those of a reference test (not necessarily a perfect gold standard), based on the outcomes of the tests when both are applied simultaneously to individuals with unknown disease state sampled from an arbitrary number of populations for which the prevalence rate of the disease in question is also unknown. This algorithm is heuristically appealing in that it also estimates the prevalence rate in each population and aids the perception of the effects of numerical constraints imposed on some of the rate parameters. Several illustrative examples are provided.