Estimates of Sensitivity and Specificity in a Multistage Screen for Medical Diagnosis

Abstract

A multistage screen is used when k different medical tests are available to the physician, and a patient is subjected to Test j only if Test j1 yielded a positive result, 2 j < k. In observational studies, a multivariate random vector, X(j), of frequencies results from Stage j. This random vector also contains information from patient dropouts, i.e. those patients who discontinue even though they had positive test results at all stages through Stage j. For j 2, the conditional distribution of X(y) is the product of two multinomial distributions; it is conditional because the sample sizes of the two multinomial distributions depend on the outcomes of the previous stage. A certain subset of (X(1), . . ., X(k)) has an unconditional distribution which is multinomial, and the estimation of sensitivity and specificity is formulated from this subset. A numerical example for the diagnosis of open spina bifida in human fetuses is provided.