Methods are proposed for comparing two diagnostic tests for the same d
ata where a threshold for positive for each test is specified. One met
hod contrasts the diagnostic tests' estimated risks. A. second method
compares the two tests' kappa coefficients. When thresholds for positi
ve test results are specified a priori, maximum likelihood estimators
and their asymptotic variances are derived and test statistics are pre
sented for both case-control and naturalistic methods of sampling. The
bootstrap is proposed as a method to assess differences in risk estim
ators when thresholds for positive test results are chosen by scanning
the data. Examples are given to illustrate the methods.