Comparing two diagnostic tests against the same ''gold standard'' in the same sample

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