Sensitivity and specificity have traditionally been used to assess the performance of a diagnostic procedure. Diagnostic procedures with both high sensitivity and high specificity are desirable, but these procedures are frequently too expensive, hazardous, and/or difficult to operate. A less sophisticated procedure may be preferred, if the loss of the sensitivity or specificity is determined to be clinically acceptable. This paper addresses the problem of simultaneous testing of sensitivity and specificity for an alternative test procedure with a reference test procedure when a gold standard is present. The hypothesis is formulated as a compound hypothesis of two non-inferiority (one-sided equivalence) tests. We present an asymptotic test statistic based on the restricted maximum likelihood estimate in the framework of comparing two correlated proportions under the prospective and retrospective sampling designs. The sample size and power of an asymptotic test statistic are derived. The actual type I error and power are calculated by enumerating the exact probabilities in the rejection region. For applications that require high sensitivity as well as high specificity, a large number of positive subjects and a large number of negative subjects are needed. We also propose a weighted sum statistic as an alternative test by comparing a combined measure of sensitivity and specificity of the two procedures. The sample size determination is independent of the sampling plan for the two tests.