On simultaneous assessment of sensitivity and specificity when combining two diagnostic tests

Diagnostic tests are seldom adopted in isolation. Few tests have high sensitivity and specificity simultaneously. In these cases, one can increase either the sensitivity or the specificity by combining two component tests under either the 'either positive' rule or the 'both positive' rule. However, there is a tradeoff between sensitivity and specificity when these rules are applied. We propose three statistical procedures to simultaneously assess the sensitivity and specificity when combining two component tests. Measurements of interest include rate difference and rate ratio. Our empirical results demonstrate that (i) the asymptotic test procedures for both measurements and approximate test procedure for rate difference possess inflated type I error rate; (ii) the exact test procedures for both measurements possess deflated type I error rate; and (iii) the approximate (unconditional) test procedure for rate ratio becomes an reliable alternative and nicely controls the actual type I error rate in small to moderate sample sizes. Moreover, the approximate (unconditional) test procedure is computationally less intensive than the exact (unconditional) test procedure. We illustrate our methodologies with a real example from a residual nasopharyngeal carcinoma (RNP) study.