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

Abstract

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.

Efficient Noninferiority Testing Procedures for Simultaneously Assessing Sensitivity and Specificity of Two Diagnostic Tests

“…Tang [ 9 ] has studied the E approach and the M approach for comparing sensitivity and specificity when combining two diagnostic tests. The E approach has been shown to be a reliable testing procedure.…”

“…The M approach could be conservative when the actual type I error is much less than the test size [ 5 , 9 ]. To overcome this disadvantage of exact unconditional approaches, Lloyd [ 21 ] proposed a new exact unconditional approach based on estimation and maximization (referred to as the E + M approach).…”

“…It is well known that the asymptotic method behaves poorly when the sample size is small. Therefore, it is not necessary to comprehensively evaluate type I error rate [ 9 – 14 ].…”

Appropriate statistical methods are required to assess diagnostic tests for replacement, add-on, and triage

“…Variance formulas are in the Appendix (A13 and A14; available on the journal's website at www.elsevier.com). Although the aforementioned approach separately assesses sensitivity and specificity, it can also assess sensitivity and specificity simultaneously [18].…”

An economic evaluation of positron emission tomography (PET) and positron emission tomography/computed tomography (PET/CT) for the diagnosis of breast cancer recurrence

“…For probabilistic sensitivity analysis, we preserved the relationship between these characteristics by sampling the test characteristics for PET/CT and conventional work-up separately, and then calculating the test characteristics for the combined test using the methods just described. The methods we have used have been used elsewhere [53][54][55] and are referred to by some authors as the 'either positive rule' . 55 In the sensitivity analysis, we considered the situation in which the sensitivity of the test increases, as per the base case, but we assumed that these additional positive cases were 'truepositives' and so we maintained the specificity at the level estimated for conventional work-up alone -for which the value is 0.76.…”