Simultaneous Non‐inferiority Test of Sensitivity and Specificity for Two Diagnostic Procedures in the Presence of a Gold Standard

Abstract

SummarySensitivity 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.

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

“…We would consider comparing the E + M approach with the E approach in this context as a future work. The intersection-union method may be considered for testing sensitivity and specificity [ 8 ].…”

“…The estimate of based on a restricted maximum likelihood estimation approach [ 3 , 19 , 20 ] is used, and the associated form is , where There are two reasons for using this estimate instead of some other estimates [ 2 ]. First, it has been shown to perform well [ 8 , 20 ]. Second, it is applicable to a 2 × 2 contingency table with off-diagonal zero cells.…”

“…A new test statistic based on a restricted maximum likelihood method was then proposed by Nam [ 3 ] and was shown to have good performance with actual type I error rates closer to the desired rates. This test statistic was used by Chen et al [ 8 ] to compare sensitivity and specificity simultaneously in the presence of a gold standard. Actual type I error rates for a compound asymptotic test were evaluated on some specific points in the sample space.…”