Confidence interval for rate ratio in a 2 × 2 table with structural zero: An application in assessing false-negative rate ratio when combining two diagnostic tests

In this article, we consider problems with correlated data that can be summarized in a 2 × 2 table with structural zero in one of the off-diagonal cells. Data of this kind sometimes appear in infectious disease studies and two-step procedure studies. Lui (1998, Biometrics 54, 706-711) considered confidence interval estimation of rate ratio based on Fieller-type, Wald-type, and logarithmic transformation statistics. We reexamine the same problem under the context of confidence interval construction on false-negative rate ratio in diagnostic performance when combining two diagnostic tests. We propose a score statistic for testing the null hypothesis of nonunity false-negative rate ratio. Score test-based confidence interval construction for false-negative rate ratio will also be discussed. Simulation studies are conducted to compare the performance of the new derived score test statistic and existing statistics for small to moderate sample sizes. In terms of confidence interval construction, our asymptotic score test-based confidence interval estimator possesses significantly shorter expected width with coverage probability being close to the anticipated confidence level. In terms of hypothesis testing, our asymptotic score test procedure has actual type I error rate close to the pre-assigned nominal level. We illustrate our methodologies with real examples from a clinical laboratory study and a cancer study.