Empirical likelihood-based confidence intervals for the sensitivity of a continuous-scale diagnostic test at a fixed level of specificity

Abstract

For a continuous-scale diagnostic test, it is often of interest to find the range of the sensitivity of the test at the cut-off that yields a desired specificity. In this article, we first define a profile empirical likelihood ratio for the sensitivity of a continuous-scale diagnostic test and show that its limiting distribution is a scaled chi-square distribution. We then propose two new empirical likelihood-based confidence intervals for the sensitivity of the test at a fixed level of specificity by using the scaled chi-square distribution. Simulation studies are conducted to compare the finite sample performance of the newly proposed intervals with the existing intervals for the sensitivity in terms of coverage probability. A real example is used to illustrate the application of the recommended methods.