Confidence Interval Estimation for Sensitivity at a Fixed Level of Specificity for Combined Biomarkers

Abstract

In diagnostic studies, we often need to combine several biomarkers to increase the diagnostic accuracy. For continuous-scaled biomarkers or diagnostic tests, it is often of interest to estimate the confidence interval for sensitivity at a fixed level of specificity. Despite the fact that there exist many literature reports on confidence interval estimation of sensitivity at a fixed level of specificity for a single marker, the inference procedures for sensitivity at a fixed level of specificity for combined markers have rarely been addressed. This article fills this gap by investigating a generalized variable procedure for this purpose. The performance of the proposed generalized approach is numerically studied. For the optimal linear combination proposed by Su and Liu (1993), simulation study demonstrates that the proposed approach generally can provide confidence intervals with excellent coverage probabilities. The robustness of the proposed approach is investigated for categorical data. In the end, the proposed approach is applied to a real-life data set.

Key Words:

• Diagnostic accuracy
• Generalized pivot
• Generalized test variable
• Receiver operating characteristic (ROC) curve

Notes

Note. (λ₁, λ₂) denote the diagonal elements of covariance matrix for <b > Y < /b >₁. See section 4 for details. GV: the proposed generalized variable approach.

Note. (λ₁, λ₂, λ₃) denote the diagonal elements of covariance matrix for <b > Y < /b >₁. See section 4 for details. The settings for (λ₁, λ₂, λ₃) are: I, (0.1, 0.1, 0.1,); II, (0.5, 0.5, 0.5); III, (0.9, 0.9, 0.9); IV, (0.1, 0.5, 0.9); V, (0.25, 0.5, 0.75). GV: the proposed generalized variable approach.

Note. The settings for this robust study are described in section 4.